Keywords: Robust adaptive control
Abstract: As a feedback designer, I know no harder problem than adaptive control: simultaneous stabilization and identification, under unlimited parametric uncertainty. With his sigma-modification (1983), Petros Ioannou secured the survival of adaptive control in the face of non-parametric uncertainties. And his students Tsakalis, Polycarpou, as well as Tao, Sun, Datta, and others, took robust adaptive control, through the rest of the 1980s and 1990s, to the limits of possibilities. For time-varying parameters, nonlinear systems, and unmodeled dynamics. Among various “robustification” tools, sigma-modification remained the best option for 40 years. Alas, sigma-modification’s regulation bias is unknown and irreducible. Decades of unsuccessful attempts to improve robust adaptive control, rather than a hard mathematical evidence of fundamental limitations for adaptive control, created a belief that adaptive control is pointless and somehow “cursed,” since under nonparametric uncertainties only properties that are not much more precise than boundedness are achieved. Then, seemingly out of nowhere, an NTUA mathematician appears, Iasson Karafyllis, with no prior history in adaptive control. He cracks the code for how to move robust adaptive control forward after 40 years: adaptation with a deadzone, plus control with nonlinear damping under a dynamic gain. At last, asymptotic performance is arbitrarily close to perfect, under unlimited disturbances and parametric uncertainty. How exactly? Please join me for the lecture and find out.

Keywords: Adaptive control, Randomized algorithms, Automotive
Abstract: Model Predictive Control (MPC) is widely used in control systems due to its proficiency in managing input and state constraints while optimizing controller performance. Nevertheless, applying MPC to systems with uncertain disturbances and unknown dynamics presents formidable challenges. To handle this issue, we propose a learning scenario-MPC approach. An auto-regressive model with exogenous input is iteratively identified, and its parameters are randomly sampled from an updated zonotopic feasible parameter set. The MPC framework is then implemented using the updated auto-regressive model set as dynamic constraints, with a mean cost function, computed across the predefined set of sampled scenarios. This approach leads to a low complexity adaptive control strategy with probabilistic guarantees on constraint satisfaction. The effectiveness of the proposed method is validated on a vehicle path following problem, with unknown vehicle parameters and varying curvatures, where it is shown that the strategy is able to learn the system dynamics from closed-loop data while properly tracking the requested path.

Keywords: Adaptive control, Feedback linearization, Sliding mode control
Abstract: Proton exchange membrane fuel cells (PEMFCs) are pivotal for large-scale energy applications targeting a carbon-neutral future. Achieving reliable and efficient energy system integration necessitates advanced control strategies. This paper introduces a novel method for regulating the oxygen excess ratio (OER) in PEMFC air supply systems. The system model is revisited from a control perspective, followed by the design of a reference controller using input-output feedback linearization. An innovative control strategy that combines sliding mode control (SMC) and model reference adaptive control (MRAC) is then developed. The proposed strategy is validated through numerical simulations based on real experimental data. Notably, the integration of SMCMRAC ensures consistent OER regulation with significantly lower control input variations, as evidenced by the reduced applied compressor voltage, thereby enhancing overall system efficiency.

Keywords: Adaptive control, Servo control, Robotics
Abstract: We propose a method for visual servo-control of robots using images from an uncalibrated camera that constructs compact state representations of the robot's configuration and uses transition dynamics learned from collected execution traces to compute control velocities to reach a desired goal state identified directly by its image. The key step of the proposed method is the estimation of a homography transform between the image positions of distinct keypoints belonging to the robot in the current image and those in a reference image, which can be done quickly and robustly even when not the same set of keypoints is observed at each time step, making it robust to noise and variations in illumination. The estimated homography is then used to represent the robot configuration as the image coordinates of a minimal number of virtual points moving with the robot. The method was verified experimentally for planar motion of a fully actuated manipulator arm as well as an underactuated mobile robot with a nonholonomic constraint.

Keywords: Adaptive systems, Decentralized control, Uncertain systems
Abstract: In this research, we introduce a novel distributed adaptive controller via a command governor mechanism for driving second-order multi-agent systems’ states to the user-assigned positions. The anomalies considered in our problem formulations are agent-based uncertainties and unknown control effectiveness. In the control design process, we account for the actuator dynamics and we use a hedging-based reference model and propose a command governor mechanism for the reference command input to improve the transient response of the considered system. We analyze the stability of the closed-loop multi-agent system using the Lyapunov Stability Theory, and we also use Linear Matrix Inequalities to calculate the stability boundaries for the actuator bandwidths of the agents. Finally, we illustrate the performance of the proposed control algorithm on an undirected line graph with four agents, where we compare transient responses with and without the command governor mechanism.

Keywords: Adaptive systems, Energy systems, Modeling
Abstract: This paper introduces an adaptive digital twin framework that represents the time-varying energy flexibility dynamics within energy systems. The proposed digital twin captures the real-time dynamic variations in demand response, price sensitivity, and energy consumption patterns by adapting to evolving system behaviors and external influences. By utilizing recursive modeling techniques, the digital twin dynamically calibrates its parameters to reflect current system conditions, enabling accurate and responsive representation of price-demand interactions. This tool can then be utilized by aggregators and flexibility management systems to effectively and accurately predict the demand and manage demand-response in Smart Energy Operating Systems. Simulation results demonstrate the ability to adaptively maintain accuracy under varying demand profiles and price fluctuations, highlighting its potential as a valuable asset for modern, responsive energy systems.

Keywords: Adaptive systems, Observers for nonlinear systems, Nonlinear system identification
Abstract: This paper presents the design of an adaptive observer for simultaneous state estimation and parametric identification in Persidskii systems. The main assumption is that the relative degree of the system is equal to one, which allows certain matching conditions for both linear and nonlinear outputs of the system to be satisfied. The known nonlinearities are assumed to be monotone and satisfy sector condition, while the regressor associated with the unknown parameters is Lipschitz continuous. For this type of system, the adaptive observer is designed considering the presence of disturbances and measurement noise. Input-to-state stability conditions are established through Lyapunov analysis. The validity of the proposed observer is illustrated by numerical examples.

Keywords: Linear systems, Process control
Abstract: The context of this paper is periodic event-based feedback control with the sensor as the sole event source in the loop. We introduce a novel technique called fast-sensing dual-rate periodic event-based control (FSDR-PEBC), which allows the inter-event time quantum to be a multiple of the internal sensor's sampling time, to the advantage of control responsiveness while preserving low transmission burden. We also present a Lyapunov-based FSDR-PEBC event triggering rule, characterised by a single tuning parameter. We finally propose an interpretation of that parameter as a knob to trade event rate versus fidelity to a reference controller, typically designed in the continuous time, that the event-based one is expected to mimic.

Keywords: Linear systems, Uncertain systems, LMI's/BMI's/SOS's
Abstract: This paper develops a data-driven stabilization method for continuous-time linear time-invariant systems with theoretical guarantees and no need for signal derivatives. The framework, based on linear matrix inequalities (LMIs), is illustrated in the state-feedback and single-input single-output output-feedback scenarios. Similar to discrete-time approaches, we rely solely on input and state/output measurements. To avoid differentiation, we employ low-pass filters of the available signals that, rather than approximating the derivatives, reconstruct a non-minimal realization of the plant. With access to the filter states and their derivatives, we can solve LMIs derived from sample batches of the available signals to compute a dynamic controller that stabilizes the plant. The effectiveness of the framework is showcased through numerical examples.

Keywords: Linear systems, Optimization
Abstract: This paper presents a set invariance method to compute an output bound for a continuous-time linear time-invariant (LTI) system given sets of initial conditions and external disturbances. The proposed method aims to reduce conservatism compared to existing methods by incorporating the transient time information and the Lyapunov function's decay rate. Two new methods are introduced to obtain the transient time information by numerically computing an upper bound of the output derivative through matrix inequalities. Interestingly, overshoot analysis is a special case for which our approach can significantly improve the overshoot bound. The effectiveness of our method is showcased in an illustrative example of a PID-controlled-mass system.

Keywords: Adaptive control, Identification for control, Linear systems
Abstract: This paper quantifies and addresses the bias of subspace-based Data-Driven Predictive Control (DDPC) for linear, time-invariant (LTI) systems. The primary focus is the bias that arises when the training data is gathered with a feedback controller in closed-loop with the system. First, the closed-loop bias of Subspace Predictive Control is quantified using the training data innovations. Next, the bias of direct, subspace-based DDPC methods DeePC and γ-DDPC is shown to consist of two parts---the Subspace Bias, which arises from closed-loop data, and an Optimism Bias, which arises from DeePC/γ-DDPC's "optimistic" adjustment of the output trajectory. We show that, unlike subspace-based DDPC methods, Transient Predictive Control does not suffer from Subspace Bias or Optimism Bias. Double integrator experiments demonstrate that Subspace and Optimism Bias are responsible for poor reference tracking by the subspace-based DDPC methods.

Keywords: Linear systems
Abstract: Transforming an asymmetric system into a symmetric system makes it possible to exploit the simplifying properties of symmetry in control problems. We define and characterize the family of symmetrizable systems, which can be transformed into symmetric systems by a linear transformation of their inputs and outputs. In the special case of complete symmetry, the set of symmetrizable systems is convex and verifiable by a semidefinite program. We show that a Khatri-Rao rank needs to be satisfied for a system to be symmetrizable and conclude that linear systems are generically neither symmetric nor symmetrizable.

Keywords: Linear systems, Adaptive systems, Observers for linear systems
Abstract: Spectral filtering has been recently introduced as a new approach to predicting a sequence of the outputs generated by dynamical systems. The spectral filtering comes with theoretical performance guarantees, quantifying how good the predictions are. The main advantage of spectral filtering is that the filters are fixed and can be computed completely offline before starting the prediction procedure. Indeed, the filters are the eigenvectors of a known Hankel matrix, which is ill-conditioned. In this paper, we prove that the eigenvectors can be approximated by solutions to a Sturm-Liouville ordinary differential equation. The Sturm-Liouville ODE contains an unknown parameter, which hugely impacts the approximated eigenvectors and their similarity with the eigenvectors obtained from the Hankel matrix. We discuss the properties of the Sturm-Liouville ordinary differential equation, and specify the boundary conditions and domain. In addition, we introduce an orthogonality measure which quantifies the quality of the estimated solutions and could be used to form initial guesses for the unknown parameter involved in the Sturm-Liouville ordinary differential equation. The code to solve the Sturm-Liouville ordinary equation is shared on a public GitHub page.

Keywords: Robust control, Aerospace, Linear time-varying systems
Abstract: This paper presents a novel approach for robust periodic attitude control of satellites. Respecting the periodicity of the satellite dynamics in the synthesis allows to achieve constant performance and robustness requirements over the orbit. The proposed design follows a mixed sensitivity control design employing a physically motivated weighting scheme. The controller is calculated using a novel structured linear time-periodic output feedback synthesis with guaranteed optimal L2-performance. The synthesis poses a convex optimization problem and avoids grid-wise evaluations of coupling conditions inherent for classical periodic H-infinity-synthesis. Moreover, the controller has a transparent and easy to implement structure. A space solar power satellite is used to demonstrate the effectiveness of the proposed method for periodic satellite attitude control.

Keywords: Robust control, Autonomous systems, H2/H-infinity methods
Abstract: This study proposes a novel robust path tracking control (PTC) for car-trailer combinations. The motion dynamics of the car-trailer is identified using the dynamic mode decomposition with control (DMDc) algorithm. This approach does not require prior knowledge of system parameters such as mass and cornering stiffness. To account for potential modelling errors, uncertainties are considered in the identified data-driven model. Moreover, a robust H_infinity path tracking controller is designed to ensure the system's robustness against modelling errors and uncertainties. The path tracking controller is formulated as a linear matrix inequality (LMI) feasibility problem. Using the CarSim-Simulink platform, the motion of the autonomous car-trailer is simulated and the performance of the proposed technique is evaluated. Simulation results show that the maximum lateral and heading angle errors during the double lane change (DLC) maneuver at a speed of 50km/h are 20.08cm and 1.01deg. To further evaluate the performance of the controller, the reference path generated by experimental driving data is used for the performance evaluation of the proposed PTC. The maximum lateral and heading angle errors stay within the safe limits defined based on the road lane width.

Keywords: Robust control, Hybrid systems
Abstract: This paper addresses the challenge of ensuring robustness in the presence of system perturbations for symbolic control techniques. Given a discrete-time control system that is related by an alternating simulation relation to its symbolic model. In this paper, we focus on computing the maximum ro- bustness margin under which the symbolic model remains valid for a perturbed-version of the discrete-time control system. We first show that symbolic models are inherently equipped with a certain free robustness margins. We then provide constructive procedures to compute uniform and non-uniform (state and input dependent) robustness margins. We also show that the tightness of the robustness margin depends on the tightness of the reachability technique used to compute the symbolic model. We then explain how the computed robustness margin can be used for the sake of controller synthesis. Finally, we present two illustrative examples to demonstrate the effectiveness of our approach.

Keywords: Robust control, Linear systems, H2/H-infinity methods
Abstract: Static structured control refers to the task of designing a state-feedback controller such that the control gain satisfies a subspace constraint. Structured control has applications in control of communication-inhibited dynamical systems, such as systems in networked environments. This work performs H2-suboptimal regulation under a common structured state-feedback controller for a class of data-consistent plants. The certification of H2-performance is attained through a combination of standard H2 LMIs, convex sufficient conditions for structured control, and a matrix S-lemma for set-membership. The resulting convex optimization problems are linear matrix inequalities whose size scales independently of the number of data samples collected. Data-driven structured H2-regulation control is demonstrated on example systems.

Keywords: Robust control, Optimal control, Energy systems
Abstract: The random fluctuation in wind speed during wind power generation affects the smooth operation of the wind turbine as well as the stability of their generated power. In this work, the robust model predictive control (RMPC) is designed for a linearized wind turbine using a high-fidelity aeroelastic model (DNV-GL Bladed). The nonlinear wind turbine model is linearized into a state space form, and the wind fluctuation in the actual plant model is considered as a disturbance by the linearized model; that is, the control design model has no information about the disturbance. For the controller design, the feedback control law and robust invariant set are obtained by solving the linear matrix inequality that arises from the error system between the plant and the internal model. Then, the feedback control law and standard MPC will be combined to yield the robust predictive controller, which is applied to the plant model. The RMPC is tested and compared with the standard PI and MPC controllers in high wind speed in Matlab/SIMULINK. An improvement over the two controllers is achieved without compromising the aggressiveness and robustness of the controller.

Keywords: Stability of linear systems, Lyapunov methods, Optimization algorithms
Abstract: Managing noisy data is a central challenge in direct data-driven control design. We propose an approach for synthesizing model-reference controllers for linear time- invariant (LTI) systems using noisy state-input data, employ- ing novel noise mitigation techniques. We demonstrate that data-based covariance parameterization of the controller en- ables to incorporate bias-correction and instrumental variable techniques. This reduces measurement noise effects as data volume increases. The number of decision variables remains independent of dataset size, making this method scalable to large datasets. The approach’s effectiveness is demonstrated with a numerical example.

Keywords: Stability of linear systems, Linear systems, Emerging control theory
Abstract: We introduce a novel approach to feedback stability analysis for linear time-invariant (LTI) systems, overcoming the limitations of the sectoriality assumption in the small phase theorem. While phase analysis for single-input single-output (SISO) systems is well-established, multi-input multi-output (MIMO) systems lack a comprehensive phase analysis until recent advances introduced with the small-phase theorem.

A limitation of the small-phase theorem is the sectorial condition, which states that an operator's eigenvalues must lie within a specified angle sector of the complex plane. We propose a framework based on Scaled Relative Graphs (SRGs) to remove this assumption. We derive two main results: a graphical set-based stability condition using SRGs and a small-phase theorem with no sectorial assumption. These results broaden the scope of phase analysis and feedback stability for MIMO systems.

Keywords: Adaptive control, Linear systems, Automotive
Abstract: In this article, we develop a blending based multiple model pole placement adaptive control (MMPPAC) scheme for square multivariable systems defined in state space. We consider linear, time invariant systems with known, compact, convex polytopic uncertainty. A state feedback controller is developed to drive all the states to the origin. The control architecture consists of a multiple model online identification scheme, and a control scheme that guarantees boundedness of all closed-loop signals, and asymptotic regulation of the plant's state vector to the origin. Numerical simulations of motion control of lateral vehicle dynamics illustrate the stability and efficacy of the proposed MMPPAC scheme, with robustness to dynamical uncertainty and measurement noise.

Keywords: Linear systems, Aerospace, Observers for linear systems
Abstract: Estimating the relative pose (position and attitude) between two satellites is a challenging problem. Most of the existing methods tackling this problem rely on stochastic approaches, as, for example, the well-known Extended Kalman Filter (EKF). However, the use of such methods has some limits: they are based on a knowledge of the density function of sensor noises, that are hard to be obtained in practice, and do not give any guarantee on the state estimation set. In this paper, two alternative methods, based on set-membership approach, are proposed. Such methods do not need any statistical property and and provide sets guaranteed to contain the true state to be estimated. This paper focuses on zonotopic and ellipsoidal state estimation to compute bounds of the satellites relative state. Simulations are provided in order to illustrate the benefits of the methods.

Keywords: Linear systems, Mechatronics, Modeling
Abstract: This paper proposes a method to compute the generic number of system zeros of a class of linear time invariant system from a causal bond graph. The method is based on a decomposition of the bond graph representation, achieved using the concept of separators. It is shown that, after decomposition, three partial bond graphs are obtained, each with its own specific properties. These properties only hold because of the structured nature of the system. They are used to compute the generic number of zeros for each partial bond graph, which are then combined to determine the generic number of zeros for the complete bond graph.

Keywords: Identification for hybrid systems, Switched systems, Linear systems
Abstract: This paper presents a hybrid system identification approach tailored for industrial electrical networks modeled as a parallel connection of Linear Time-Invariant (LTI) systems. The proposed method aims to identify switching instants of individual system activations, accommodating constraints typical in industrial environments, such as limited input excitation and measurement noise. The algorithm involves four steps and demonstrates robustness with respect to measurement noise through simulation results.

