Keywords: Machine learning, Intelligent systems
Abstract: Over the last decade, the enormous potential of learning-based control has been shown in many application domains. Despite the significant progress, however, a number of challenges still limit its widespread success in practice. This talk focuses on the two key aspects of safety and data-efficiency. We rely on model-based techniques and demonstrate how optimization-based control can provide a powerful framework for safe and efficient learning. Safety filters as a general and modular safety concept for any learning-based controller will be presented, as well as the integration of predictive control with learning mechanisms to facilitate controller design and to enhance performance despite limited computational resources and information. Throughout the talk, the results will be highlighted using examples from robotics.

Keywords: Optimal control, Stochastic systems, Stochastic control
Abstract: We consider an optimal regulator problem for a class of nonlinear stochastic systems with a square-root nonlinearity and random coefficients, and using the quadratic-linear criterion. This represents a certain nonlinear generalisation of the stochastic linear-quadratic control problem with random coefficients. The solution if found in an explicit closed-form as an affine state-feedback control in terms of a Riccati and linear backward stochastic differential equations. As an application, we give the solution to an optimal investment problem in a market with random coefficients.

Keywords: Stochastic systems, Randomized algorithms, Computational methods
Abstract: An algorithm to estimate the state distribution of a initial value problem subject to random perturbations is proposed. The main contribution of this paper is the ability to handle state dependent probability density functions governing the state change. The task is handled by iteratively applying a generalized polynomial chaos expansion on the inverse cumulative distribution functions of the state and state change. The feasibility of the algorithm is demonstrated with a kinematic vehicle model and compared against a Monte-Carlo-Simulation.

Keywords: Stochastic systems, Robust control, Modeling
Abstract: In the last decades, feedback trading and especially simultaneously long-short (SLS) trading attracted a lot of attention in the control community. The main reason for this is the so-called robust positive expectation property, which states that under specific conditions like, e.g., continuous time trading and survival the SLS controller achieves for almost all (a.a.) parameter settings, positive expected gains not only for several price models but also in mostly model-free frameworks. In finance, topics like optimal pairs trading are of interest for research and implementation. In the intersection of pairs trading and SLS so-called cross-coupled SLS (CC-SLS) rules are analyzed. Typically the CC-SLS rule is analyzed either empirically or with specific model assumptions. In the work at hand, under specific assumptions we do not only show that a new type of cross-coupled SLS (CC*-SLS) rule achieves the robust positive expectation property but also that this CC*-SLS is in expectation for a.a. parameter settings superior to the standard SLS rule used stock by stock. Furthermore, we perform simulations to illustrate the controllers' behavior.

Keywords: Stochastic control, Stochastic systems, Optimal control
Abstract: We consider the problem of optimal investment in a market with a higher interest rate for borrowing than for lending, and the power utility from terminal wealth. The market coefficients are random and unbounded in general. A certain combined interest rate model is introduced that contains known previous models, such as the Hull-White model and the quadratic-affine model, as special cases. The solution method is based on linear backward stochastic differential equation with possibly unbounded coefficients, and the minimization of a piece-wise quadratic function. An explicit closed-form solution is obtained as a linear state-feedback control with random coefficients.

Keywords: Stochastic systems, Robust control, Modeling
Abstract: Technical trading is often based on the idea of predicting trends in prices. However, these predictions are problematic for several reasons, e.g., regime breaks over time. In control theory, there is another approach that treats markets as machines and regulates them. The presumably best understood one of these feedback-based trading rules is the so-called Simultaneously Long Short (SLS) strategy. This strategy invests equally long and short at the beginning and shifts more and more investment to the better performing side according to affine linear feedback schemes. Due to this feedback loop, it is possible that the SLS rule adapts to regime breaks. Under specific assumptions, in theory as well as in backtests, notable results could be achieved for the SLS strategy. For implementations it is important that questions concerning the choice of the parameters and - highly interlinked - the risk associated with the SLS rule are considered. In this paper we derive for relatively general market models, which are based on semimartingales with time-varying parameters, a closed-form formula for the skewness of the distribution of the gain of the SLS strategy as a function of market and control parameters. Since the skewness can be seen as both a risk indicator (but not as a risk measure) and a property some traders might prefer, this formula can be used to choose the feedback parameters according to mean-variance-skewness considerations, thus, helping traders to meet their idiosyncratic risk aversions or preferences.

Keywords: IVHS, Stochastic systems, Autonomous systems
Abstract: We investigate the coordination of autonomous vehicles (AVs) and intelligent human vehicles (IHVs) for merging on a two-lane road. An IHV is equipped with an automated system with advisory directives to the human driver to optimize its maneuver while communicating and collaborating with other vehicles. For optimal coordination of the two vehicles, modeling and incorporating stochasticity of the human driver's actions in the IHV is important. We introduce a method of cooperative driving that considers multiple stochastic human parameters in the IHV, such as human intent and human input transitions. We also model the system to account for computational delays and the driver's ability to follow advisory directives. The coordination actions for the AV and the IHV are generated in a stochastic model predictive control (sMPC) framework. Using simulated results, we demonstrate that the model considering stochastic effects of the human driver's actions performs better and can mitigate the effect due to the driver's inattentiveness while merging.

Keywords: Reduced order modeling, Computational methods, Large-scale systems
Abstract: In this work, we detail a procedure to construct a reduced order model on the basis of frequency-domain data, that preserves the non-strictly passive property and the port-Hamiltonian structure. The proposed scheme is based on Benner et al. contribution, which has been adapted to handle (i) non-strictly passive model, and (ii) to handle numerical issues observed when applying the Loewner framework on complex configurations. We validate the proposed scheme on a very complex two-dimensional wave equation, for which the discretized version preserves the port-Hamiltoninan form.

Keywords: Model/Controller reduction, Reduced order modeling, Linear systems
Abstract: In this paper, moment matching-based loop shaping design for finite-dimensional linear systems is considered. First, the time-domain moment matching model reduction problem with complex-conjugated pole-zero placement is revisited. We explicitly calculate the free parameters such that the reduced order model, achieving moment-matching at complex-conjugated interpolation points, has pairs of complex-conjugated poles and zeros placed in desired locations. Then, we recast the problem of closed-loop pole placement in terms of moment-matching, with the moments equal to -1 and 0, respectively. Consequently, the free parameters of a model achieving both moment matching at complex-conjugated points and closed-loop pole placement at prescribed locations are determined. Furthermore, we combine the classical loop shaping method with closed-loop pole placement via moment matching to design a robust controller for stable, minimum-phase systems. We illustrate the proposed moment matching-based loop shaping approach on a benchmark example.

Keywords: Model/Controller reduction, Reduced order modeling, Linear systems
Abstract: Time-domain moment matching-based model order reduction is an efficient technique that provides a family of parametrized reduced order models with identical moments evaluated in a set of points. The free parameters provide flexibility to impose additional constraints such as stability, passivity, and derivative matching. In this paper, for a single-input and single-output linear time-invariant system, we consider the problem of constructing a reduced-order model by balanced truncation via moment matching. We show that there exists an exo-system yielding a reduced order model with a desired controllability Gramian. Similarly, an exo-system of dual moment matching provides a reduced order model with a desired observability Gramian. Therefore, combining the two moment matching methods yields a reduced order model by balanced truncation, opening a door to achieve model reduction by balanced truncation via moment matching.

Keywords: Reduced order modeling, Model/Controller reduction, Differential algebraic systems
Abstract: We provide an enhancement of the notion of time-domain moments for systems of nonlinear differential-algebraic equations possessing feedforward terms. Following this, a parameterized family of systems achieving moment matching is given and, under mild conditions, it is shown that this family parameterizes all systems achieving moment matching and having dimension at least as large as that of the signal generator. Finally, we provide a demonstrative example in which a reduced order model achieving moment matching is dynamically extended in order to provide a more accurate approximation of the transient output response of the original system.