Keywords: Control over networks, Adaptive control, Fault detection and identification
Abstract: Widespread application of network in control systems has significantly increased the risk of cyber attacks. In this paper, we have investigated a specific class of cyber attack in which the adversary has partial model information of the plant. The adversary can make his attack stealthy by applying one of the well-known adaptive control approaches called model reference adaptive control (MRAC). This kind of robust covert attacks can be very dangerous as the adversary can take over the control of the plant through the communication network without being noticed by the monitoring system. A simulation example is used to illustrate the risk of this kind of robust stealthy covert attacks.

Keywords: Control over networks, Uncertain systems
Abstract: In this work, we consider the problem of designing event-triggered tracking controllers for uncertain strict-feedback systems with unknown control directions (UCDs). The proposed control scheme is static, and requires no hard calculations, analytic or numerical, to produce the control signal. The event-triggered mechanism applied on the controller-to-actuator side relies on the so-called relative threshold strategy. No prior knowledge or approximation structures regarding the system nonlinearities are required and no high-order derivatives of the desired output trajectory are incorporated in the controller design. Yet the enforcement of prescribed performance bounds on the output tracking error in terms of steady-state accuracy and convergence rate is guaranteed. Simulation results clarify and verify the theoretical findings.

Keywords: Control over networks, Distributed cooperative control over networks, Network analysis and control
Abstract: This work deals with the output consensus problem for multiagent systems over balanced digraphs. While passivity-based approaches for the analysis of undirected consensus protocols are commonly employed, they generally can not be used for directed consensus protocols. We propose a general approach capable of processing directed coupling to enable a passivity analysis. To mitigate the complexity arising from the nonlinearity and directed interconnections, we reformulate the output consensus problem as a convergence analysis on a submanifold. We provide passivity analysis and establish a sufficient condition based on passivity for achieving output agreement in multi-agent systems over balanced digraphs. The results are supported by a numerical example.

Keywords: Control over networks, Linear systems
Abstract: In order to improve cyber security, encrypted control systems have attracted much attention recently. Homomorphic encryption allows calculations to be performed directly based on ciphertexts. Especially by means of fully homomorphic encryption (FHE) schemes both signals transmitted over the network and controller parameters can be encrypted. This paper gives a brief overview of some prevalent FHE schemes as well as their applications in the control field. The focus will be put on the Brakerski/Fan-Vaikuntanathan (BFV) scheme, the Cheon-Kim-Kim-Song (CKKS) scheme and the Gentry-Sahai-Waters (GSW) scheme. A simulation study with the quadruple-tank system illustrates the FHE encrypted control systems and the computational aspects.

Keywords: Control over networks, Cooperative autonomous systems, Distributed control
Abstract: Motivated by applications in which agents need to perform collaborative tasks under limited communication, in this work we consider the asymptotic satisfaction of relative-position based spatial tasks by a leader-follower network. As opposed to existing approaches, the spatial tasks may involve non-communicating agents and/or a subset of the multi-agent team. In order to ensure the satisfaction of the constraints using local information, as a first contribution, we express the incidence matrix of the task graph in terms of the corresponding matrix of the communication graph. In addition, for undirected spanning tree communication graphs, we show that the relation of the incidence matrices of these graphs is unique. Building upon this relation, as a second contribution we propose a two-hop communication based distributed feedback control law that ensures asymptotic satisfaction of the constraints with a predetermined robustness. The proposed control law employs the line graph of the communication graph and does not require knowledge of a complete row of the constraint matrix.

Keywords: Control over networks, Optimal control, Output feedback
Abstract: The paper addresses the task of efficient synchronization for networked nonlinear identical systems via optimized output diffusive coupling. Under the assumption that the local dynamics are strictly input-output semi-passive, a sufficient condition to ensure synchronization for heterogeneous coupling gains is proposed, taking the network topology into account. Compared to previous work, which commonly adopts the same coupling gain over the network, the proposed technique uses a leader-follower structure together with optimization of gains to significantly reduce the overall effort of coupling. The effectiveness of the proposed method is shown for different numeric examples.

Keywords: Biological systems, Output feedback
Abstract: Sterile Insect Technique (SIT) is a promising control method against insect pests and insect vectors. It consists in releasing males previously sterilized in laboratory, in order to reduce or eliminate a specific wild population. We study in this paper the implementation by feedback control of SIT-based elimination campaign of Aedes mosquitoes. We provide state-feedback and output-feedback control laws and establish their convergence, as well as their robustness properties. In this design procedure, a pivotal role is played by the basic offspring number, and by the use of properties of monotone systems.

Keywords: Biological systems, Applications in neuroscience
Abstract: Robustness analysis is very important in biology and neuroscience, to unravel behavioural patterns of systems that are conserved despite large parametric uncertainties. To make studies of probabilistic robustness more efficient and scalable when addressing complex models in neuroscience, we propose an alternative to computationally expensive Monte Carlo (MC) methods by introducing and analysing the generalised polynomial chaos (gPC) framework for uncertainty quantification. We consider both intrusive and non-intrusive gPC approaches, which turn out to be scalable and allow for a fast comprehensive exploration of parameter spaces. Focusing on widely used models of neural dynamics as case studies, we explore the trade-off between efficiency and accuracy of gPC methods, and we adopt the proposed methodology to investigate parametric uncertainties in models that feature multiple dynamic regimes.

Keywords: Biological systems, LMI's/BMI's/SOS's, Stability of hybrid systems
Abstract: We study a piecewise affine (PWA) model of the spiking of neurons located in a subsystem of the olfactory system. Our longterm goal is to understand the stability properties of a network of such neurons and as a first step towards this goal we consider the simplest case of the interaction between two types of neurons (excitatory and inhibitory). Due to the discontinuous nature of the PWA model, it is challenging to find a continuous Lyapunov function, we therefore utilize a recently proposed constructive method to find a discontinuous Lyapunov function. In order to utilize this method, it is necessary to define a suitable polyhedral partition of the state-space and carefully investigate the dynamics at the boundaries. As an additional step, we propose extending the analysis by employing tools from the input-to-state stability framework.

Keywords: Biological systems, Lyapunov methods, Network analysis and control
Abstract: We show how certain classes of biological networks, with arbitrary "rate functions", can be modeled as dynamical flow networks. This characterization of a biological network allows us to construct a linear co-positive Lyapunov function whose drift can be computed explicitly, and hence to assess the stability as well as the Input-to-State Stability (ISS) properties of the system, by only analyzing the properties of the rate functions in their limits. We also provide sufficient conditions for ISS with respect to small inputs when the rate functions are subject to saturation, as is the case for Michaelis-Menten and Hill functions. We exemplify our proposed method for stability analysis by considering a model for glucose absorption where one of the rate functions is non-monotonic.

Keywords: Biological systems, Modeling, Stochastic systems
Abstract: Determining the optimal way to sustainably harvest an ecological population is a key challenge in natural resource management. Our contribution employs the stochastic logistic model, which accounts for random birth-death processes, to identify optimal harvesting strategies that maximize the integrated yield over time while considering nonzero probability of extinction. Harvesting is modeled to occur at either a constant or state-dependent rate with individuals being harvested with a certain probability at each harvesting event. A special case of state-dependent harvesting is a threshold-based strategy, where harvesting occurs once the population exceeds a specific threshold. Using moment closure schemes, we approximate analytical formulas to quantify mean and optimal yield. We verify these approximations using the Finite-State Projection (FSP) method. Through this numerical method, we estimate not only the optimal harvesting rate, but also the extinction probabilities over a given time interval. Our results show that the threshold-based strategy is most effective in maximizing yield by reducing population fluctuations and minimizing extinction events.

Keywords: Genetic regulatory systems, Biological systems, Biomolecular systems
Abstract: Metabolic burden is a critical limiting factor in the design of synthetic circuits, affecting both their reliability and performance. To mitigate its effects, distributing control functions across different cell populations within a multicellular control architecture offers a promising solution, while simultaneously enhancing modularity and re-usability of the circuits. We first present a model that explicitly accounts for limited ribosome availability within cells. Using this framework, we then derive a mathematical model of a multicellular antithetic integral controller that incorporates these shared resources. Through numerical bifurcation analysis and in silico agent-based experiments in BSim, we compare the multicellular controller against its traditional single-cell (embedded) implementation, evaluating both resource utilization and stability.

Keywords: Agents networks, Optimal control of communication networks, Concensus control and estimation
Abstract: This paper addresses the positive synchronization of interconnected systems on undirected graphs. For homogeneous positive systems, a static feedback protocol design is proposed, based on the Linear Regulator problem. The solution to the algebraic equation associated to the stabilizing policy can be found using a linear program. Necessary and sufficient conditions on the positivity of each agent's trajectory for all nonnegative initial conditions are also provided. Simulations on large regular graphs with different nodal degree illustrate the proposed results.

Keywords: Agents and autonomous systems, Constrained control, Optimization
Abstract: This paper introduces the notion of input-to-task redundancy in multi-agent systems and extends the dynamic control allocation paradigm to input-constrained multi-agent systems. In particular, it is shown that a proper selection of a subset of the system outputs can entail a weak redundancy condition with respect to a given task to be executed, thereby providing additional degrees of freedom to cope with potential input constraints. Moreover, we propose a way of quantitatively characterizing the additional freedom in the controllability of the system by means of a {em redundancy degree} suitably defined. The efficacy of the approach has been tested and validated by numerical simulations in a platooning application.

Keywords: Agents and autonomous systems, Observers for nonlinear systems, Distributed control
Abstract: We propose a distributed control strategy to allow the control of a multi-agent system requiring k-hop interactions based on the design of distributed state and input observers. In particular, we design for each agent a finite time convergent state and input observer that exploits only the communication with the 1-hop neighbors to reconstruct the information regarding those agents at a 2-hop or more distance. We then demonstrate that if the k-hop based control strategy is set-Input to State Stable with respect to the set describing the goal, then the observer information can be adopted to achieve the team objective with stability guarantees.

Keywords: Agents and autonomous systems, Predictive control for nonlinear systems, Optimal control
Abstract: In this paper, we propose a methodology that ensures robust connectivity for resilient consensus in multi-agent systems subject to dynamic topology. It also ensures the use of optimal control inputs for tracking desired trajectories even in the presence of non-cooperative agents. The methodology has three components: a) the reconfiguration protocol ensures robust connectivity, b) the sliding window mean subsequence reduced (SW-MSR) approach ensures resilient consensus, and c) the nonlinear model predictive control (NMPC) generates optimal control inputs to achieve the desired topology while tracking respective desired trajectories. The associated analytical results demonstrate the asymptotic consensus and stability of the system. The simulation experiments validate the effectiveness of the proposed methodology that can be used for real-world applications.

Keywords: Agents and autonomous systems, Traffic control, Machine learning
Abstract: Autonomous vehicles can improve urban traffic safety and efficiency. Nevertheless, safely and efficiently operating them is an ongoing research problem. This paper specifically studies the task of navigating autonomous vehicles through unsignalized intersections. We model the system as a Decentralized Partially Observable Markov Decision Process. Decentralized algorithms for each vehicle are trained using deep reinforcement learning through the QMIX method. Building upon the QMIX approach, we encode the intentions of a selected number of neighboring vehicles. Moreover, the reward function is designed to combine both individual performance (i.e., fuel consumption, speed, and trip completion) with global safety and fairness. This work shows improved performance compared to an existing conventional driving algorithm in reward, driving speed, and safety.

Keywords: Agents networks, Distributed control, Predictive control for linear systems
Abstract: This paper explores the dependencies of local costs within multi-agent systems under model predictive control (MPC) actions. Specifically, we identify, for each point in each agent’s local state-space, the minimal and maximal influence of neighboring decisions. This is used to provide a bound between the global performance costs attained by noncooperative versus centralized MPC implementations, as well as to identify regions where the difference between the two is small. As such, this analysis provides suboptimality guarantees in distributed MPC schemes, particularly relevant for scenarios with reduced, and potentially dynamic, communication and coordination require- ments. We illustrate the new tools in a numerical simulation of two masses coupled with springs and dampers.

Keywords: Concensus control and estimation, Agents networks, Communication networks
Abstract: In this paper, the consensus problem is studied for linear multi-agent systems on undirected graphs. Based on relative output feedback, we propose a distributed protocol for each agent to achieve consensus without continuous communication among agents. Time- and event-triggered sampling mechanisms with event separation properties are designed for different signals and are guaranteed to have a positive minimum inter-event time. Compared with existing results, the clock variable in the event-triggering mechanism is not restricted to be monotonically decreasing but has the potential to increase, thus improving inter-event times. Moreover, different from [1], the two sampling mechanisms in this paper are decoupled, providing more design convenience. Finally, the theoretical results are demonstrated and verified by numerical simulations.

Keywords: Concensus control and estimation, Distributed cooperative control over networks, Constrained control
Abstract: In this paper, we consider the consensus control problem of multi-agent systems with dynamics in unknown strict-feedback form subject to input constraints. We propose a novel distributed prescribed performance control scheme which ensures that each agent’s output converges to the leader’s trajectory with predefined transient and steady-state performance while respecting input saturation limits. We introduce a distributed reference modification mechanism that adjusts local consensus errors in response to local control input saturation, preventing internal instability. Rigorous theoretical analysis establishes the stability and convergence properties of the proposed distributed control scheme and guarantees the boundedness of all closed-loop signals. Simulation results involving nonlinear agents demonstrate the effectiveness of the proposed method.

Keywords: Complex systems, Robotics, Biological systems
Abstract: Achieving consensus in collective systems is essential for coordinated behaviour, yet the presence of strongly opinionated minorities can disrupt the overall dynamics. In this work, we study consensus dynamics in stochastic swarms of finite size, focusing on the impact of disruptive agents on group decision-making. First, we propose how to quantify robustness of consensus, by defining consensus as a parametrised property expressed in bounded linear temporal logic (BLTL). Then, we use statistical model checking to compute and compare the robustness landscape in several scenarios where the group decides between two options of different (asymmetric) quality. Finally, we analyse the effects of swarm size to the consensus landscape over two representative models and two types of disruptive agents. Our results reveal that, surprisingly, when groups are deciding between asymmetric options, disruptive agents can play a constructive role towards the optimal group decisions.

Keywords: Concensus control and estimation, Control over networks, Network analysis and control
Abstract: In this paper, we investigate the problem of dual-rate consensus under transmission delays, where the control updates happen at a faster rate than the measurements being received. We assume that the measurements are delayed by a fixed delay and show that for all delays and rates, the system reaches a consensus if and only if the communication graph of the agents is connected and the control gain is chosen in a specific interval. Based on these results we dive deeper into the convergence properties and investigate how the convergence changes when we change the rate for sending measurements. We observe that in certain cases there exists a sweet spot for choosing the sampling rate of the measurements, which can improve the convergence to the consensus point. We then formulate an optimization problem to find a sampling rate to improve the convergence speed and provide a necessary and sufficient condition for the existence of a finite optimizer of this problem. Our results are verified with numerical simulations.

Keywords: Concensus control and estimation, Distributed estimation over sensor nets, Distributed cooperative control over networks
Abstract: This paper deals with the distributed estimation and the attitude coordination problem for a network of heterogeneous satellites with flexible appendages. For the estimation task, the agents employ a distributed observer in a minimal-order formulation to obtain the angular rates of a non-collaborative target, starting from partial measurements of its angular positions. It is proven that, for an undirected topology, the estimation error asymptotically converges to zero if the consensus gain is greater than a certain threshold. The main feature of such an observer is the reduction of its order compared to other approaches in the literature when the observed system can be expressed in an integral state-space form. For the control task, a consensus protocol is shown to achieve attitude coordination among the satellites even though they share only their partial target information. Finally, the separation principle assures that the coupled implementation of the estimation and control procedures gives rise to a stable system. Numerical examples illustrate the results for a mixed network of sensing and non-sensing agents.

Keywords: Concensus control and estimation, Optimal control, Optimal control of communication networks
Abstract: In this paper, we introduce a novel optimization strategy aimed at reducing energy consumption in multi-agent systems. We consider a network represented by a graph with time-varying edge weights and employ the Frechet discrete gradient method to optimize these weights over a fixed time horizon. The objective is to minimize a cost function associated with the control input energy while preserving consensus performance. The proposed gradient-based approach effectively reduces energy consumption during the transient and guarantees convergence for any chosen step size. Simulation results are provided to demonstrate the effectiveness and validate the theoretical properties of the method.

Keywords: Coverage control, Agents and autonomous systems, UAV's
Abstract: The main contribution of this paper is a methodology for multiple non-cooperating swarms of unmanned aerial vehicles to independently cover a common area. In contrast to previous research on coverage control involving more than one swarm, this paper does not assume cooperation between distinct swarms but considers them as independent units following their own objectives. Using Voronoi tessellation, collision-free motion of agents within the same swarm has been proven before. However, as is shown in Example 1 of this paper, in the case of multiple swarms with inter-swarm but without intra-swarm collaboration, these guarantees do not hold. We address this issue by proposing an algorithm to achieve maximum coverage with multiple swarms while avoiding collisions between agents. More specifically, the Optimal Reciprocal Collision Avoidance method used for safe navigation in multi-agent scenarios is adapted to suit the needs of Voronoi-based coverage control with more than one swarm. The functionality of the proposed technique is validated through Monte Carlo simulations.

Keywords: Coverage control, Cooperative control, Agents and autonomous systems
Abstract: Coverage control presents a promising method for addressing challenges such as environmental monitoring of specific fields. However, when applied to robots, coverage control typically assumes data sampling continuously both in time and space, whereas many external sensors gather data at discrete points and times. To address this issue, this paper investigates a novel cooperative data sampling that reflects the discrete nature of sensors to estimate scalar fields based on the sparse online Gaussian process (SOGP). The control goal of the present problem is formulated by a constraint on the decay rate of the variance function given by the SOGP. We then design a partially distributed constraint-based controller that enforces the constraint in the transient state, while also considering safety constraints. We then point out a drawback inherent in the present ``myopic'' control strategy through simulation studies. In order to overcome the drawback, we present a hierarchical control architecture, where the high-level path planner generates the optimal path based on a long-term perspective, and the low-level constraint-based control meets the decay rate constraint, while referring to the designed path for designing the nominal control. Finally, the present controller's effectiveness is demonstrated through simulations.

Keywords: Cooperative autonomous systems, Transportation systems, Autonomous robots
Abstract: This paper presents the development of a tangible platform for demonstrating the practical implementation of cooperative adaptive cruise control (CACC) systems, an enhancement to the standard adaptive cruise control (ACC) concept by means of Vehicle-to-Everything (V2X) communication. It involves a detailed examination of existing longitudinal controllers and their performance in homogeneous vehicle platoons. Moreover, extensive tests are conducted using multiple autonomous experimental vehicle platform topologies to verify the effectiveness of the controller. The outcomes from both simulations and field tests affirm the substantial benefits of the proposed CACC platooning approach in longitudinal vehicle platooning scenarios. This research is crucial due to a notable gap in the existing literature; while numerous studies focus on simulated vehicle platooning systems, there is lack of research demonstrating these controllers on physical vehicle systems or robot platforms. This paper seeks to fill this gap by providing a practical demonstration of CACC systems in action, showcasing their potential for real-world application in intelligent transportation systems.

Keywords: Cooperative autonomous systems, Distributed cooperative control over networks, Agents and autonomous systems
Abstract: We present a cooperative decentralized obstacle avoidance approach for a group of ground-based robots moving in an environment with dynamic obstacles. The objectives of this work are to ensure safety, on the one hand, and to embed coordinated behavior, on the other. While Control Barrier Functions (CBFs) have proven to be effective while guaranteeing safety, they often lead to overly conservative behavior and deadlocks in dense environments. In this paper, we propose a framework in which agents use the dynamics of opinion for decision making. Since CBFs do not consider any cooperative strategies for avoiding collisions and deadlocks in the presence of dynamic obstacles, we introduce two heuristics, which effect the opinion evolution model: the local attention mechanism, focusing on reacting to collisions with nearby obstacles; the global attention mechanism, which further facilitates cooperation between agents. The simulation results demonstrate that our proposed method reduces deadlocks, improves trajectory smoothness, and shortens the task completion time compared to the only CBF strategies.

Keywords: Autonomous robots, Robotics, Autonomous systems
Abstract: Autonomous navigation in agricultural applications presents several challenges in perception and control due to the environment's variability and irregularity. This paper introduces a novel approach to address this task, relying only on local data and without pre-defined paths. The proposed system enables the robot to execute two key manoeuvres: maintaining straight-line navigation within rows and performing precise turns at row ends. A unified control law, driven by a computer vision system, dynamically switches between these behaviours, exploiting a smooth transition function inspired by bumpless transfer control techniques. This method ensures a continuous control signal, achieving robust navigation in variable and dynamic agricultural setting. Simulation results and real-world validations are provided to demonstrate the effectiveness and performance of the proposed control strategy.

Keywords: Autonomous systems, Automotive
Abstract: Improving trust in the operation of autonomous vehicle (AV) control systems is an actual challenge for overcoming the trough of disillusionment in the development phase. There are identified critical gaps in the field that motivate the development of new theoretically grounded methods: most of the existing methods can be used for specific systems without generality applicability, and the achieved explainability level is aimed only engineers and specialists. This paper aims to provide a user-centered method in order to be able to explain the operation for general users. The research question is: How is it possible to transform complex control systems to approximating systems with explainable operation? In this paper a decision-tree-based solution is proposed that results in a low-order approximating system in explainable form. The application of the method is illustrated through the example of an AV safety detector. The operation of the complex detector is described through decision-tree-based rules that are visualized to explain the original system.

Keywords: Optimal control, Hybrid systems, Computational methods
Abstract: Constrained dynamical systems are systems such that, by some means, the state stays within a given set. Two such systems are the (perturbed) Moreau sweeping process and the recently proposed extended Projected Dynamical System (ePDS). We show that under certain conditions solutions to the ePDS correspond to the solutions of a dynamic complementarity system, similar to the one equivalent to ordinary PDS. We then show that the perturbed sweeping process with time varying set can, under similar conditions, be reformulated as an ePDS. In this paper, we leverage these equivalences to develop an accurate discretization method for perturbed first-order Moreau sweeping processes via the finite elements with switch detection method. This allows the efficient optimal control of systems governed by ePDS and perturbed first-order sweeping processes.

Keywords: Optimal control, Hybrid systems, Machine learning
Abstract: Online model predictive control (MPC) for piecewise affine (PWA) systems requires the online solution to an optimization problem that implicitly optimizes over the switching sequence of PWA regions, for which the computational burden can be prohibitive. Alternatively, the computation can be moved offline using explicit MPC; however, the online memory requirements and the offline computation can then become excessive. In this work we propose a solution in between online and explicit MPC, addressing the above issues by partially dividing the computation between online and offline. To solve the underlying MPC problem, a policy, learned offline, specifies the sequence of PWA regions that the dynamics must follow, thus reducing the complexity of the remaining optimization problem that solves over only the continuous states and control inputs. We provide a condition, verifiable during learning, that guarantees feasibility of the learned policy's output, such that an optimal continuous control input can always be found online. Furthermore, a method for iteratively generating training data offline allows the feasible policy to be learned efficiently, reducing the offline computational burden. A numerical experiment demonstrates the effectiveness of the method compared to both online and explicit MPC.

Keywords: Optimal control, Optimization, Observers for nonlinear systems
Abstract: In this paper, we introduce turnpike arguments in the context of optimal state estimation. In particular, we show that the optimal solution of the state estimation problem involving all available past data serves as turnpike for the solutions of truncated problems involving only a subset of the data. We mathematically formalize this phenomenon and derive a sufficient condition that relies on a decaying sensitivity property of the underlying nonlinear program. As second contribution, we show how a specific turnpike property can be used to establish performance guarantees when approximating the optimal solution of the full problem by a sequence of truncated problems, and we show that the resulting performance (both averaged and non-averaged) is approximately optimal with error terms that can be made arbitrarily small by an appropriate choice of the horizon length. In addition, we discuss interesting implications of these results for the practically relevant case of moving horizon estimation and illustrate our results with a numerical example.

Keywords: Optimal control, Predictive control for nonlinear systems
Abstract: This paper introduces and compares two model predictive control (MPC) formulations for time-optimal point-to-point motion planning that are tailored to facilitate reaching distant points. The formulations overcome the need for a large number of decision variables and result in an invariant structure of the underlying nonlinear programming problem, both facilitating the deployment process. The first approach, a dual stage method, divides the prediction horizon into two stages: a time-optimal one with constant system sampling intervals and a free-time stage with variable sampling to reach distant points while ensuring terminal state compliance. The second approach uses an artificial reference with exponential error weighting, guiding the reference toward the target as the system's motion progresses. Both strategies reduce the computational complexity associated with traditional time-optimal MPC by maintaining a consistent problem structure and minimizing the required sampling points. This makes them well-suited for real-time applications and practical hardware implementation. The effectiveness of each approach is demonstrated through simulations of a unicycle performing point-to-point motion in obstacle-laden environments.

Keywords: Optimal control, Constrained control, Stochastic control
Abstract: In this paper, we investigate a model-free optimal control design that minimizes an infinite horizon average expected quadratic cost of states and control actions subject to a probabilistic risk or chance constraint using input-output data. In particular, we consider linear time-invariant systems and design an optimal controller within the class of linear state feedback controls. Two different policy gradient (PG) based algorithms, natural policy gradient (NPG) and Gauss-Newton policy gradient (GNPG) are developed and compared to deep deterministic policy gradient (DDPG), the optimal risk-neutral linear-quadratic regulator (LQR), chance constrained LQR, and a scenario-based model predictive control (MPC). The convergence properties and the accuracy of all the algorithms are compared numerically. We also establish analytical convergence properties of the NPG algorithm under the known model scenario, while convergence analysis for the unknown model scenario is part of our ongoing work.

Keywords: Optimal control, Predictive control for nonlinear systems, Robust control
Abstract: Providing formal guarantees for constraint satisfaction is a crucial problem in safety-critical applications. We address this problem by combining robust optimal control with set-based reachability analysis of nonlinear systems. Our algorithm is built on a recently proposed scheme for optimizing affine feedback policies by iterating between solving a perturbed nominal optimal control problem and synthesizing linear feedback controllers - however, constraint satisfaction is not guaranteed. To overcome this limitation, we leverage concepts from robust controller synthesis and set-based reachability analysis. Our experiments show only a modest decrease in performance compared to an approach without formal guarantees, while we outperform state-of-the-art approaches that guarantee constraint satisfaction.

Keywords: Modeling, Emerging control applications
Abstract: Stemming from the work of Henry M. Paynter introducing bond graphs in the late 1950s, the system theory of port-Hamiltonian systems has quickly developed thanks the pioneering work of Bernhard Maschke and Arjan van der Schaft. And yet, such powerful ideas are not as widely spread as they should even if they give solutions to many problems in modeling and control of complex physical systems. In this presentation I will introduce the basics of such ideas and show the power in its application in modeling the complex interaction of a fluid and the deformable elasticity of the wings of a robotics bird.

Keywords: Emerging control theory
Abstract: Why should a controller act only when the clock says so, rather than when it actually matters? Event-triggered control and its cousin self-triggered control challenge the traditional approach of periodic control by closing feedback loops only when needed. These smart, resource-aware approaches have attracted great interest in areas like networked systems or real-time computing - promising efficiency without compromising control objectives.

But with great flexibility comes great theoretical challenges. Which design frameworks can we use to find performant triggering conditions? How do we rigorously analyze sampling behavior? What trade-offs emerge between control performance and trigger frequency?

In this talk, we will take a tour through research trends in event-based control, highlighting both breakthroughs and unresolved challenges in the field. We will give a perspective on its connections to areas like neuromorphic control and event-based vision, examining its origins and future prospects.

Keywords: Adaptive control, Neural networks, Constrained control
Abstract: In this paper, a neuro–adaptive controller with weight norm constraints is proposed for uncertain Euler‒Lagrange systems. The boundedness of the weights in the neuro–adaptive controller design is important to prevent excessively large control inputs and system instability. To ensure the boundedness of the weights, the weight norm constraints are imposed as inequality constraints in the weight adaptation. The adaptation law is derived based on the constrained optimization method. The stability of the proposed controller is analyzed in the sense of Lyapunov, ensuring the boundedness of the tracking error and weight estimation. For the comparative study, two benchmark controllers and the proposed controller were evaluated through a numerical simulation of a two-link manipulator system and compared in terms of tracking performance and parameter dependency. The comparative study verified that the proposed controller has better tracking performance and lower parameter dependency.

Keywords: UAV's, Constrained control, Robust adaptive control
Abstract: In this work, we introduce a novel control strategy for target tracking and obstacle avoidance for quadrotors, designed to operate under both actuation and performance constraints. The proposed control framework guarantees precise trajectory tracking while complying to predefined safety constraints, dynamically adjusting performance characteristics to correspond with real-time operational conditions. The stability of the closed-loop system is validated through a Lyapunov-based analysis. Finally, comprehensive experiments confirm the robustness and demonstrate the effectiveness of the control sheme in a real-life setting.

Keywords: Algebraic/geometric methods, Nonlinear system theory, Constrained control
Abstract: In this paper, we give sufficient conditions for and deduce a control law under which a mechanical control system converges exponentially fast to a virtual linear nonholonomic constraint that is control invariant via the same feedback control. Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Virtual nonholonomic constraints, similarly to mechanical nonholonomic constraints, are a class of virtual constraints that depend on velocities rather than only on the configurations of the system.

Keywords: Constrained control, Robotics
Abstract: Prescribed-time reach-avoid-stay (PT-RAS) specifications are crucial in applications requiring precise timing, state constraints, and safety guarantees. While control carrier functions (CBFs) have emerged as a promising approach, providing formal guarantees of safety, constructing CBFs that satisfy PT-RAS specifications remains challenging. In this paper, we present a novel approach using a spatiotemporal tubes (STTs) framework to construct CBFs for PT-RAS tasks. The STT framework allows for the systematic design of CBFs that dynamically manage both spatial and temporal constraints, ensuring that the system remains within a safe operational envelope while achieving the desired temporal objectives. The proposed method is validated with two case studies: temporal motion planning of an omnidirectional robot and temporal waypoint navigation with obstacles for a multi-UAV payload carrying setup, using higher-order CBFs.

Keywords: Constrained control, Uncertain systems, Nonlinear system theory
Abstract: In this paper, we propose a novel prescribed performance control (PPC) scheme for uncertain Euler-Lagrange systems subject to input constraints. Traditional PPC methods often struggle with input limitations, requiring potentially unbounded control efforts to meet performance specifications. To address this challenge, we introduce a reference modification mechanism that adjusts only the virtual reference signal for the velocity whenever the control input saturates. This approach ensures that the position tracking errors remain within predefined prescribed performance bounds, achieving precise tracking without steady-state error despite input constraints. We derive lower bounds for the input saturation levels that guarantee the feasibility of the control scheme and prove that all closed-loop signals remain bounded. Simulation results on a BlueRov2 underwater vehicle model demonstrate the effectiveness of the proposed method.

Keywords: Constrained control, Stability of nonlinear systems, Uncertain systems
Abstract: When a system is operated with controllers designed via the prescribed performance control (PPC) methodοlogy, internal instability may appear as an effect of control input magnitude and rate saturation. In this paper we propose a switching control framework to effectively alleviate this phenomenon. Two control units are utilized; a PPC and a Safety Controller (SC). Initially, control action is given to PPC, which switches to SC only when PPC becomes saturated and the risk of instability is high. The SC unit is designed to maintain system operation whenever PPC fails; thus avoiding the appearance of controller instability. Control is given back to PPC unit when the probability of internal instability is low. The proposed control solution is of low-complexity and achieves performance attributes on the output tracking error while preserving the boundedness of all signals in the closed-loop. Simulations clarify and verify the theoretical findings.

Keywords: Nonlinear system theory, Robust control, Lyapunov methods
Abstract: The main objective of this study is to devise a control structure for robot manipulators actuated by brushless direct current (BLDC) motors while accounting for uncertainties in kinematic, dynamic, and electrical models. Robustness properties of sliding mode control techniques are employed to address uncertainties associated with dynamic and electrical models, whereas a gradient-based adaptive approach is utilized for handling kinematic model uncertainties. To keep the control efforts at reasonable limits, the known nominal values of the dynamical and electrical model parameters are also employed in the controller design. As part of the backstepping based methodology, a novel continuous virtual controller design strategy is tailored as well. The stability of the closed-loop system is analyzed rigorously utilizing Lyapunov-type arguments and global asymptotic stability is ensured. Experimental results obtained from a custom-built two degree-of-freedom planar robot manipulator actuated by BLDC motors demonstrated the efficacy of the proposed control framework where the task space tracking errors remained below 0.8 millimeters.

Keywords: Lyapunov methods, Optimal control
Abstract: Given a Control Lyapunov Function (CLF), Son- tag’s famous Formula provides a nonlinear state-feedback guaranteeing asymptotic stability of the setpoint. At the same time, a cost function that depends on the CLF is minimized. While there exist methods to construct CLFs for certain classes of systems, the impact on the resulting performance is unclear. This article aims to make two contributions to this problem: (1) We show that using the value function of an LQR design as CLF, the resulting Sontag-type controller minimizes a classical quadratic cost around the setpoint and a CLF-dependent cost within the domain where the CLF condition holds. We also show that the closed-loop system is stable within a local region at least as large as that generated by the LQR. (2) We show a related CLF design for feedback-linearizable systems resulting in a global CLF in a straight-forward manner; The Sontag design then guarantees global asymptotic stability while minimizing a quadratic cost at the setpoint and a CLF-dependent cost in the whole state-space. Both designs are constructive and easily applicable to nonlinear multi-input systems under mild assumptions.

Keywords: Lyapunov methods, Uncertain systems, Feedback linearization
Abstract: The exact feedback linearization technique with partial state feedback and stable zero dynamics ensures local exponential stability. However, the method requires an accurate model, without uncertainties. The paper proposes an extension of the method for input-affine nonlinear systems with stable zero dynamics and matched uncertainties. Moreover, the weighted closed-loop sensitivity function is imposed using the mathcal{L}_2-gain analysis. The advantage of the proposed extension is that it ensures both robust stability and performance (tailored to reference tracking) for the uncertain nonlinear system affected by the limitations of zero dynamics. The two methodologies are then illustrated on a given academic example.

Keywords: Power electronics, Lyapunov methods, Stability of nonlinear systems
Abstract: The alternative method of the voltage modulated-direct power control (VM-DPC) approach, is used as the basis for a novel controller design that effectively achieves accurate power regulation of grid-tied voltage source inverters (VSI). The proposed control schemes realize PI-type active and reactive power regulators which are substantially stabilized by introducing suitable damping terms in their structure. To avoid steady state errors, an appropriate adaptation mechanism is proposed which eliminates the damping terms in steady-state, while simultaneously it enables them to act exclusively during transient periods. Contrary to the conventional approach, the whole design does not require the use of a fast phase locked loop (PLL) mechanism and does not depend on any system parameters, since it does not include the commonly employed feed-forward decoupling terms in its structure and hence it displays significant robustness properties. These properties are also enhanced particularly against dc voltage variations since a division by the dc voltage state is not further needed. The theoretical analysis of the resulting closed-loop system is performed on the full nonlinear model. Stability properties are extracted by exploiting some critical structure characteristics, whereas suitable nonlinear analysis tools are used to establish stability and convergence properties under some mild conditions. Finally, the theoretical results that guarantee enhanced dynamic behavior of the system are validated by conducting a detailed simulation procedure.

Keywords: Linear parameter-varying systems, H2/H-infinity methods, Lyapunov methods
Abstract: Control design for Linear Parameter-Varying (LPV) systems based on linear matrix inequalities requires the designer to provide basis functions. Usually, these basis functions are picked based on the intuition of how the system dynamics depends on its scheduling parameters. This paper presents a novel method of obtaining these basis functions from the state-space data of grid-based LPV systems in an automatic fashion. The method yields a small number of basis functions that often achieve better control performance and reduced computation time for control synthesis compared to their hand-picked counterparts. This is accomplished by applying the tensor product model transformation to the tensor formed from the state-space matrices of the grid-based LPV system. Our MATLAB implementation of the algorithm described in this paper is open-source and available on GitHub.