Keywords: Flexible structures, Reduced order modeling, Model/Controller reduction
Abstract: The paper develops the Loewner approach for data-based modeling of a linear distributed-parameter system. This approach is applied to a controlled flexible beam model coupled with a spring-mass system. The original dynamical system is described by the Euler-Bernoulli partial differential equation with the interface conditions due to the oscillations of the lumped part. The transfer function of this model is computed analytically, and its sampled values are then used for the data-driven design of a reduced model. A family of approximate realizations of the corresponding input-output map is constructed within the Loewner framework. It is shown that the proposed finite-dimensional approximations are able to capture the key properties of the original dynamics over a given range of observed frequencies. The robustness of the method to noisy data is also investigated.

Keywords: Aerospace, Identification for control, H2/H-infinity methods
Abstract: This paper deals with the suppression of flutter -- a type of dynamic instability provoked by the interaction of aerodynamic, inertial, and flexible forces acting over a flexible structure immersed in a fluid -- through robust control methods. Since this problem is heavily dependent on flight conditions (such as altitude, speed, etc), an accurate controller synthesis requires a representative model. The Loewner framework offers tools for the generalized realization problem, allowing the construction of such a model using sampled frequency data responses and simple algebraic machinery. This tool helps build a parametric model of an aeroelastic system used then to synthesize a scheduled, dynamic output-feedback robust control law that damps the flexible mode responsible for the appearance of flutter.

Keywords: Automotive, Predictive control for nonlinear systems, Robotics
Abstract: In recent years, nonlinear model predictive control (NMPC) has been extensively used for solving automotive motion control and planning tasks. In order to formulate the NMPC problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the NMPC related optimization problem, involving a Cartesian and a Frenet coordinate frame (CCF/ FCF) in a single nonlinear program. We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints. With this approach, we exploit the simpler formulation of opponent vehicle constrains in the CCF, as well as road aligned costs and constraints related to the FCF. Comparisons to other approaches from literature in a simulation framework highlight the advantages of the proposed approaches.

Keywords: Predictive control for nonlinear systems, Robust control
Abstract: This work proposes a robust data-driven predictive control approach for unknown nonlinear systems in the presence of bounded process and measurement noise. Data-driven reachable sets are employed for the controller design instead of using an explicit nonlinear system model. Although the process and measurement noise are bounded, the statistical properties of the noise are not required to be known. By using the past noisy input-output data in the learning phase, we propose a novel method to over-approximate reachable sets of an unknown nonlinear system. Then, we propose a data-driven predictive control approach to compute safe and robust control policies from noisy online data. The constraints are guaranteed in the control phase with robust safety margins through the effective use of the predicted output reachable set obtained in the learning phase. Finally, a numerical example validates the efficacy of the proposed approach and demonstrates comparable performance with a model-based predictive control approach.

Keywords: Automotive, Predictive control for nonlinear systems, Optimal control
Abstract: This paper is presenting the implementation of an Adaptive Cruise Control (ACC) functionality built up on a Model Predictive Path Following Controller (MPFC). The solution is focusing on safety, comfort, efficiency, and tracking of the car ahead. Based on formulations for the expected behavior and the possible states that can be used, a concept for extending the cost function of an MPFC to react on vehicles ahead is shown. Furthermore, this novel approach is using a reference velocity trajectory for safety reasons and smooth minimum functions to form the distance and velocity error values. Simulations of different scenarios validate the performance of the proposal in specified test cases.