Keywords: Lyapunov methods, Neural networks, Stability of nonlinear systems
Abstract: This work presents an approach to synthesize a Lyapunov-like function to ensure incrementally input-to-state stability (delta-ISS) property for an unknown discrete-time system. To deal with challenges posed by unknown system dynamics, we parameterize the Lyapunov-like function as a neural network, which we train using the data samples collected from the unknown system along with appropriately designed loss functions. We propose a validity condition to test the obtained function and incorporate it into the training framework to ensure provable correctness at the end of the training. Finally, the usefulness of the proposed technique is proved using two case studies: a scalar non-linear dynamical system and a permanent magnet DC motor.

Keywords: Uncertain systems, Robust control, Linear time-varying systems
Abstract: The assessment of robust stability and performance of systems affected by Linear Time-Invariant (LTI) and Linear Time-Varying (LTV) uncertainties with bounded rates of variation is still an open problem and yet of importance. To this purpose, Integral Quadratic Constraints (IQCs) can be used to derive sufficient conditions in terms of Frequency Domain Inequalities (FDIs), which are usually cast into state-space Linear Matrix Inequalities (LMIs). The present paper proposes a new approach to perform robustness analysis directly in the frequency domain. By doing so, two main advantages are gained with respect to previous approaches. Firstly, the LTI uncertainties are described with the well-known frequency-by-frequency independent scalings of µ-analysis, which are less conservative than state-space multipliers and do not require choosing arbitrary transfer matrices. Secondly, suboptimal solutions can be obtained by separately optimizing constant and frequency-dependent variables in an iterative way, which lightens the computational burden. The implemented algorithms are eventually applied to test cases of increasing complexity and compared with a classical IQC technique.

Keywords: Stability of linear systems, Robust control, LMI's/BMI's/SOS's
Abstract: This article studies dynamic output-feedback stabilization for linear time-invariant input-output autoregressive systems, directly from measured data. The input-output data are assumed to be corrupted by measurement noise, with both energy and instantaneous bounds considered. For each case, a data-driven parametrization of all systems compatible with the data is derived via a matrix elimination result. Leveraging Petersen’s lemma and a lossy matrix S-procedure, we formulate linear matrix inequalities to synthesize controllers that stabilize all compatible systems. The effectiveness of the proposed methods is demonstrated through numerical examples.

Keywords: Robust control, Predictive control for nonlinear systems, Control over networks
Abstract: Model predictive control (MPC) is capable of controlling nonlinear systems with guaranteed constraint satisfaction and stability. However, MPC requires solving optimization problems online periodically, which often exceeds the local system's computational capabilities. A potential solution is to leverage external processing, such as a central industrial server. Yet, this central computer typically serves multiple systems simultaneously, leading to significant hardware demands due to the need to solve numerous optimization problems concurrently. In this work, we tackle this challenge by developing an event-triggered model predictive control (ET-MPC) that provably stabilizes multiple nonlinear systems under disturbances while solving only optimization problems for a fixed-size subset at any given time. Unlike existing ET-MPC methods, which primarily reduce average computational load yet still require hardware capable of handling all systems simultaneously, our approach reduces the worst-case computational load. This significantly lowers central server hardware requirements by diminishing peak computational demands. We achieve our improvements by leveraging recent advancements in distributed event-triggered linear control and integrating them with a robust MPC that employs constraint tightening.

Keywords: Robust control, Stability of nonlinear systems, Lyapunov methods
Abstract: The paper focuses on the robustness analysis of a time-invariant hyperexponentially stabilizing control for linear systems. Both qualitative (input-to-state stability) and quantitative (class of disturbances that can be rejected) robustness properties of the system are investigated. The theoretical findings are validated through numerical examples.

Keywords: H2/H-infinity methods, Linear systems, LMI's/BMI's/SOS's
Abstract: In this paper we propose a non-conservative dynamic output-feedback controller synthesis method for discrete-time linear time-invariant systems. The synthesis goal is to minimize H_infty norm of the closed-loop system, while the system dynamics is partially represented by noisy input/state/output data. The controller synthesis is performed with respect to all systems which are consistent with data, and it is formulated in terms of a linear matrix inequality parametrized by a scalar variable, so that the synthesis can be performed using line search and convex optimization.

Keywords: Robust control, UAV's, Fuzzy systems
Abstract: This paper focuses on the longitudinal notion control of unmanned aerial vehicles (UAVs) with modeling uncertainties to maintain a stationary altitude or track a desired longitudinal trajectory while carrying dynamic loads in the air. In pursuit of developing a control methodology with broad applicability, a generic model based approach has been adopted. Some of the dynamic and fluctuating uncertainties in both the model and the carried load are compensated by estimating them through a adaptive fuzzy network, an canceling these estimates within a recently developed high-gain control design that involves tanh(cdot) function-based proportional integrator derivative compensation of tracking errors. The closed-loop stability and tracking error convergence properties for the proposed control scheme are established through a Lyapunov analysis procedure. Numerical simulations have been conducted to validate the theoretical findings and demonstrate the effectiveness of the proposed approach.

Keywords: Distributed parameter systems, Delay systems, Stability of nonlinear systems
Abstract: This paper deals with nonlinear boundary stabilization of a 1D reaction-diffusion equation with input delay. Using the modal decomposition approach, we propose a homogeneous-based predictor feedback for stabilizing the unstable modes. We prove the stability of the closed-loop system via the construction of a suitable Lyapunov functional. We present numerical simulations to support the analytical results and compare our proposed controller to linear predictor feedback regarding closed-loop performance and peaking effect.

Keywords: Distributed parameter systems, Observers for linear systems, UAV's
Abstract: This paper uses mobile sensors to consider the state estimation of systems governed by parabolic partial differential equations. These equations are often used to model the dispersion of a species' concentration in the environment, which is generated by moving sources that release contaminants. Using an abstract framework theory, the partial differential equation is written as an evolution equation in a functional space forced by an exosystem that describes the dynamics of a moving platform carrying the contaminant release with the mass release rate capturing the temporal signal of the disturbance. Using an optimal filter to reconstruct the concentration state provides computational challenges as one must solve a large-scale covariance equation (differential Riccati equation) in real-time. To address this challenge, a domain decomposition filter considers the Kalman filter in a subdomain with a naive observer implemented in the remainder of the spatial domain. To further the computational savings, a restricted Kalman filter is implemented in the inner domain, thus providing the filter kernel's sought-after sparsity. Extensive simulation studies are presented over a large spatial domain and demonstrate the implementability of the real-time restricted Kalman filter for partial differential equations with a performance-based guided moving sensor and an unknown moving source.

Keywords: Distributed parameter systems
Abstract: This paper uses computational geometry techniques to partition position and velocity sensor distributions for second order in time PDEs representing structural systems. These distributions are assumed to be idealization of sensor distributions obtained by optimization enhancing system theoretic properties of the system such as approximate observability and improved filter performance. To ensure that realistic sensor devices can be used, a network of sensor distributions representing available sensing devices is used to approximate the ideal distributions. This approximation is based on a modification of the Centroidal Voronoi Tessellations (CVT) which ensures that the ideal distributions are partitioned into cells of equal areas of the distributions thus ensuring equal sensor authority. A single pointwise sensor is placed in each cell and an associated weight for that pointwise sensor is obtained via optimization. A filter is subsequently designed for the system with the approximate realistic sensors and compared to the filter utilizing ideal but unrealizable sensor distributions.

Keywords: Distributed parameter systems, H2/H-infinity methods, Computational methods
Abstract: We consider the nonlinear Kuramoto-Sivashinsky equation and its linear part on a finite interval subject to periodic boundary conditions. The linear part can have a finite number of unstable eigenvalues so we assume that there are point actuators that allow a linear feedback to move all the unstable eigenvalues into the open left half plane. Such a linear feedback law is found by the well-known technique of Linear Quadratic Regulation (LQR). This leads to a new Riccati partial differetial equation for quadratic Fredholm kernel of the optimal cost. From this quadratic kernel we obtain the linear kernel of the optimal feedback. We prove that this feedback moves all the unstable eigenvalues into the open left half plane. But it has little effect on the open loop eigenvalues that were already stable. This linear feedback locally stabilizes the nonlinear Kuramoto-Sivashinsky equation but nonLinear nonQuadratic Regulation (nLnQR), which we discuss in this paper, can be used to find a cubic feedback that stabilizes it faster and/or with less control energy.

Keywords: Distributed parameter systems
Abstract: We develop a backstepping control design for a class of continuum systems of linear hyperbolic PDEs, described by a coupled system of an ensemble of rightward transporting PDEs and a (finite) system of m leftward transporting PDEs. The key analysis challenge of the design is to establish well-posedness of the resulting ensemble of kernel equations, since they evolve on a prismatic (3-D) domain and inherit the potential discontinuities of the kernels for the case of n+m hyperbolic systems. We resolve this challenge generalizing the well-posedness analysis of Hu, Di Meglio, Vazquez, and Krstic to continua of general, heterodirectional hyperbolic PDE systems, while also constructing a proper Lyapunov functional.

Keywords: Machine learning, Stochastic filtering, Fluid flow systems
Abstract: This paper presents the combination of recursive Gaussian process regression with a Kalman Filter to learn data-based models for non-measurable outputs in real time. The algorithm utilizes a Kalman Filter with an auxiliary parameter for a disturbance estimate. In parallel, the estimated disturbance estimate is employed in a recursive Gaussian process regression for the identification of a corresponding disturbance model. This disturbance model is in turn leveraged to improve the Kalman Filter prediction step. The proposed algorithm is compared in simulations with an alternative baseline implementation. Exemplarily, an experimental validation of the algorithm is presented for the learning of a heat-transfer coefficient in a vapor compression cycle as used in refrigeration systems and heat pumps.

Keywords: Network analysis and control, Agents networks, Agents and autonomous systems
Abstract: The Friedkin-Johnsen (FJ) model has been extensively explored and validated, spanning applications in social science, systems and control, game theory, and algorithmic research. In this paper, we introduce an advanced generalization of the FJ model, termed FJ-MM which incorporates both memory effects and multi-hop (higher-order neighbor) influence. This formulation allows agents to naturally incorporate both current and previous opinions at each iteration stage. Our numerical results demonstrate that incorporating memory and multi-hop influence significantly reshapes the opinion landscape; for example, the final opinion profile can exhibit reduced polarization. We analyze the stability and equilibrium properties of the FJ-MM model, showing that these properties can be reduced to those of a comparison model--namely, the standard FJ model with a modified influence matrix. This reduction enables us to leverage established stability results from FJ dynamics. Additionally, we examine the convergence rate of the FJ-MM model and demonstrate that, as can be expected, the time lags introduced by memory and higher-order neighbor influences result in slower convergence.

Keywords: Network analysis and control, Adaptive systems, Optimal control
Abstract: When controlling network systems through pinning, distributed adaptive strategies have been devised to increase the coupling and control gains until convergence onto the desired equilibrium configuration is attained. However, in the presence of persistent perturbations, the gains would indefinitely increase, making control energetically inefficient. Here, we propose a novel adaptation law that overcomes this limitation by optimally selecting the setpoint for the coupling and control gains, so that the network rejects local perturbations with the minimum control energy. Extensive numerical simulations on paradigmatic networks of nonlinear systems demonstrate the robustness of the proposed approach to large perturbations from the desired equilibrium.

Keywords: Network analysis and control, Large-scale systems, Linear systems
Abstract: The Altafini model, also known as opposing dynamics, is an opinion dynamics model on signed graphs. In this paper, we study an extension of this model to signed graphons, mathematical objects that approximate large undirected graphs.

After defining natural extensions of the notions of connectivity and structural balance to signed graphons, we analyze the asymptotic behavior of the dynamics, through the use of semigroup theory and the study of the properties of the opposing Laplacian operator.

Our results are consistent with known facts about the classical Altafini model on signed graphs: on a connected signed graphon with degree essentially bounded away from zero, the dynamics converges to a bipartite consensus if the signed graphon is structurally balanced, and converges to zero if it is not.

Keywords: Network analysis and control, Large-scale systems, Uncertain systems
Abstract: Water distribution networks (WDNs) are critical systems for our society and detecting leakages is important for minimizing losses and water waste. This makes optimal sensor placement for leakage detection very relevant. Existing sensor placement methods rely on simulation-based scenarios, often lacking structure and generalizability, or depend on the knowledge of specific parameters of the WDN as well as on initial sensor data for linearization and demand estimation. Motivated by this, this paper investigates the observability of an entire WDN, based on structural observability theory. This allows us to establish the conditions for the observability of the WDN model, independently of parameter uncertainties. Additionally, a sensor placement algorithm is proposed, that leverages such observability conditions and graph theory and accounts for the industrial and material costs. To demonstrate the effectiveness of our approach, we apply it to a hydraulic-transient WDN model.

Keywords: Network analysis and control, Nonlinear system theory, Optimization
Abstract: In this article, we explore the problem of the region of synchronization (ROS) for complex networks with nonlinear dynamics. Given a pair of state- and target- sets, our goal is to estimate the ROS such that the trajectories originating within it reach the target set (i.e., synchronization manifold), without leaving the state set before the first hitting time. In order to do so, an exponential guidance-barrier function is proposed to construct the ROS along the synchronization manifold, and the corresponding sufficient conditions for estimating the ROS are developed. The resulting conditions lead to a sum-of-squares programming problem, thereby affording a polynomial-time solvability. Furthermore, when the synchronization manifold reduces to an equilibrium point, our method not only estimates a larger ROS compared to existing results but also allows the ROS to take more general shapes. Finally, we present two numerical examples to demonstrate the effectiveness of the theoretical results.

Keywords: Network analysis and control, Optimization algorithms, Control over networks
Abstract: Finding the optimal subset of individuals to observe in order to obtain the best estimate of the average opinion of a society is a crucial problem in a wide range of applications, including policy-making, strategic business decisions, and the analysis of sociological trends. We consider the opinion vector X to be updated according to a DeGroot opinion dynamical model with stubborn agents, subject to perturbations from external random noise, which can be interpreted as transmission errors. The objective function of the optimization problem is the variance reduction achieved by observing the equilibrium opinions of a subset K of agents in V. We demonstrate that, under this specific setting, the objective function exhibits the property of submodularity. This allows us to effectively design a Greedy Algorithm to solve the problem, significantly reducing its computational complexity. Simple examples are provided to validate our results.

Keywords: Biomedical systems, Predictive control for linear systems, Quantized systems
Abstract: This study introduces an enhanced pulsatile Zone Model Predictive Control (pZMPC) approach for managing blood glucose in patients with Type 1 Diabetes Mellitus (T1DM). Building on the prior work of Licini et al. [1], the proposed method aims to counteract the effects of physical activity through two novel extensions: (i) a dual-action MPC that incorporates both insulin infusion and hypoglycemic treatment (HT) suggestions, and (ii) the inclusion of a non-standard Insulin On Board (IOB) constraint along with an asymmetric cost function that penalizes hypoglycemia more than hyperglycemia. These innovations help to improve BG control by addressing the challenges posed by increased insulin sensitivity and glucose consumption during physical activity. Our simulation results show that the enhanced MPC maintains safe BG levels with fewer hypoglycemic events compared to single-action approach.

Keywords: Applications in neuroscience, Machine learning, Biomedical systems
Abstract: Accurate localization of epileptogenic tissue is paramount in epilepsy surgery. This paper proposes a novel approach using system identification techniques to analyze stereo-electroencephalographic (SEEG) recordings for improved epileptogenic zone (EZ) delineation. By treating adjacent SEEG contacts as coupled systems, we extract frequency response characteristics that capture local network dynamics. Transfer function features fed an XGBoost-based classifier to differentiate between electrode contacts within and outside the EZ. Using ictal data from 11 drug-resistant epilepsy patients who reached seizure freedom post-surgery, our system identification approach achieved 58% sensitivity and 70% specificity, outperforming reference biomarkers in accuracy, F1-score and Index of Balanced Accuracy. Moreover, our method delivers higher computational efficiency and operates independently of both signal amplitude and sampling frequency. These results suggest that system identification features could provide valuable complementary information for EZ delineation in clinical practice.

Keywords: Applications in neuroscience, Biological systems, Stability of nonlinear systems
Abstract: Epilepsy is a common neurological disorder characterized by abrupt seizures. Although seizures may appear random, they are often preceded by early warning signs in neural signals, notably, critical slowing down, a phenomenon in which the system’s recovery rate from perturbations declines when it approaches a critical point. Detecting these markers could enable preventive therapies. This paper introduces a multi-stable slow-fast system to capture critical slowing down in epileptic dynamics. We construct regions of attraction for stable states, shedding light on how dynamic bifurcations drive pathological oscillations. We derive the recovery rate after perturbations to formalize critical slowing down. A novel algorithm for detecting precursors to ictal transitions is presented, along with a proof-of-concept event-based feedback control strategy to prevent impending pathological oscillations. Numerical studies are conducted to validate our theoretical findings.

Keywords: Applications in neuroscience
Abstract: Action-potential-mediated release of neurotransmitters at chemical synapses is fundamental to interneuronal communication. More specifically, presynaptic Action Potentials (APs) trigger the fusion of docked vesicles which subsequently empty their neurotransmitter content into the synaptic cleft and drive transient changes in the postsynaptic membrane potential. An excitatory synaptic connection leads to depolarization of the membrane potential, and a postsynaptic AP is elicited when it reaches a critical threshold level. Such postsynaptic AP ``firings" are classically modeled using the integrate-and-fire model, where the threshold is fixed. In the paper we consider a revised model where the threshold changes in response to recent firing activity. Our analysis reveals that the adaptive threshold can lead to a band-pass effect where the postsynaptic AP frequency is maximized to an intermediate presynaptic AP frequency.

Keywords: Biomedical systems, Robotics, Intelligent systems
Abstract: Robotic-Assisted Minimally Invasive Surgery (RAMIS) has gained the attention of researchers worldwide, as it minimizes the infection risk and iatrogenic harm done to the patient, due to the fact that the surgical tool enters the human body through a tiny incision. A critical issue in RAMIS is to ensure that the incision (tool entrance) is not further damaged due to excessive stress applied by the surgical tool. In this work, a vision-to-haptics control scheme for a leader-follower robotic setup is proposed, that provides the surgeon with the appropriate force/torque feedback for avoiding further stress applied to the incision, in real-time. In the core of the method, a Deep Convolutional Neural Network (DCNN) is employed that is able to identify and quantify potentially harmful situations. The proposed method is proven to be passive and it is experimentally evaluated using a leader-follower setup. The results show the reduction of the deformation of the incision hole by the tool shaft, as compared to the case in which no force-feedback was provided to the human-user.

Keywords: Biological systems, Nonlinear system theory, Linear time-varying systems
Abstract: We consider a general class of translation-invariant systems with a specific category of output nonlinearities motivated by biological sensing. We show that no dynamic output feedback can stabilize this class of systems to an isolated equilibrium point. To overcome this fundamental limitation, we propose a simple control scheme that includes a low-amplitude periodic forcing function akin to so-called ``active sensing'' in biology, together with nonlinear output feedback. Our analysis shows that this approach leads to the emergence of an exponentially stable limit cycle. These findings offer a provably stable active sensing strategy and may thus help to rationalize the active sensing movements animals make when performing certain motor behaviors.

Keywords: Agents and autonomous systems, Cooperative control, Decentralized control
Abstract: This paper presents an accelerated distributed receding horizon controller for cooperative network estimation problems using multiple autonomous agents. Our approach accelerates decision-making by integrating a novel heuristic-based ranking system, significantly reducing the dependency on computationally expensive Nonlinear Programs (NLPs). The reduction of computational complexity enables real-time responses and scalability to large systems while maintaining high levels of estimation accuracy. To mitigate the small loss of performance, we further introduce a method that aims at generating the best solution within a given computational time constraint by leveraging both the newly introduced ranking scheme and the traditional NLP solutions. Numerical simulations demonstrate competitive performance when benchmarked against data-driven offline policies (e.g., RL), showing that our methods achieve good results while having enhanced flexibility and robustness properties due to their online nature.

Keywords: Agents and autonomous systems, Decentralized control, Lyapunov methods
Abstract: Distance-based formation control on minimally rigid graphs is known to suffer from flip ambiguities, which can lead to incorrect formation patterns. Even advanced distance-based controllers that incorporate additional controlled variables often face challenges, either requiring specific conditions to avoid such ambiguities or failing to guarantee that reflected ambiguities are resolved. In this study, we address both flipped and reflected ambiguities in shape formation control by revisiting the essence of hybrid geometrical constraints and integrating them with traditional distance-based formation control. We propose a new formation controller that ensures convergence to the desired formation framework without requiring additional conditions. Experimental results using the TigerSquare platform are presented to demonstrate the efficacy of the proposed controller, highlighting its ability to avoid formation ambiguities.

Keywords: Agents and autonomous systems, Stability of nonlinear systems, Cooperative control
Abstract: This paper proposes two novel error models for power evolution in social opinion network dynamics with stubborn agents. One is formulated to improve the required bound related to stubborn coefficients of agents. Another one uses an approximated equilibrium point to guarantee exponential convergence where a less conservative bound is found based on a numerical method. Examples and simulations are presented to verify the effectiveness of the proposed method.

Keywords: Agents networks, Communication networks, Fault tolerant systems
Abstract: In recent years, the security and resilience of distributed algorithms have become a feature of utmost importance in the context of Industrial Control Systems. In this paper, we consider a two-level security framework: (i) the level of the interconnected devices in the field, for which we develop a distributed consensus algorithm robust to false data injection attacks; (ii) the upper level of a verifier that poses authentication challenges to the underlying agents. Thanks to the collaboration between the two layers, it is possible to implement a recovery procedure that involves re-allocating the mass of the agent recognized as malicious starting from the last authenticated trustworthy value. This procedure ensures that the consensus algorithm will converge to the correct average of the initial conditions of all agents, despite the presence of attackers. A simulation campaign completes the paper and demonstrates its effectiveness experimentally.

Keywords: Agents networks, Concensus control and estimation, Communication networks
Abstract: In this paper, we propose a distributed algorithm (herein called HARQ-QAC) that enables nodes to calculate the average of their initial states by exchanging quantized messages over a directed communication network. In our setting, we assume that our communication network consists of unreliable communication links (i.e., links suffering from packet drops). For countering link unreliability our algorithm leverages narrowband error-free feedback channels for acknowledging whether a packet transmission between nodes was successful. Additionally, we show that the feedback channels play a crucial role in enabling our algorithm to exhibit finite-time convergence. We analyze our algorithm and demonstrate its operation via an example, where we illustrate its operational advantages. Finally, simulations corroborate that our proposed algorithm converges to the average of the initial quantized values in a finite number of steps, despite the packet losses. This is the first quantized consensus algorithm in the literature that can handle packet losses and converge to the average. Additionally, the use of the retransmission mechanism allows for accelerating the convergence.

Keywords: Optimization algorithms, Distributed cooperative control over networks, Agents and autonomous systems
Abstract: In this paper, we address the distributed optimization problem over unreliable error-prone directed networks. We propose a distributed gradient-tracking optimization algorithm (referred to as ARQ-OPT), which exploits packet retransmissions via an Automatic Repeat reQuest (ARQ) error control protocol. Nodes utilize acknowledgement messages transmitted over one-bit error-free channels to trigger retransmissions of packets that were previously received in error. This ensures reliable propagation of information throughout the network, even in the presence of packet errors. We analyze the convergence properties of the proposed algorithm, by augmenting the consensus matrices to align with the retransmission mechanism. Subsequently, we show that by appropriately choosing the maximum number of retransmission attempts, ARQ-OPT can achieve B-step consensus contractivity which allow us to establish asymptotic convergence to the unique optimal solution with probability one. Numerical simulations conducted under various channel conditions validate our findings.

Keywords: Distributed control, Adaptive systems, Adaptive control
Abstract: This paper proposes a novel distributed adaptive discrete control design for high-order uncertain multiagent systems in the presence of coupled dynamics. Here, an observer is designed to use within the discrete-time adaptive control design to deal with unmeasurable coupled dynamics and uncertainties, where the asymptotic convergence of the multiagent system tracking error is concluded. Finally, a numerical simulation example is presented to demonstrate the efficacy of the proposed architecture.

Keywords: Distributed control, Fault tolerant systems, Control over communication
Abstract: This paper considers synchronization of heterogeneous pulse-coupled oscillators (PCOs), where some oscillators might be faulty or malicious. The oscillators interact through identical pulses at discrete instants and evolve continuously with different frequencies otherwise. Despite the presence of misbehaviors, benign oscillators aim to reach synchronization. To achieve this objective, two resilient synchronization protocols are developed in this paper by adapting the real-valued mean-subsequence reduced (MSR) algorithm to pulse-based interactions. The first protocol relies on packet-based communication to transmit absolute frequencies, while the second protocol operates purely with pulses to calculate relative frequencies. In both protocols, each normal oscillator periodically counts the received pulses to detect possible malicious behaviors. By disregarding suspicious pulses from its neighbors, the oscillator updates both its phases and frequencies. The paper establishes sufficient conditions on the initial states and graph structure under which resilient synchronization is achieved in the PCO network. Specifically, the normal oscillators can either detect the presence of malicious nodes or synchronize in both phases and frequencies. A comparison between the two algorithms reveals a trade-off between relaxed initial conditions and reduced communication burden.

Keywords: Distributed control, Linear systems, Network analysis and control
Abstract: Laplacian flows model the rate of change of each node’s state as being proportional to the difference between its value and that of its neighbors. Typically, these flows capture diffusion or synchronization dynamics and are well-studied. Expanding on these classical flows, we introduce a pseudoinverse Laplacian flow system, substituting the Laplacian with its pseudoinverse within complex-valued networks. Interestingly, for undirected graphs and unsigned weight-balanced digraphs, Laplacian and the pseudoinverse Laplacian flows exhibit an interdependence in terms of consensus. To show the same, we first present the conditions for achieving consensus in the pseudoinverse Laplacian flow system using the property of real eventually exponentially positivity. Thereafter, we show that the pseudoinverse Laplacian flow system converges to consensus if and only if the Laplacian flow system achieves consensus in the above-mentioned networks. However, these are only the sufficient conditions for digraphs. Further, we illustrate the efficacy of the proposed approach through examples, focusing primarily on power networks.

Keywords: Decentralized control, Lyapunov methods, Electrical power systems
Abstract: This paper addresses the voltage regulation problem in DC microgrids supplying the so-called ZIP loads through boost converters. More precisely, we propose a decentralized differential passivity-based dynamic controller that relies solely on voltage and current feedback and guarantees the closed-loop stability against unknown loads by using a Krasovskii-type Lyapunov function. We also estimate a so-called feasible region of attraction, within which every closed trajectory satisfies the underlying physical constraints. Finally, extensive simulations and experimental validations confirm the effectiveness of the proposed controller, particularly its robustness against load variations.

Keywords: Decentralized control, Agents networks, Network analysis and control
Abstract: In this work, we consider a strongly connected group of individuals involved in decision-making. The opinions of the individuals evolve using the Friedkin-Johnsen (FJ) model. We consider that there are two competing `influencers' (stubborn agents) vying for control over the final opinion of the group. We investigate the impact of modifying the network interactions on their respective control over the final opinions (influence centrality). We use signal flow graphs (SFG) to relate the network interactions with the influence that each `influencer' exerts on others. We present the sufficient conditions on the edge modifications which lead to the increase of the influence of an `influencer' at the expense of the other. Interestingly, the analysis also reveals the existence of redundant edge modifications that result in no change in the influence centrality of the network. We present several numerical examples to illustrate these results.

Keywords: Decentralized control, Linear systems, Output regulation
Abstract: In order to reduce water wastage in irrigation channels, implementing an appropriate control strategy is crucial. Two commonly used strategies are immediate upstream and distant downstream control. In this paper, we focus on distant downstream control since it results in less water wastage in demand-driven systems. It has been shown in the literature that a feedback with feedforward (FBFF) configuration yields better performance than feedback alone. In the FBFF configuration, the control action of a gate is fed forward to its upstream gate. We propose a variation of FBFF configuration where, instead of control actions, the water level deviations in a pool are fed forward to its upstream pool and we show the two configurations are equivalent under certain conditions. We analyse the error propagation for both configurations and compare them in simulations of 7-pool systems, considering both identical and non-identical pools. A system-model mismatch is also considered in the simulations.

Keywords: Distributed control, Energy systems, Large-scale systems
Abstract: This paper presents a non-cooperative distributed model predictive controller for the control of large-scale District Heating Networks. To enable the design of this controller, a novel information transmission scheme and feasibility restoration method are created, allowing the local controllers to achieve a global consensus while minimizing a local cost function. The effectiveness of this controller is demonstrated on an 18-user District Heating Network decomposed into six subsystems. The results show that the developed control scheme effectively uses flexibility to manage the buildings' heat demands, reducing the total losses by 14% and the return temperature by 37%.

Keywords: Autonomous robots, Robotics
Abstract: This paper presents a novel, data-driven motion planning strategy for autonomous mobile robots navigating in dynamic environments with human interactivity. The proposed approach utilizes a receding-horizon optimization framework that integrates predictive models of the robot motion with unknown-form safety constraints encapsulating human movement uncertainties, and complex dynamics of human-human and human-robot interactions. The functional form of constraints is unknown instead, we obtain only measurements and gradients of the constraint i.e. 1st order online optimization. Specifically, data-driven log barrier functions enforce safety constraints by penalizing closeness to constraint boundaries. The proposed strategy enables reliable, efficient, and safe robot navigation in high-density environments, making it particularly suitable for applications in pedestrian and other interactive spaces. Finally, realistic simulation studies validate the effectiveness of the proposed framework in balancing safety with operational efficiency.

Keywords: Autonomous systems, Autonomous robots, Cooperative control
Abstract: Optimizing energy consumption is a critical challenge in autonomous mobile robotics, essential for extending battery life. Mechanical and computational components are the primary energy consumers, and studies show that dynamically co-managing their power usage—such as adjusting processing frequency relative to mechanical speed—significantly improves efficiency. This improvement is primarily due to the relationship between decision-making processes based on mechanical speed and computational workload. In this paper, we propose an agile reinforcement learning algorithm for dynamic co-management, tested on a rover equipped with a brushless motor, a Jetson TX2 processor, and an event-based camera. Our approach effectively addresses scalability and accuracy issues in prior methods, achieving energy efficiency improvements between 16.98% and 60.86% compared to the most efficient existing techniques

Keywords: Autonomous systems, Adaptive control, Optimal control
Abstract: This paper presents a novel approach to solving the docking problem for Autonomous Surface Vessels (ASVs) while considering the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs). The proposed method combines computational geometry, numerical optimal control, and a collision avoidance (COLAV) system to generate a collision-free path from an initial location to the docking point. The proposed approach first performs Voronoi partitioning of the non-convex area to create waypoints, forming a roadmap that ensures safe distances from harbors and obstacles. A search algorithm then finds the waypoint sequence corresponding to the shortest collision-free path. Subsequently, a nonlinear optimal control problem (NOCP) further refines the optimal trajectory and generates control inputs corresponding to this trajectory. The efficiency of our approach is demonstrated by simulations. Our results indicate that the proposed approach is suitable for transit and docking applications, where intricate and safe maneuvering at low speeds is often a necessity.

Keywords: Distributed cooperative control over networks, Concensus control and estimation, Robotics
Abstract: This paper presents a decentralized strategy for a team of N robotic manipulators cooperatively grasping and manipulating an object. A two-step strategy has been designed. In the first step, each robot runs N-1 consensus-based estimators to estimates the wrenches applied to the object by its teammates even when direct all-to-all communication is unavailable. In the second step, each manipulator runs a local compliance controller to adjust its end-effector compliance, thereby reducing internal stresses and preventing potential damage to the object. The effectiveness of the proposed scheme is validated through simulations of a work-cell with four 7-DOFs manipulators by using a realistic dynamic simulator. Simulation results confirm the capability of the approach to limit internal wrenches, even under restricted communication conditions.

Keywords: Supervisory control, Distributed control, Manufacturing processes
Abstract: Motivated by the expansion of the modern wafer semiconductor industry, where the manufacturing process consists of multiple cluster tools, including robots and process modules, a coordination tool is developed based on supervisory control theory. The tool is parametric with respect to the number of cluster tools, the number of process modules of each cluster tool, and the number of product types, treated simultaneously in the cluster tools. In the present paper, a fully parametric model of semiconductor manufacturing processes will be developed, using the models of the robots and the models of the process modules. The desired operational specifications for the coordination of the subsystems of the process will be developed. The development of the supervisor design, realizing these specifications, will be initiated by the translation of the specifications to appropriate sets of regular languages. Next, each regular language will be realized by a respective supervisor automaton, expressed in parametric form. The supervisor design will be completed by the determination of the automaton of the total controlled process and the examination of its satisfactory performance, by proving the controllability of the desired languages and the nonblocking property of the total controlled process.

Keywords: Optimal control, Flexible structures, Large-scale systems
Abstract: In this contribution, we present a variational space-time formulation which generates an optimal feed-forward controller for geometrically exact strings. More concretely, the optimization problem is solved with an indirect approach, and the space-time finite element method translates the problem to a set of algebraic equations. Thereby, only the positional field and the corresponding adjoint variable field are approximated by continuous shape functions, which makes the discretization of a velocity field unnecessary. In addition, the variational formulation can be solved using commercial or open source finite element packages. The entire approach can also be interpreted as a multiple-shooting method for solving the optimality conditions based on the semi-discrete problem. The performance of our approach is demonstrated by a numerical test.

Keywords: Optimal control, Linear systems
Abstract: This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the region of exponential convergence of both algorithms. In the case where there is uncertainty on the value of the system matrices, we provide input-to-state stability results capturing the effect of model parameter uncertainties. Our findings offer new insights into these algorithms at the heart of several approximate dynamic programming schemes, highlighting their convergence and robustness behaviors. Numerical examples illustrate the significance of some of the theoretical results.

Keywords: Optimal control, LMI's/BMI's/SOS's
Abstract: We use moment-SOS (Sum Of Squares) relaxations to address the optimal control problem of the 1D heat equation perturbed with a nonlinear term. We extend the current framework of moment-based optimal control of PDEs to consider a quadratic cost on the control. We develop a new method to extract a nonlinear controller from approximate moments of the solution. The control law acts on the boundary of the domain and depends on the solution over the whole domain. Our method is validated numerically and compared to a linear-quadratic controller.

Keywords: Optimal control, Optimization algorithms, Safety critical systems
Abstract: Convex optimization algorithms are increasingly used in embedded trajectory planning for safety-critical systems, requiring verification to meet safety standards. Previous research has shown that formal verification methods can be applied to convex solvers for linear problems. This paper explores a specific implementation of the successive convexification approach for trajectory planning using linear programming. We focus on a new implementation of the successive convexification algorithm based on the Frank-Wolfe method (fwscvx), aiming at demonstrating that it maintains algorithm performance and is suitable for embedded systems. We also analyze the convergence of the fwscvx{} algorithm and provide numerical evaluations to support our proposal. This work contributes to the formal verification of advanced trajectory planning algorithms in safety-critical embedded systems.