Keywords: Optimal control, Predictive control for nonlinear systems, Autonomous systems
Abstract: In this article the development of an optimal controller for a special type of tractor, commonly referred to as gantry tractor, is presented. A Model Predictive Controller (MPC) based on a single track model controls the global kinematic behavior of the tractor. The formulation of the optimal control problem aims at guaranteeing an extremely accurate path tracking. In a subsequent step, the controls for the individual four wheels are calculated following a no-slip hypothesis. A high frequency controller corrects the lateral behavior of the vehicle to ensure higher tracking accuracy. The performance of the MPC is compared to that of a pure pursuit controller in terms of their respective tracking accuracy.

Keywords: Predictive control for nonlinear systems, Iterative learning control, Automotive
Abstract: This paper presents an Adaptive Model Predictive Controller (AMPC) for vehicle trajectory tracking. The general goal is to adapt the vehicle model’s yaw intensification, to compensate for lost tracking accuracy caused by model errors and condition changes. The approach combines a classic Model Predictive Controller (MPC) with an online learning algorithm based on a trajectory-dynamic lookup table. This lookup table is updated periodically according to the trajectory dynamics and the tracking performance of the controller. In contrast to current research, the proposed AMPC is able to adapt repeatedly to condition changes and transfer learned behavior to unknown trajectories. The feasibility of this approach is evaluated via simulation experiments in CarMaker and Matlab/Simulink on several closed loop circuits with additional weight to emulate condition changes.

Keywords: Robotics, Optimal control, Autonomous robots
Abstract: Model Predictive Control (MPC) has been increasingly adopted in robotics in recent years for several tasks including the real-time control of mobile robots. The main advantage of using the MPC is the possibility of adopting an optimal control policy under a set of constraints which can be used to enforce safety, like collision-free manoeuvres. In literature a well-known approach to ensure real-time collision avoidance for multi-agent systems is the Velocity Obstacle (VO) paradigm which considers the robot as a point-mass, neglecting its dynamic and kinematic constraints. In this paper, we propose an MPC-based motion planning solution that directly considers the dynamics and the kinematics of the mobile robots, exploiting the VO as a constraint on the configuration space of the controlled system. We evaluated the proposed solution in simulation using holonomic and non-holonomic kinematic and dynamic models.

Keywords: Identification, Randomized algorithms, Identification for control
Abstract: In this article, a randomized subspace identification (RandSID) method for estimating combined deterministic-stochastic LTI state-space models corresponding to large input-output data is proposed. The main computational burden in conventional subspace methods is due to QR factorization and Singular Value Decomposition (SVD) of various matrices composed of recordings of system inputs and outputs. In the proposed method, these data matrices are first compressed by multiplying with an appropriately sized random matrix. It is shown that the system parameters can be equivalently identified, with no significant degradation in accuracy, by performing the QR and SVD steps on these compressed (smaller) matrices instead of the original ones. Due to this data compression step, the proposed algorithm is significantly faster as compared to conventional methods. The advantages of this method, in terms of computation complexity, are theoretically computed and also demonstrated numerically via various case studies.

Keywords: Optimization algorithms, Modeling, Identification
Abstract: We consider the problem of parameters estimation in the situation where a subset of parameters of the underlying model has already been estimated. Potential errors in the pre-estimated parameters limit the accuracy in the computation of the still unknown parameters in a way that crucially depends on the symmetries of the data set. In this article, we develop an optimization approach that minimizes the sensitivity to errors in the determination of parameters by determining optimal weights that depend on both the model and the input data in the situation where the data are incomplete. We apply the method to the problem of calibrating the sensor positions in an array of magnetometers whose scale factors and biases have been estimated beforehand.

Keywords: Process control, Chemical process control, Identification for control
Abstract: In continuous process plants controlled by model predictive control, model-plant mismatch (MPM), due to the aging of processes, causes degradation of control performance. We propose a concept called Model Life Extension (MLE) and its implementation to mitigate this degradation in a non-invasive manner. The purpose of MLE is to continually update (re-identify) process models by using routine operating data on the assumption that the timescale of aging is much larger than the interval of excitation of reference signals. We implemented MLE by estimating MPM via L1 regularized regression and by finding an optimal regularization parameter via cross-validation and showed through numerical experiments that an optimal parameter can exist and be found by cross-validation for a pilot-scale distillation column. We then constructed the updated model based on the found parameter to demonstrate the possibility of correcting static-gain mismatch and transport-delay mismatch without injecting excitation signals to process inputs.

Keywords: Identification, Linear systems, Optimization
Abstract: This paper considers the realization of discrete-time linear time-invariant dynamical systems using input-output data. Starting from a generalized state-space representation that accounts for static offsets, a state-independent system representation is derived using the Cayley-Hamilton theorem and characteristic parameters are introduced to describe the system dynamics in an alternative way. Given input-output data, we present two formulations to address model deviations and to identify characteristic parameters by minimizing considered error terms in a least squares sense. The applicability of the proposed subspace identification method is demonstrated with physical data of the identification database DaISy.

Keywords: Nonlinear system identification, Identification, Identification for control
Abstract: The article deals with the non-linear identification using a block structure to reproduce the behavior of a unknown non-linear system which presents two equilibria: a static equilibrium point, which is in our case unstable, and a dynamic equilibrium, which can correspond, for example, to a Limit Cycle Oscillation (LCO). This non-linear system is representative of a supercritical model which appears in the Hopf bifurcation. The generic proposed methodology is based on three identification steps: firstly the linear identification of the static equilibrium, called the fixed point, secondly, the identification of a Wiener feedback structure to reproduce the LCO, and lastly the tuning of a Wiener-Hammerstein feedback structure to improve the accuracy level of the identified non-linear model. Finally, time-domain simulations are performed to evaluate and compare results with the original non-linear system.

Keywords: Identification for control, Adaptive systems, Optimal control
Abstract: Model predictive control (MPC) for buildings finds an increasing interest in research with mostly thermal models being investigated. There are, however, buildings with internal vapor loads, where humidity is a dominating factor for control of heating, ventilation and air conditioning (HVAC). In this paper, data-based hygrothermal models of an aquaculture hall and its HVAC-unit are investigated using real-life data from over six months. In a forward selection needed model complexity is investigated. A model is selected that shows average model deviations of around 0.5 ℃ and 1.4 % for temperature and relative humidity (RH) in the validation period of two weeks. Over longer periods, the selected model shows drift. Implementing an extended Kalman filter (EKF) for adaptive modeling enabled 24 hour predictions with average model deviations of around 0.5 ℃ and 1.8 % over the whole time period. To support future research, the model and the underlying dataset is shared publicly.

Keywords: Aerospace, Computational methods, UAV's
Abstract: Being a fully algorithmic procedure, symbolic controller synthesis offers weighty advantages over other established synthesis procedures. In fact, the returned controllers provably enforce the given specification to the control loop making verification steps obsolete. However, the curse-of-dimensionality prevents this scheme to be applied to industrial problems. Applications to real experiments are indeed rare. In this note, we demonstrate how to utilize symbolic optimal control in order to control miniature quadcopters on the level of mission guidance. Specifically, a firefighting scenario using a Crazyflie 2.1 drone is considered, which involves reach-avoid and reach-and-stay control tasks. Furthermore, we present a runtime monitor, automatically derived from the synthesized symbolic controller. Based on the methodologies of plan recognition, this monitor is observing the drone’s flightpath and infers the current controller mode. Thus, it is able to predict the upcoming manoeuvres of the drone.

Keywords: Aerospace, Machine learning, Optimization
Abstract: An optimal gain prediction method is proposed for VTOL aircraft controllers. The proposed method exploits parameterized convexity to quickly and reliably predict the optimal gain for a given initial state. The parameterized convexity is secured by using the parameterized log-sum-exp (PLSE) network, which is a shape-preserving universal approximator for parameterized convex continuous functions. A PLSE network is trained in the sense of supervised learning to approximate the cost function of initial state and gain. For a given initial state, the optimal gain is predicted by convex optimization. The result of numerical simulation demonstrates that the proposed method can perform real-time optimal gain prediction and outperforms compared to other network or ad-hoc approaches for the attitude and altitude control of VTOL aircraft.