Keywords: Optimal control, Predictive control for nonlinear systems, Nonlinear system theory
Abstract: The Koopman operator stands as a powerful framework to transform nonlinear dynamical systems into equivalent linear ones within a lifted state space. Its application can be extended to nonlinear optimal control problems, enabling their efficient solution in the linear Koopman space. However, a systematic methodology to analytically derive a suitable basis of Koopman observables and handle the operator infinite-dimensionality is still lacking. In this paper, we propose a comprehensive analytical framework to efficiently solve Nonlinear Model Predictive Control (NMPC) problems in the linear Koopman space. We present a general procedure to derive a basis of observables that lifts both the nonlinear prediction model and nonlinear state constraints of NMPC, obtaining a quadratic program in the Koopman lifted space (denoted as Koopman NMPC, in short K-NMPC) that closely approximates the original NMPC solution. Additionally, we propose a general method to arbitrarily reduce the dimensionality of the Koopman lifted space, lowering the K-NMPC complexity and handling the infinite-dimensional case. We validate our K-NMPC approach in simulation, showcasing its solid performance and execution times, which are over ten times lower than classic NMPC.

Keywords: Communication networks, Optimal control, Markov processes
Abstract: This paper addresses the computation of a non-asymptotic lower bound, given by the nonanticipative rate-distortion function (NRDF), for the discrete-time zero-delay variable-rate lossy compression of discrete Markov sources under per-stage single-letter distortion constraints. We first derive a new information structure for the NRDF and new convexity results that allow reformulating the problem as an unconstrained partially observable finite-horizon stochastic dynamic program (DP) using Lagrange duality theorem subject to a belief state that summarizes past information and evolves in a continuous space. Rather than directly approximating the DP, we derive implicit optimal conditions via the Karush-Kuhn-Tucker (KKT) conditions and propose a novel alternating minimization (AM) scheme to approximate both the control policy and cost-to-go function through backward recursions with provable convergence guarantees. We evaluate the control policies and cost-to-go functions per-stage using an online forward algorithm that executes for any finite horizon. Our methodology yields a near-optimal approximation of the NRDF as the belief state space becomes sufficiently large. Simulation results using time-varying binary Markov sources validate the effectiveness of our approach.

Keywords: Game theoretical methods, Decentralized control, Markov processes
Abstract: This tutorial-style talk introduces dynamic incentive design for socio-technical resource allocation problems that arise in transportation, energy, communication, and many other critical applications. The focus is on theoretical tools for modelling and control using karma economies, a novel dynamic incentive scheme that achieves fair and efficient socio-technical resource allocations without relying on financial instruments. The tutorial covers the following topics: a) Fundamental limitations of static incentive design in jointly achieving fairness and efficiency, and how dynamics enable overcoming these limitations; b) basic constituents of a dynamic socio-technical resource allocation problem and its connection to mean-field games; c) introduction to mean-field games and their reduction to (static) population games; d) computation of mean-field equilibria using evolutionary dynamics; e) modelling of karma economies as a mean-field game: existence of karma mean-field equilibria, and mean-field game models for first price vs. second price karma auctions; and f) analysis of karma mean-field equilibria and the resulting resource allocation fairness and efficiency. Interactive teaching elements will be used, including a coding exercise and an online experiment.

Keywords: Game theoretical methods, Decentralized control, Markov processes
Abstract: We review the experimental learning in games literature, and identify avenues for behavioral mechanism design. The focus of this review will be on recent results that investigate the effects of feedback and information on the behavior of humans in dynamic environments involving other humans and algorithms. These dynamic environments include repeated double-sided auctions and karma auctions. We also review methods to quantify dynamic effects

Keywords: Traffic control, Game theoretical methods, Markov processes
Abstract: This talk demonstrates the use of CARMA (=karma for cars) as a fair solution to the morning commute congestion. We consider heterogeneous commuters traveling through a single bottleneck that differ in the value of time (VOT), generalizing the notion of VOT to vary dynamically on each day (e.g., according to trip purpose and urgency) rather than being a static characteristic of each individual. In our CARMA scheme, the bottleneck is divided into a fast lane that is kept in free flow and a slow lane that is subject to congestion. Commuters use karma to bid for access to the fast lane, and those who get outbid or do not participate in the scheme instead use the slow lane. At the end of each day, karma collected from the bidders is redistributed, and the process repeats day by day. We specialize the karma economy mean-field game model to this setting and analyze pthe roperties of its mean-field equilibrium. Unlike existing monetary schemes, CARMA is demonstrated to achieve (a) an equitable traffic assignment with respect to heterogeneous income classes and (b) a strong Pareto improvement in the long-term average travel disutility with respect to no policy intervention. Moreover, CARMA can retain the same congestion reduction as an optimal monetary tolling scheme under uniform karma redistribution and even outperforms tolling under a well-designed redistribution scheme.

Keywords: Game theoretical methods, Agents and autonomous systems, Intelligent systems
Abstract: Strategic agents and automated decision-making systems increasingly interact in modern infrastructure systems, raising challenges around trust and inducing truthful behavior for the system operators. We study a Stackelberg game where a principal (or a system operator) designs a two-stage contract for a non-myopic agent whose type is unknown to the principal. While the agent's first-stage action can reveal their type under truthful play, they may misrepresent themselves to gain higher second-stage incentives. We show that when the agent is non-myopic and their type is in a continuous space, simultaneously learning agent behavior and optimizing incentives is impossible for the principal under linear contracts. However, there is a possibility of achieving this task with discrete types. We interpret this result by resorting to arguments from adverse selection and moral hazard in contract theory. To address this limitation, we develop a novel nonlinear contract design incorporating an adjustment mechanism that penalizes inconsistent behavior across stages, which is shown to induce truthful behavior by forcing the agent to be consistent. This approach successfully mitigates information asymmetry and ensures truthful play while allowing for more flexible incentive functions.

Keywords: Delay systems, Optimal control, Computational methods
Abstract: Time delays are ubiquitous in industrial processes, and they must be accounted for when designing control algorithms because they have a significant effect on the process dynamics. Therefore, in this work, we propose a simultaneous approach for numerical optimal control of delay differential equations with distributed time delays. Specifically, we linearize the delayed variables around the current time, and we discretize the resulting implicit differential equations using Euler's implicit method. Furthermore, we transcribe the infinite-dimensional optimal control problem into a finite-dimensional nonlinear program, which we solve using Matlab's fmincon. Finally, we demonstrate the efficacy of the approach using a numerical example involving a molten salt nuclear fission reactor.

Keywords: Delay systems, Switched systems, Stability of linear systems
Abstract: The key challenges in design of predictor-based control laws for switched systems with arbitrary switching and long input delay are the potential unavailability of the future values of the switching signal (at current time) and the fact that dwell time may be arbitrary. In the present paper, we resolve these challenges developing a new predictor-based control law that is, essentially, an average of exact predictor feedbacks, each one corresponding to an exact predictor-feedback law for a system that operates only in a single mode. Because the predictor state in our control design does not correspond to an exact predictor, stability can be guaranteed under a restriction on the differences among the system’s matrices and controller’s gains. This is an unavoidable limitation, for a switching signal whose future values may be unavailable, when no constraint is imposed on the values of delay and dwell time (as it is the case here). We establish (uniform) stability of the closed-loop system employing a Lyapunov functional. The key step in the stability proof is constructive derivation of an estimate of the mismatch between an exact predictor feedback and the average of predictor feedbacks constructed. We illustrate the performance of the proposed predictor-based control law in simulation, including comparisons with alternative, predictor-based control laws.

Keywords: Delay systems, Lyapunov methods, Stability of nonlinear systems
Abstract: The analysis of the stability of systems' equilibria plays a central role in the study of dynamical systems and control theory. This note establishes an extension of the celebrated Krasovskiu{i} stability theorem for functional differential equations (FDEs) in the extended sense. Namely, the FDEs hold for t geq t_0 almost everywhere with respect to the Lebesgue measure. The existence and uniqueness of such FDEs were briefly discussed in J.K Hale's classical treatise on FDEs, yet a corresponding stability theorem was not provided. A key step in proving the proposed stability theorem was to utilize an alternative strategy instead of relying on the mean value theorem of differentiable functions. The proposed theorem can be useful in the stability analysis of cybernetic systems, which are often subject to noise and glitches that have a countably infinite number of jumps. To demonstrate the usefulness of the proposed theorem, we provide examples of linear systems with time-varying delays in which the FDEs cannot be defined in the conventional sense.

Keywords: Optimal control, Delay systems, Computational methods
Abstract: Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized discretization methods and the time delays may depend on the manipulated inputs or state variables. Therefore, in this work, we propose to linearize the delayed states around the current time. This results in a set of implicit differential equations, and we compare the steady states and the corresponding stability criteria of the DDEs and the approximate system. Furthermore, we propose a simultaneous approach for NOC of DDEs based on the linearization, and we discretize the approximate system using Euler’s implicit method. Finally, we present a numerical example involving a molten salt nuclear fission reactor.

Keywords: Stability of nonlinear systems, Delay systems, Lyapunov methods
Abstract: For an even power convex or concave function of a scalar variable having a global and unique extremum, an algorithm of the extremum seeking is proposed, which does not use any dither excitation signal, hence, being asymptotically exact, and it is based on online time derivative estimation of the measured output. Two approaches are discussed, first, with utilization of the super-twisting differentiator, and second, where the derivative is estimated via the time-delay method. For analysis of the latter, an extension of the invariance principle is formulated for functional differential inclusions. The efficiency of the suggested extremum seeking algorithms is illustrated through numeric experiments.

Keywords: Delay systems, Output feedback, Adaptive control
Abstract: This paper proposes a setpoint regulation algorithm for linear systems with input delay based on a memoryless delay-adaptive feedback scheme. The scheme provides integral action and is guaranteed to be stable for arbitrarily large bounded time-varying delay so long as the nominal system is open-loop stable. Furthermore, since full-state measurements are required in the proposed control scheme, we suggest an output feedback design based on an Unknown Input Observer.

Keywords: Nonlinear system identification, Identification
Abstract: Nonlinear system identification (NL-SI) has proven to be effective in obtaining accurate models for highly complex systems. In particular, recent encoder-based methods for artificial neural networks state-space (ANN-SS) models have achieved state-of-the-art performance on various benchmarks, while offering consistency and computational efficiency. Inclusion of prior knowledge of the system can be exploited to increase (i) estimation speed, (ii) accuracy, and (iii) interpretability of the resulting models. This paper proposes an encoder-based model augmentation method that incorporates prior knowledge from first-principles (FP) models. We introduce a novel linear-fractional-representation (LFR) model structure that allows for the unified representation of various augmentation structures including the ones that are commonly used in the literature, and an identification algorithm for estimating the proposed structure together with appropriate initialization methods. The performance and generalization capabilities of the proposed method are demonstrated in a hardening mass-spring-damper simulation.

Keywords: Nonlinear system identification, Electrical power systems, Neural networks
Abstract: In future power systems, the detailed structure and dynamics may not always be fully known. This is due to an increasing number of distributed energy resources, such as photovoltaic generators, battery storage systems, heat pumps and electric vehicles, as well as a shift towards active distribution grids. Obtaining physically-based models for simulation and control synthesis can therefore become challenging. Differential equations, where the right-hand side is represented by a neural network, i.e., neural ordinary differential equations (NODEs), have a great potential to serve as a data-driven black-box model to overcome this challenge. This paper explores their use in identifying the dynamics of droop-controlled grid-forming units based on inputs and state measurements. In numerical studies, various NODEs structures used with different numerical solvers are trained and evaluated. Moreover, they are compared to the sparse identification of nonlinear dynamics (SINDy) method. The results demonstrate that even though SINDy yields more accurate models, NODEs achieve good prediction performance without prior knowledge about the system’s nonlinearities which SINDy requires to work best.

Keywords: Nonlinear system identification, Identification, Cellular dynamics
Abstract: Cells play a vital role in maintaining tissue integrity, making it essential to understand their mechanisms for effectively staging vascular tissue diseases. However, addressing the complexity of cellular systems remains challenging and requires a structured identification framework. To meet this need, an indentation measurement setup is employed, utilizing accessible human tissue samples to investigate smooth muscle cell dynamics from a control systems perspective. This paper compares multiple black-box identification approaches to accurately model smooth muscle cell behavior and evaluate each models' performance in capturing system dynamics. The effectiveness of various techniques is demonstrated on measured data, and the results indicate a promising approach for modeling complex biological systems, with potential applications in vascular smooth muscle cell mechanobiology.

Keywords: Nonlinear system identification, Identification for control, Identification
Abstract: This work presents a data-driven method for automatically identifying the observed relative degrees of general nonlinear systems. The concept of relative degree plays a critical role in many feedback control design techniques for nonlinear systems. However, no general data-driven methods are available for identifying relative degrees from input-output data samples besides techniques optimised for sliding mode control. To address this gap, this work introduces the concept of a signal footprint, which enables the analysis of system responses and detection of the observed relative degree. Validation results demonstrate that the proposed approach is both accurate and efficient in identifying relative degrees from input-output data.

Keywords: Nonlinear system identification, Machine learning, Statistical learning
Abstract: Recently introduced by some of the authors, the in-context identification paradigm aims at estimating, offline and based on synthetic data, a meta-model that describes the behavior of a whole class of systems. Once trained, this meta- model is fed with an observed input/output sequence (context) generated by a real system to predict its behavior in a zero- shot learning fashion. In this paper, we enhance the original meta-modeling framework through three key innovations: by formulating the learning task within a probabilistic framework; by managing non-contiguous context and query windows; and by adopting recurrent patching to effectively handle long context sequences. The efficacy of these modifications is demon- strated through a numerical example focusing on the Wiener- Hammerstein system class, highlighting the model’s enhanced performance and scalability.

Keywords: Nonlinear system identification, Network analysis and control, Neural networks
Abstract: We study the identifiability of nonlinear network systems with partial excitation and partial measurement when the network dynamics is linear on the edges and nonlinear on the nodes. We assume that the graph topology and the nonlinear functions at the node level are known, and we aim to identify the weight matrix of the graph. Our main result is to prove that fully-connected layered feed-forward networks are generically locally identifiable by exciting sources and measuring sinks in the class of analytic functions that cross the origin. This holds even when all other nodes remain unexcited and unmeasured and stands in sharp contrast to most findings on network identifiability requiring measurement and/or excitation of each node. The result applies in particular to feed-forward artificial neural networks with no offsets and generalizes previous literature by considering a broader class of functions and topologies.

Keywords: Stability of nonlinear systems, Sampled data control, Robust control
Abstract: In this paper, we propose a novel controller design approach for unknown nonlinear systems using the Koopman operator. In particular, we use the recently proposed stability- and certificate-oriented extended dynamic mode decomposition (SafEDMD) architecture to generate a data-driven bilinear surrogate model with certified error bounds. Then, by accounting for the obtained error bounds in a controller design based on the bilinear system, one can guarantee closed-loop stability for the true nonlinear system. While existing approaches over-approximate the bilinearity of the surrogate model, thus introducing conservatism and providing only local guarantees, we explicitly account for the bilinearity by using sum-of-squares (SOS) optimization in the controller design. More precisely, we parametrize a rational controller stabilizing the error-affected bilinear surrogate model and, consequently, the underlying nonlinear system. The resulting SOS optimization problem provides explicit data-driven controller design conditions for unknown nonlinear systems based on semidefinite programming. Our approach significantly reduces conservatism by establishing a larger region of attraction and improved data efficiency. The proposed method is evaluated using numerical examples, demonstrating its advantages over existing approaches.

Keywords: Sampled data control, Linear parameter-varying systems, Process control
Abstract: This paper presents a data-driven min-max model predictive control (MPC) scheme for linear parameter-varying (LPV) systems. Contrary to existing data-driven LPV control approaches, we assume that the scheduling signal is unknown during offline data collection and online system operation. Assuming a quadratic matrix inequality (QMI) description for the scheduling signal, we develop a novel data-driven characterization of the consistent system matrices using only input-state data. The proposed data-driven min-max MPC minimizes a tractable upper bound on the worst-case cost over the consistent system matrices set and over all scheduling signals satisfying the QMI. The proposed approach guarantees recursive feasibility, closed-loop exponential stability and constraint satisfaction if it is feasible at the initial time. We demonstrate the effectiveness of the proposed method in simulation.

Keywords: Sampled data control, Nonlinear system theory, Stability of nonlinear systems
Abstract: In many sampled-data applications, observers are designed based on approximately discretized models of continuous-time systems, where usually only the discretized system is analyzed in terms of its detectability. In this paper, we show that if the continuous-time system satisfies certain linear matrix inequality (LMI) conditions, and the sampling period of the discretization scheme is sufficiently small, then the whole family of discretized systems (parameterized by the sampling period) satisfies analogous discrete-time LMI conditions that imply detectability. Our results are applicable to general discretization schemes, as long as they produce approximate models whose linearizations are in some sense consistent with the linearizations of the continuous-time ones. We explicitly show that the Euler and second-order Runge-Kutta methods satisfy this condition. A batch-reactor system example is provided to highlight the usefulness of our results from a practical perspective.

Keywords: Sampled data control, Stability of nonlinear systems
Abstract: In this paper, we investigate the problem of extending the operability of the prescribed performance control (PPC) methodology to address discrete-time control with time-varying transmission intervals. Given a continuous-time PPC scheme, capable of enforcing pre-specified and user-defined performance characteristics on the output tracking error, we develop a dynamic control protocol to produce the sampling time instants in real-time, such that the stability of the closed-loop system as well as the output tracking performance attributes, are preserved. By allowing for flexible transmission intervals that depend on the current distance of the errors from the corresponding performance bounds, we achieve their extension, thus reducing communication frequency and enhancing effectiveness and reliability. We further show that strict performance requirements lead to smaller transmission intervals, while relaxed requirements allow for larger ones. The theoretical results are verified via simulation studies.

Keywords: Control over networks, Sampled data control, Predictive control for linear systems
Abstract: This paper proposes an event-triggered parameterized control method using a control Lyapunov function approach for discrete time linear systems with external disturbances. In this control method, each control input to the plant is a linear combination of a fixed set of linearly independent scalar functions. The controller updates the coefficients of the parameterized control input in an event-triggered manner so as to minimize a quadratic cost function subject to quadratic constraints and communicates the same to the actuator. We design an event-triggering rule that guarantees global uniform ultimate boundedness of trajectories of the closed loop system and non-trivial inter-event times. We illustrate our results through numerical examples and we also compare the performance of the proposed control method with other existing control methods in the literature.