Keywords: Aerospace, Military applications
Abstract: An explicit midcourse guidance law is proposed for a multi-stage antiballistic missile with solid propellant. The powered explicit guidance scheme is modified to consider the ballistic missile intercept mission with the solid propellant. The solid propellant propulsion system does not have cutoff capability, which can only consider the fixed burnout time. In this study, the modified powered explicit guidance algorithm is modified to satisfy the desired position and velocity direction constraints. By appropriately selecting the predicted intercept point based on target ballistic missile dynamics, the desired position and velocity can be determined. The modified algorithm is based on the optimal control theory to minimize the final flight time, which does not require an iterative computation along with the velocity increment at the cutoff time. Numerical simulation is performed to demonstrate the effectiveness of the proposed method for a three-dimensional multi-stage antiballistic missile.

Keywords: Aerospace, Reduced order modeling, Identification
Abstract: This article deals with the damping estimation of a single mode for multiple-input–multiple-output high-order linear time-invariant systems. The mode of interest is isolated by an optimal blending of the input and output vectors. Since the blended model appears similar to a single-input-single-output second order system, we propose a dynamic observer aiming at the damping estimation of such a reduced-order model. Applying the interconnection and damping assignment passivity-based observer technique for the design, the asymptotic convergence of the observer is shown using the LaSalle's invariance principle. Finally, the damping estimator is illustrated through numerical simulations of a generic flexible aircraft model obtained from frequency samples provided by AIRBUS.

Keywords: Modeling, Aerospace
Abstract: Shimmy is an oscillatory behavior that causes various accidents and malfunctions in the nose landing gear. This study has proposed a control method based on gamma stability due to damping the shimmy via the PIR (Proportional-Integral-Retarded) controller. Hence, we introduced various initial studies and results about the controller parameters. The simulations and performance analysis also assess the PIR approach. Lastly, the PIR form displays a thriving performance in shimmy damping.

Keywords: Predictive control for nonlinear systems, Output feedback, Robust control
Abstract: Autonomous navigation around minor bodies is a challenging technology to be developed in order to increase the efficiency and science return of space exploration missions. Addressing the challenge, we propose a robust Guidance, Navigation and Control(GNC) system in the loop for circumnavigation around small Asteroids. A neural network-based method is utilised to provide a monocular optical navigation solution. The Guidance and Control (G&C) system is based upon Output-feedback Tube Model Predictive Control (OTMPC), giving a robust guidance planning and control assessment under the estimation uncertainties from the navigation system (the aforementioned neural network-based method, trained for the asteroid Bennu, named Bennunet). The OTMPC is reduced to solving a single quadratic optimization problem at each control assessment iteration, and, when combined with Bennunet, gives a computationally efficient GNC scheme applicable for deep-space probes and missions. The GNC system is demonstrated in the environment of the asteroid Bennu, where a spacecraft performs circumnavigation, a challenging nonconvex scenario.

Keywords: Mechatronics, Optimization, Process control
Abstract: This paper aims to design the optimal sliding mode and super twisting sliding mode controllers for the nonlinear Shape Memory Alloy (SMA) wire actuators. The parameters of the proposed controllers are optimally tuned using the metaheuristic Grey Wolf Optimizer algorithm and a comparative analysis is carried out. All control structures are validated by simulations using an accurate evolved Takagi-Sugeno-Kang fuzzy model of SMA wire actuators and their control performance is evaluated.