Keywords: Automotive, Fuzzy systems, Communication networks
Abstract: This work concerns the event-triggered vehicle direct yaw control to improve its stability and its handling during critical maneuver. An adaptive sampled event-triggered scheme, based on the logistic function, is proposed for reducing over-consumption of network, computing and energy resources. A novel approach to deal with the premises asynchronicity is introduced to reduce the number of design conditions. The reference trajectory tracking problem is solved with the presented sufficient Linear Matrix Inequality (LMI) based conditions. The effectiveness of the proposed approach is demonstrated via a co-simulation with the high-fidelity simulation software Carsim.

Keywords: Fault detection and identification, Cooperative autonomous systems, Machine learning
Abstract: This paper presents a novel approach addressing fault detection challenges for multi-agent systems through a machine-learning method using recurrent autoencoders. The main advantage lies in its ability to handle heterogeneous multi-agent systems with unknown dynamics. The approach features a distributed detection architecture based on a cluster representation that depends solely on the agents' relative outputs, integrating stable image representation and orthogonal projection. Unlike traditional observer-based methods, the fault detection framework employs distributed autoencoders for residual generation, offering a data-driven and model-free solution. The autoencoders are carefully designed for effective time-series data learning, incorporating gated recurrent units and neural networks. Simulation results validate the effectiveness of the proposed method, demonstrating excellent fault detection capabilities and highlighting the promising extension to more complex and generic systems.

Keywords: Maritime, Predictive control for nonlinear systems, Energy systems
Abstract: Solid Oxide Fuel Cells (SOFCs) represent a promising technology in the field of electric power generation, particularly suited for alternative fuels and large-scale applications. With the marine industry targeting a full de-carbonization by year 2050, there is a significant effort towards the adoption of SOFCs in cargo ships and other vessels. However, their effective adoption in marine transportation requires improved reliability, especially regarding cell degradation, which directly affects their functional lifetime. This paper proposes a novel Degradation-Conscious control strategy for SOFCs, integrating direct control of cell voltage degradation. First, we propose a novel state space model comprising a reduced order model of SOFC dynamics and the voltage degradation model of the cell. Second, we develop the Degradation-Conscious controller using a nonlinear Model Predictive Controller, which integrates degradation management into standard SOFC dynamical control. Simulation results demonstrate the proposed strategy's ability to reduce degradation while meeting dynamical performance requirements.

Keywords: Fault diagnosis, Fault detection and identification, Adaptive control
Abstract: This paper proposes a robust fault diagnosis method for nonlinear uncertain systems with multiple faults, addressing the possible occurrence of two consecutive faults in each state equation. A model-based monitoring module with two submodules is developed, enabling the diagnosis of both faults. The first submodule incorporates decision-making schemes for detecting and isolating the primary fault, enabling its partial or full isolation. The second submodule is introduced to detect the secondary fault while simultaneously determining the partial or full isolation of both the primary and secondary faults. A key design aspect of the proposed fault diagnosis method is that it effectively uses the information from the primary fault isolation process, particularly when partial isolation occurs, to detect and isolate a secondary fault in each system state equation. The boundedness of the system variables and the robustness of the proposed fault diagnosis scheme are analytically shown. Finally, the effectiveness and applicability of the developed framework is demonstrated through numerical simulations.

Keywords: Robust control, Randomized algorithms
Abstract: This paper addresses data-driven robust control design for Single-Input Single-Output (SISO) multi-model systems with mixed uncertainties. The proposed scheme tackles uncertainties arising from three sources: model estimation variance, measurements noise, and plant behavior variations across operating points. These uncertainties are combined into a single global output multiplicative uncertainty, encompassing the variability of all local models. The uncertainty quantification utilizes: (i) kernel methods for identifying the model of the plant, and (ii) a randomized approach for estimating the uncertainty region, guaranteeing a high probability of capturing the true plant behavior within the estimated uncertainty region. The designed robust controller for multi-model systems is evaluated in simulation on a model of a reconfigurable industrial oven employed in the packaging industry.

Keywords: Machine learning, Intelligent systems, Robotics
Abstract: Reinforcement learning (RL) algorithms have been successfully applied to control tasks associated with unmanned aerial vehicles and robotics. In recent years, safe RL has been proposed to allow the safe execution of RL algorithms in industrial and mission-critical systems that operate in closed loops. However, if the system operating conditions change, such as when an unknown fault occurs, typical safe RL algorithms cannot adapt while retaining past knowledge. Continual RL algorithms have been proposed to address this issue. However, the impact of continual adaptation on the system's safety is an understudied problem. In this paper, we study the intersection of safe and continual RL. First, we empirically demonstrate that a popular continual RL algorithm, elastic weight consolidation, does not satisfy safety constraints in nonlinear systems subject to varying operating conditions. Specifically, we study the MuJoCo HalfCheetah and Ant environments with velocity constraints and sudden joint loss non-stationarity. Then, we show that an agent trained using constrained policy optimization, a safe RL algorithm, experiences catastrophic forgetting in continual learning settings. With this in mind, we explore a simple reward-shaping method to ensure that elastic weight consolidation prioritizes remembering both safety and task performance for safety-constrained, nonlinear, and non-stationary systems.

Keywords: Fault tolerant systems, Machine learning, Predictive control for nonlinear systems
Abstract: The traditional fault-tolerant control method based on model switching cannot adapt to the control needs of gas turbines in realistic scenarios. Addressing this problem, this paper introduces a neural network-based adaptive model predictive control approach for gas turbine in degradation scenarios. Firstly, an online estimation method for gas turbine efficiency coefficient and flow coefficient based on extreme learning machine model is proposed. Secondly, a gas turbine rotation speed prediction model considering the degradation coefficients is established using the extreme learning machine. Based on the degradation estimation and speed prediction model, the model predictive control of the gas turbine is realized. Simulation experiments have proved that the extreme learning machine can achieve highly accurate degradation estimation and speed prediction. The proposed method has adaptive fault tolerance under different degradation degrees and variable operating conditions. Compared with traditional PID control, the proposed method has better control accuracy and can effectively improve the surge margin and economy. The proposed method also has more robust anti-interference ability. The proposed method has attracted attention for its superior control effect and practicality.

Keywords: Neural networks, Switched systems, Optimization
Abstract: We present a method for representing the closed-loop dynamics of piecewise affine (PWA) systems with bounded additive disturbances and neural network-based controllers as mixed-integer (MI) linear constraints. We show that such representations enable the computation of robustly positively invariant (RPI) sets for the specified system class by solving MI linear programs. These RPI sets can subsequently be used to certify stability and constraint satisfaction. Furthermore, the approach allows to handle nonlinear systems based on suitable PWA approximations and corresponding error bounds, which can be interpreted as the bounded disturbances from above.

Keywords: Neural networks, Stability of nonlinear systems, Nonlinear system identification
Abstract: Recurrent Neural Networks (RNNs) have shown remarkable performances in system identification, particularly in nonlinear dynamical systems such as thermal processes. However, stability remains a critical challenge in practical applications: although the underlying process may be intrinsically stable, there may be no guarantee that the resulting RNN model captures this behavior. This paper addresses the stability issue by deriving a sufficient condition for Input-to-State Stability based on the infinity-norm (ISS∞) for Long Short-Term Memory (LSTM) networks. The obtained condition depends on fewer network parameters compared to prior works. A ISS∞-promoted training strategy is developed, incorporating a penalty term in the loss function that encourages stability and an ad hoc early stopping approach. The quality of LSTM models trained via the proposed approach is validated on a thermal system case study, where the ISS∞-promoted LSTM outperforms both a physics-based model and an ISS∞-promoted Gated Recurrent Unit (GRU) network while also surpassing non-ISS∞-promoted LSTM and GRU RNNs.

Keywords: Cooperative autonomous systems, Distributed control, Neural networks
Abstract: In this work, we propose a data-driven potential-based control framework for multi-robot coordination. Each robot is equipped with an interaction device, i.e., a device that allows a robot to communicate with or perceive another robot, such as a camera or an antenna, which can be used to gather data regarding the quality of the interaction. This data is leveraged to build data-driven pairwise potential functions, which may be difficult or impossible to derive in a closed analytical form as typical in potential-based control frameworks. To achieve this, we model a pairwise potential function using a neural network, where, to ensure system stability for multi-robot coordination, we impose the necessary properties drawn from analytical potential-based multi-robot frameworks. Simulation results with different interaction devices and laboratory experimental results validate the proposed approach.

Keywords: Neural networks, Identification, Optimization
Abstract: This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression for the globally optimal weights is obtained alongside a quadratic input-output equation for the network. These properties make the network a viable tool in system theory by enabling further analysis, such as the sensitivity of the output to perturbations in the input, which is crucial for safety-critical systems such as aircraft or autonomous vehicles. The least squares method is compared to previously proposed strategies for training quadratic networks and to a back-propagation-trained ReLU network. The proposed method is applied to a system identification problem and a GPS position estimation problem. The least squares network is shown to have a significantly reduced training time with minimal compromises on prediction accuracy alongside the advantages of having an analytic input-output equation. Although these results only apply to 2-layer networks, this paper motivates the exploration of deeper quadratic networks in the context of system theory.

Keywords: Neural networks, Robotics, Identification for control
Abstract: In this paper, we introduce the notion of neural simulation gap functions, which formally quantifies the gap between the mathematical model and the model in the high-fidelity simulator, which closely resembles reality. Many times, a controller designed for a mathematical model does not work in reality because of the unmodelled gap between the two systems. With the help of this simulation gap function, one can use existing model-based tools to design controllers for the mathematical system and formally guarantee a decent transition from the simulation to the real world. Although in this work, we have quantified this gap using a neural network, which is trained using a finite number of data points, we give formal guarantees on the simulation gap function for the entire state space including the unseen data points. We collect data from high-fidelity simulators leveraging recent advancements in Real-to-Sim transfer to ensure close alignment with reality. We demonstrate our results through two case studies - a Mecanum bot and a Pendulum.

Keywords: Neural networks, Signal processing, Energy systems
Abstract: Detecting partial discharge (PD) in high-voltage cables is an effective method for assessing cable insulation. Traditional PD detection methods often struggle in real-world environments due to strong noise interference. Deep learning presents a promising direction for PD detection, but it typically necessitates paired datasets where each collected noisy PD signal needs a corresponding pure PD signal. However, obtaining such paired signals is impossible in real-world scenarios. In this paper, we propose a novel PD detection method based on CycleGAN and transfer learning. Using CycleGAN can address the challenge that the pure PD signals corresponding to noisy PD signals are unavailable, which makes it well-suited for real-world applications. Moreover, we employ a transfer learning strategy, utilizing abundant numerically simulated data to develop a high-quality pre-trained model. Subsequently, based on this pre-trained model, we can achieve a well-performing model by fine-tuning it with the limited laboratory data based on physical setup. We also design a comprehensive loss function that builds upon the loss of CycleGAN by incorporating a new item, i.e. soft dynamic time warping (Soft-DTW) loss. This Soft-DTW loss effectively evaluates the similarity between signals, even when they are distorted or twisted, thus enhancing the performance of PD signal detection. Extensive experiments on both the simulation dataset and laboratory dataset validate the effectiveness of our method.

Keywords: Emerging control applications, Energy systems
Abstract: Noise pollution from heat pumps (HPs) has been an emerging concern to their broader adoption, especially in densely populated areas. This paper explores a model predictive control (MPC) approach for building climate control, aimed at minimizing the noise nuisance generated by HPs. By exploiting a piecewise linear approximation of HP noise patterns and assuming linear building thermal dynamics, the proposed design can be generalized to handle various HP acoustic patterns with mixed-integer linear programming (MILP). Additionally, two computationally efficient options for defining the noise cost function in the proposed MPC design are discussed. Numerical experiments on a high-fidelity building simulator are performed to demonstrate the viability and effectiveness of the proposed design. Simulation results show that the proposed approach can effectively reduce the noise pollution caused by HPs with negligible energy cost increase.

Keywords: Emerging control applications, Identification for control, Robust control
Abstract: Power savings is a key research topic in High-Performance Computing (HPC). We present a control-based approach to regulate the power usage of an HPC application while maintaining its performance. Power capping is performed using the RAPL actuation and sensing mechanism, which is known to have noise and inaccuracies. Additionally, actuation is performed at the processor level, while the number of processors in an HPC setup can vary. To tackle these challenges of noise, actuator inaccuracies, and variable signal dimensions, our approach incorporates a cascade control design with robust controllers. One controller monitors real-time progress of the application and dynamically applies power caps via the RAPL actuator; the other controller adjusts the actuator power cap value, which we found to be inaccurate in meeting the commanded power limit. Additionally, we use a robust control approach to tune the controllers, where the PI parameters are selected to meet H∞ performance criteria, balancing robustness and disturbance rejection, ensuring stability and performance under varying conditions. This approach provides a robust solution to power control in the presence of system uncertainties. The experiments run the Embarrassingly Parallel (EP) compute-intensive HPC benchmark on various clusters of the Grid'5000 platform. Using this approach, we improved the accuracy of RAPL and reduced power consumption by 25%, with a trade-off of a 10% reduction in performance.

Keywords: Emerging control theory, Cooperative control, Electrical power systems
Abstract: This research study devises a new dynamic output feedback cooperative control scheme relying on the Negative Imaginary (NI) toolkit to address the secondary voltage synchronisation issue of the inverter-based Distributed Generating Units (DGUs) that constitute an AC microgrid. Each DGU can be modelled by a nonlinear descriptor system, which, upon being feedback-linearised, gives a double integrator map from the auxiliary input to the d-component of the output voltage. As a double integrator dynamics intrinsically exhibits the NI property, the feedback-linearised DGUs connected via a network manifest the multi-agent NI property. Therefore, a distributed Strictly NI (SNI) control law can achieve the desired voltage synchronisation among the DGUs of a microgrid. The proof of consensus invokes the Eigenvalue Loci technique, for which a complicated Lyapunov theory-based derivation is not necessary. The scheme is resilient to bounded disturbances and variation in the interaction topology and can handle plug-and-play operations. The paper also examines the performance of various first-order and second-order distributed SNI controllers in achieving the desired voltage consensus.

Keywords: Power electronics, Nonlinear system theory, Stability of nonlinear systems
Abstract: High-power fast charging units for electric vehicles (EVs) usually consist of multiple modules which are connected in parallel in order to achieve high power density and ratings. Considering the fact that these units are integrated within the modern smart grid infrastructure, there is always the danger of cyber-attacks and failures in measurement/sensor/communication links. In this paper, an EV fast charging unit consisting of multiple parallel connected dual active bridge (DAB) converters is considered and a novel nonlinear resilient controller (NLRC) is proposed for accurate output power regulation during abnormal scenarios, while inherently limiting each individual DAB converter current. Furthermore, taking into account the multiple parallel connected module structure of the charging unit, equal power distribution among the modules is accomplished. Utilizing the invariant set and ultimate boundedness theory, it is proved that the power (or current) delivered to the EV battery by each converter is always bounded below a maximum value. Based on the dynamics of the NLRC, it is shown that when an abnormal event (setpoint attack, sensor fault) occurs at one or more converters, the output current of the corresponding module is limited, while the remaining unaffected modules regulate their power, in a way that the delivered to the battery power equals to the reference value. Extensive simulation scenarios, including both normal and abnormal situations, were implemented to prove the effectiveness of the proposed NLRC, considering an EV charger that consists of three DAB converter modules.

Keywords: Constrained control, Power electronics
Abstract: A novel concept, termed the conditioning function, is introduced, leading to the development of a new nonlinear reference conditioning method called the conditioning-function-based reference governor (CF-RG). To achieve faster and more efficient responses, an enhanced version, referred to as the fast conditioning-function-based reference governor (FCF-RG), is proposed. This technique is based on an approximate calculation of the inverse of the nominal loop transfer function, allowing for rapid adjustments. The effectiveness of the proposed methods is demonstrated through both a mathematical example and an application to overshoot mitigation in active power control of a three-phase grid-connected converter. The results show that the proposed approaches provide an additional safety layer to the nominal controller, effectively limiting the output.

Keywords: Electrical power systems, Optimization, Energy systems
Abstract: This paper addresses the energy management control problem for railway systems, focusing on a hybrid train equipped with hydrogen fuel cells and lithium-ion batteries, also enhanced by regenerative braking, capable of operating both with and without a catenary connection. Initially, a detailed electrical model is developed, ensuring an accurate representation of the train. This model is then simplified for control purposes, enhancing computational efficiency while maintaining accuracy. Hence, a model predictive control (MPC) strategy with an economic cost is designed, focusing on optimizing energy management and minimizing power losses, while ensuring that the levels of the batteries and fuel cells remain within their optimal ranges. The work, relying on real data provided by the industrial partner Alstom, concludes with a comparative analysis against a heuristic approach, with satisfactory performance in terms of efficiency and reliability.

Keywords: Agents and autonomous systems, Adaptive control, Robotics
Abstract: In this paper we consider the regular polygon formation control problem of a mobile multi-robot system via a Nash Equilibrium (NE) seeking approach. We aim to steer the mobile robots towards the Nash equilibrium of a suitably defined virtual static game. In this game, the actions are the desired final positions of the robots and the cost functions include terms that penalize positions which are not vertices of a regular polygon with fixed center, while also taking into account deviations from their starting positions. As a result, the unique NE of the game defines a formation which is close to that of a regular polygon. Distributed adaptive control laws are then designed for seeking the NE of the aforementioned game. Simulation results verify the validity of the proposed methodology.

Keywords: Lyapunov methods, Optimal control, Autonomous robots
Abstract: We propose a learning-based Control Barrier Function (CBF) to reduce conservatism in collision avoidance for car-like robots. Traditional CBFs often use the Euclidean distance between robots' centers as a safety margin, which neglects their headings and approximates their geometries as circles. Although this simplification meets the smoothness and differentiability requirements of CBFs, it may result in overly conservative behavior in dense environments. We address this by designing a safety margin that considers both the robot’s heading and actual shape, thereby enabling a more precise estimation of safe regions. Because this safety margin is non-differentiable, we approximate it with a neural network to ensure differentiability. In addition, we propose a notion of relative dynamics that makes the learning process tractable. In a case study, we establish the theoretical foundation for applying this notion to a nonlinear kinematic bicycle model. Numerical experiments in overtaking and bypassing scenarios show that our approach reduces conservatism (e.g., requiring 33.5% less lateral space for bypassing) without incurring significant extra computation time. Code: https://github.com/bassamlab/sigmarl

Keywords: Agents and autonomous systems, Safety critical systems, Autonomous robots
Abstract: This study presents a multi-agent negotiation-based framework to obtain collision-free paths while performing prescribed-time reach-avoid-stay (RAS) tasks for agents with unknown dynamics and bounded disturbance. By employing spatiotemporal tubes to generate time-varying state constraints, we ensure that all agents adhere to RAS specifications using synthesized controllers. To prevent inter-agent collisions, a negotiation mechanism is proposed where successful negotiations result in spatiotemporal tubes for each agent fulfilling desired tasks. This approach results in a completely distributed, approximation-free control law for each agent. The effectiveness of this mechanism was validated through simulations of multiagent robot navigation and drone navigation tasks involving prescribed-time RAS specifications and collision avoidance.

Keywords: Agents and autonomous systems, Adaptive control, Autonomous robots
Abstract: This paper studies adaptive steering control of a sensory vehicle toward a planar circumnavigation orbit around a signal field source using the signal intensity measurements of the vehicle along its motion path. The signal field is approximated by a quadratic function of location, and has its extremum (maximum) at the signal source location. The proposed adaptive motion control design is based on on-line estimation of the gradient parameters of the signal field. Stability analysis is provided for the proposed adaptive estimation and motion control schemes, establishing asymptotic convergence of the gradient parameter estimates to their true values and settlement of the vehicle on an orbital trajectory on which the signal intensity is equal to a predefined constant value. Simulation test results verify the established properties of the proposed scheme as well as robustness to signal measurement noise.

Keywords: Adaptive control, UAV's, Lyapunov methods
Abstract: This paper investigates the problem of controlling an autonomous agent to simultaneously localize and circumnavigate an unknown stationary target using bearing-only measurements (without explicit differentiation). To improve the convergence rate of target estimation, we introduce a novel adaptive target estimator that enables the agent to accurately localize the position of the unknown target with a tunable, predefined convergence time. Following this, we design a controller integrated with the estimator to steer the agent onto a circular trajectory centered at the target with a desired radius. The predefined-time stability of the overall system including the estimation and control errors are rigorously analyzed. Extensive simulations and experiments using unmanned aerial vehicles (UAVs) illustrate the performance and efficacy of the proposed estimation and control algorithms.

Keywords: Adaptive control, Agents and autonomous systems, Robotics
Abstract: This work addresses the problem of designing a visual servo controller for a multirotor vehicle, with the end goal of tracking a moving spherical target with unknown radius. To address this problem, we first transform two bearing measurements provided by a camera sensor into a bearing-angle pair. We then use this information to derive the system's dynamics in a new set of coordinates, where the angle measurement is used to quantify a relative distance to the target. Building on this system representation, we design an adaptive nonlinear control algorithm that takes advantage of the properties of the new system geometry and assumes that the target follows a constant acceleration model. Simulation results illustrate the performance of the proposed control algorithm.

Keywords: Distributed cooperative control over networks, Optimization algorithms, Distributed estimation over sensor nets
Abstract: In this paper, we propose MAcroscopic Consensus and micRoscopic gradient-based OPTimization (MACROPT), a novel distributed method able to learn the probabilistic macroscopic model of a network of agents (e.g. the detection capabilities of a network of sensors) and concurrently optimize it acting on the microscopic agents’ states. The macroscopic model is defined through the aggregation of local kernels each representing a probabilistic feature of a single agent (e.g., its local sensing model), while the optimization is done with respect to a given cost index, e.g., the Kullback-Leibler divergence with respect to a target distribution. MACROPT improves the macroscopic model by microscopically coordinating the agents according to a distributed gradient-based policy. Concurrently, it allows each agent to locally learn the macroscopic model through a consensus-based mechanism. We analyze the result- ing interconnected method through the lens of system theory. We demonstrate that MACROPT asymptotically converges to the set of stationary points of the nonconvex cost function. The theoretical findings are supported by numerical simulations in a multi-agent event-detection scenario.

Keywords: Distributed cooperative control over networks, Agents and autonomous systems, Optimization algorithms
Abstract: This paper addresses the problem of collaboratively satisfying long-term spatial constraints in multi-agent systems. Each agent is subject to spatial constraints, expressed as inequalities, which may depend on the positions of other agents with whom they may or may not have direct communication. These constraints need to be satisfied asymptotically or after an unknown finite time. The agents' objective is to collectively achieve a formation that fulfills all constraints. The problem is initially framed as a centralized unconstrained optimization, where the solution yields the optimal configuration by maximizing an objective function that reflects the degree of constraint satisfaction. This function encourages collaboration, ensuring agents help each other meet their constraints while fulfilling their own. When the constraints are infeasible, agents converge to a least-violating solution. A distributed consensus-based optimization scheme is then introduced, which approximates the centralized solution, leading to the development of distributed controllers for single-integrator agents. Finally, simulations validate the effectiveness of the proposed approach.

Keywords: Distributed cooperative control over networks, Optimization algorithms, Agents and autonomous systems
Abstract: This paper addresses a multi-agent cooperative source seeking problem, with a particular focus on scenarios involving input saturation and limited communication. The objective is to guide the average position of a number of agents to the optimal point of a specified unknown scalar field function while maintaining the desired formation based on the field values measured by the agents. The difficulty of the above task arises due to the strong nonlinearity introduced by the saturation function and the limited communication among agents. To address this challenge, we propose a gradient-free formation-based collaborative source seeking algorithm, featuring both centralized and distributed implementations. In addition, we construct a proper composite Lyapunov function to establish the stability of the closed-loop system leveraging the nonlinear small-gain theorem. The proposed method estimates the gradient of an unknown scalar field through collaborative formation, eliminating the need for prior knowledge of the field function. Finally, the effectiveness of the proposed method is illustrated by a numerical simulation.

Keywords: Distributed cooperative control over networks, Safety critical systems, Predictive control for nonlinear systems
Abstract: Society relies on critical infrastructure, which is subject to an increasing threat of cyber attacks. This paper presents a method for designing distributed optimising controllers for critical infrastructure. The proposed method keeps local cost functions and constraints private in case of passive and eavesdropping attacks. The method is based on distributing a Model Predictive Control (MPC) problem using Alternating Direction Method of Multipliers (ADMM), which is made privacy-preserving through the use of Secure Multi-Party Computation (SMPC). The privacy-preserving controller is tested in a laboratory environment, emulating a Water Distribution Network (WDN), with real noise and disturbances, where it performs equally to a centralised model predictive controller. Thereby, the only cost of implementing the privacy-preserving controller is longer computation time and increased communication.

Keywords: Cooperative control, Coverage control, Cooperative autonomous systems
Abstract: In this paper we introduce the Adversarial Voronoi Regions (AVR) as a way of evaluating and updating the states of opposing teams. While many multi-agent problems focus on cooperative tasks like search and rescue, task allocation, or distributed sensing, there are also adversarial settings where teams compete to maximize their own outcomes, often at the expense of the opposing team. Such scenarios include zero-sum games, various team sports, pursuit-evasion problems, and business competition.

We show how the AVR concept can be used to formulate an optimization problem that captures the utility of the positions of agents in adversarial scenarios, such as competing business locations, team sport tactics, and security agents handling potential threats. We also derive the analytical gradient of the AVR utility and show how this can be used to dynamically control the team over time, or to find locally optimal configurations. Then we show that for an agent with a single adversarial neighbor, the gradient drives the agent closer to its neighbor and toward the center of mass of the edge separating them. Finally, we illustrate the approach with practical examples, demonstrating its adaptability in dynamic and competitive scenarios.

Keywords: Agents and autonomous systems, Concensus control and estimation, Fault tolerant systems
Abstract: We consider the problem of average consensus in a distributed system wherein a subset of the nodes comprising the system becomes faulty. To address this problem, we rely on a class of averaging algorithms whereby each node maintains a collection of variables, which it iteratively updates as a linear combination of other variables received by the node from its in-neighbors, i.e., nodes from which it receives information directly. Algorithms within this class exhibit, throughout their execution, certain invariance properties that are local to each node and reflect the conservation of certain quantities capturing an aggregate of all the values received by a node from its in-neighbors and all the values sent by said node to its out-neighbors, i.e., nodes that receive its information directly. In this paper, we exploit one such invariance property to enable each node to check whether or not any of its in-neighbors becomes faulty during the execution of the algorithm. In addition, we provide a shadow-banning mechanism to remove faulty nodes from the execution, and nullify the information they have broadcast up to the time when they were declared faulty.

Keywords: Electrical power systems, Safety critical systems, Optimization algorithms
Abstract: Incorporating renewable energy sources into modern power grids has significantly decreased system inertia, which has raised concerns about power system vulnerability to disturbances and frequency instability. The conventional methods for evaluating transient stability by bounding frequency deviations are often conservative and may not accurately reflect real-world conditions and operational constraints. To address this, we propose a framework for assessing the resilience of power systems against disturbances while adhering to realistic operational frequency constraints. Our approach leverages the Lur’e system representation of power system dynamics and Signal Temporal Logic (STL) to capture the essential frequency response requirements set by grid operators. This enables us to translate frequency constraints into formal robustness semantics. We then formulate an optimization problem to identify the maximum disturbance that the system can withstand without violating these constraints. The resulting optimization is translated into a scenario optimization while addressing the uncertainty in the obtained solution. The proposed methodology has been simulated on the Single Machine Infinite Bus case study and 9-Bus IEEE benchmark system, demonstrating its effectiveness in assessing resilience across various operating conditions and delivering promising results.

Keywords: Fault detection and identification, Linear systems, Safety critical systems
Abstract: This paper proposes a data-driven framework to identify the attack-free sensors in a networked control system when some of the sensors are corrupted by an adversary. An operator with access to offline input-output attack-free trajectories of the plant is considered. Then, a data-driven algorithm is proposed to identify the attack-free sensors when the plant is controlled online. We also provide necessary conditions, based on the properties of the plant, under which the algorithm is feasible. An extension of the algorithm is presented to identify the sensors completely online against a class of replay attacks and network delay attacks, respectively. The efficacy of our algorithm is depicted through numerical examples.

Keywords: Control over networks, Safety critical systems, Optimization
Abstract: Zero dynamics attacks (ZDAs) have received considerable attention in the control systems literature, as they can be disruptive while being almost virtually to detect from the measured output of the plant. However, as ZDAs require an unbounded input sequence, the effect of physical constraints on the actuators, in the form of saturation, must be taken into account. In this work, we show that conventional methods for constructing ZDAs, when subject to input saturation, can make these attacks no longer disruptive, stealthy, or both. While this might imply that some systems are safe from ZDAs, we introduced a new attack called a relaxed ZDA, which can be disruptive and practically stealthy even under input constraints. For the construction of relaxed ZDAs, we propose a method that involves solving an optimization problem offline. We demonstrate the versatility of the proposed method and show it succeeds where conventional ZDAs fall short by means of an illustrative example on a cyber-physical system (CPS).

Keywords: Transportation systems, Robust control, Automotive
Abstract: In this paper, it is shown that the problem of finding a ecentralized dynamic output feedback cooperative adaptive ruise controller (CACC controller) can equivalently be ormulated as a robust control problem. It is shown that the internal dynamics are rendered globally asymptotically table by a CACC controller if the states of the predecessing vehicle are regarded as disturbances. Furthermore, the ecoupling of the input of the predecessor from the spacing error can be regarded as the minimization of the calH_infty norm of the transfer function from u_{i-1} to the spacing error. These observations result in the formulation of an calH_infty problem and dynamic output feedback controller that solve this calH_infty problem can be synthesized using LMI techniques. Finally, the results are illustrated through simulations.

Keywords: Cooperative autonomous systems, Control over communication, Safety critical systems
Abstract: With the fusion of intelligent transportation systems and telecommunication technologies, research and development of vehicular communication-based control algorithms is rapidly evolving. These new algorithms are implemented in complex systems, rely on an increasing number of connected devices, and are often used in safety-critical applications. Since the communication is wireless, the probability of packet loss, radio interference, and communication failures rises alongside the number of communicating agents, necessitating detailed testing of algorithms, particularly in corner cases. This paper provides a proof of concept method for realizing a mixed-reality test system for connected vehicles that uses a software-defined radio to generate radio interference in the physical domain. A measurement campaign was conducted with three vehicles equipped with automotive industrial vehicular communication devices. One of the vehicles simulated the communication of virtual traffic in an aggregated (mesoscopic) manner. Results showed that using the software-defined radio can induce packet losses during mixed-reality testing in a controlled and precise manner. Unlike software-based packet drops, this method offers a more realistic and comprehensive approach by introducing physical interference, better reflecting real-world conditions.

Keywords: Optimization, Predictive control for nonlinear systems, Autonomous systems
Abstract: Trajectory optimization is valuable for a wide range of applications, from motion planning for mobile robots, to aircraft flight planning. However, nonlinear dynamic models lead to challenging nonconvex trajectory optimization problems. Many existing approaches formulate them as multistage programs and rely on derivatives of each stage to obtain a local approximation at each iteration, in which case quality of approximation when solving the optimization program has significant impact on convergence behavior. In this work, we develop a novel approach for obtaining improved local approximations when solving nonconvex trajectory optimization problems. By performing an input-to-state reformulation of system dynamics, we use trajectory sensitivities, which are derivatives of the entire system trajectory with respect to control inputs, to form local approximations. Local convergence guarantees for the proposed method are presented. The method is applied to generate trajectories for an autonomous vehicle, and is extended to include scenario with static obstacles. Simulation on a variety of reference paths show that the proposed method outperforms the traditional Sequential Quadratic Programming (SQP) in terms of local approximation accuracy, allowable trust-region radius, iterations to converge, and total solver time, and is less prone to failure when handling multiple obstacles with a complex reference.

Keywords: Optimization, Stability of nonlinear systems, Optimization algorithms
Abstract: Online Feedaback Optimization (OFO) is a control approach to drive a dynamical plant to an optimal steady-state. By interconnecting optimization algorithms with real-time plant measurements, OFO provides all the benefits of feedback control, yet without requiring exact knowledge of plant dynamics for computing a setpoint. On the downside, existing stability guarantees for gls{OFO} require the controller to evolve on a sufficiently slower timescale than the plant, possibly affecting transient performance and responsiveness to disturbances. In this paper, we prove that, under suitable conditions, OFO ensures stability without any timescale separation. In particular, the condition we propose is independent of the time constant of the plant, hence it is scaling-invariant. Our analysis leverages a composite Lyapunov function, which is the max of plant-related and controller-related components. We corroborate our theoretical results with numerical examples.

Keywords: Optimization, Aerospace, Traffic control
Abstract: With advancements in technology, commercial aircraft formation flying is becoming increasingly feasible as an efficient and environmentally friendly flight method. However, gaps remain in practical implementation, particularly in collision avoidance for aircraft formations. Existing avoidance algorithms mainly focus on single aircraft or unmanned aerial vehicle swarms, lacking comprehensive studies on the complex interactions within commercial aircraft formations. To address this, this paper proposes an optimization model designed to generate safe and effective collision avoidance solutions for commercial aircraft formations. This model demonstrates avoidance paths for formations facing intruders and offers insights for developing formation flight strategies. This study explores response strategies for commercial aircraft formations encountering intruders, considering the difficulty of pilot maneuvers. The findings provide theoretical support for the practical implementation of commercial formation flying and may advance the adoption of this technology.

Keywords: Optimization, Constrained control, Aerospace
Abstract: Control allocation methods such as redistributed scaled pseudoinverse (RSPI), exact redistributed pseudoinverse (ERP), and sequential least squares active set (SLS-AS) are crucial for safety-critical overactuated systems. This paper addresses the need for efficient and reliable control allocation in these systems. While the RSPI and ERP are based on the cascaded generalized inverses (CGI) method, SLS-AS is derived from quadratic programming optimization techniques. Despite the fact that RSPI and ERP were developed independently and differ in formulations, we demonstrate that they are equivalent. Additionally, we show significant parallels between RSPI with null space transition (NST) and SLS-AS, suggesting that RSPI is a special variant of SLS-AS. This paper evaluates the similarities and differences between RSPI and SLS-AS. Numerical comparisons are conducted using data from a real multicopter. This analysis gives valuable insight into both algorithms and lays the basis for further improvement towards a compromise between computational effort and optimal results.

Keywords: Optimization, Optimization algorithms
Abstract: Rural areas face significant logistical challenges, including inadequate infrastructure, safety risks, and high transfer costs. Traditional inventory routing models often overlook these complexities, particularly the need for alternative routes and backhaul integration, where routes include deliveries and pickups. This study introduces a Multi-Objective Inventory Routing Problem in a Multigraph with Backhauls (MO-IRPMGB) and employs the Non-dominated Sorting Genetic Algorithm II (NSGA-II) for optimization, achieving average savings of seven to fourteen percent.

Keywords: Optimization, Differential algebraic systems, Chemical process control
Abstract: In the future, power grid operators must mitigate fluctuations in the large amounts of energy produced from renewable energy sources. Power-to-X plants can support the operators in this regard by 1) enabling intermittent energy storage in green fuels and chemicals and 2) operating flexibly in order to provide ancillary services. Therefore, in this work, we propose a multi-stage optimization approach that determines optimal operating points for a plastic waste-to-methanol (PWtM) plant for given time-varying electricity prices. The plastic is gasified in a fluidized bed reactor (FBR), and an electrolysis unit supplies both oxygen for the gasification and the hydrogen needed to upgrade the produced synthetic gas that is converted to methanol. PWtM plants can also support a circular plastics economy where the methanol is used to produce new plastic. We assume that all chemical reactions in the FBR reach equilibrium instantaneously, and the main operational constraint is that only trace amounts of solid carbon are allowed to form. Finally, we present numerical examples of the solutions to both single- and multi-stage optimization problems.