Keywords: Feedback linearization
Abstract: An innovative fuzzy discrete control technique is presented in this paper. An analytical discrete tracking control strategy offering high dynamic efficiency is developed using the gain scheduling methodology combined with the feedback linearization theory. For the stability analysis study, an enlarged basin of attraction around operating points is estimated using a non-Lyapunov method. In order to ensure a high trajectory tracking accuracy with specified dynamics, a numerical approach is implemented with the use of fuzzy logic reasoning. While

optimizing the running time of the designed algorithm, the control strategy is shown to be easy to implement. As a result, the trajectory tracking objective is achieved with satisfactory

dynamic characteristics. Through numerical simulation analysis, the efficiency of the designed strategy is established.

Keywords: Markov processes, Output feedback, Lyapunov methods
Abstract: In this paper, we discuss the problem of resiliente observer-based control for a class of nonlinear discrete-time singular Markovian jump systems (DSMJSs) with uncertainty. It consists of the following main features: (i) it involves the design of an observer to estimate the unmeasured states of the system (ii) Observer and controller uncertainties are introduced and sufficien tcondition sare derived so that the resulting closed-loop system may be robust and stochastically admissible. To conclude, simulations on a DC motor system are presented to demonstrate potential applications as well as verify the effectiveness of the scheme proposed.

Keywords: Emerging control applications, Delay systems, Linear systems
Abstract: It was recently demonstrated that the Harmonic Control Array (HCA) method is a successful control strategy for systems with periodic references or disturbances. To construct the required control signal to achieve zero steady-state error, the HCA appropriately modifies the complex levels of the harmonic components of the system input. In a real-time application, a discrete-time implementation is required for the method to be applied through a digital device since the signals and parameters involved are complex-valued. An efficient MATLAB/Simulink modeling of HCAs is explained step-by-step in this paper with an implementation on a typical test system. Then, the HCA performance is compared with an internal model control application on a hot rolling mill process.

Keywords: Optimization, Adaptive control, Electrical power systems
Abstract: In this paper, we propose a novel approach to minimize the effects of small duty cycle perturbations, due to extremum seeking control (ESC), on the output current of a photovoltaic (PV) cell array connected to the electrical grid. Specifically, we formulate a bilevel optimization problem that incorporates the power maximization objective together with a current quality objective. Next, by means of monotone operator theory, we show how to solve the problem via optimized ESC. Finally, we test the effectiveness of the proposed approach on a numerical simulation example.

Keywords: Fault detection and identification, Identification, Network analysis and control
Abstract: The reconstruction problem is an inverse problem and, in general, has no unique solution. We consider the problem of reconstructing all possible topologies with their edge resistance values of an unknown circular planar passive resistive network, whose response matrix is known apriori. The response matrix is used to deduce a set of all possible connections (such as 1-connection, 2-connection,. . ., k-connection [6]) in the unknown circular planar network. Since number of such connections are large, a reduced set of connections is derived. For each connection in reduced connection set, we generate all possible path permutations along with there graph representations. The graph representations of all path permutations are used to generate several candidate planar graphs using union and edge deletion operations. A method is proposed wherein, the candidate planar graphs are posed as a set of non-linear multivariate polynomials. We then use the Gr¨obner basis to simultaneously reconstruct all possible topologies and the edge resistance values of an electrical network enclosed inside a black box. Numerical simulation establishes the effectiveness of the proposed strategy.

Keywords: Emerging control applications, Autonomous systems, Cooperative control
Abstract: This paper proposes a new formation tracking and containment control methodology for multi-agent systems using Negative Imaginary (NI) systems theory. The proposed control scheme consists of a two-loop configuration in which the inner loop applies an appropriate feedback linearising control law to transform the nonlinear dynamics of each agent into a double integrator system, while the outer loop deploys an NI-based formation tracking and containment control protocol on the linearised double integrator agents. This methodology utilises the characteristic loci technique rather than the well-known Lyapunov-based approaches to establish the asymptotic convergence of the formation and containment trajectory tracking errors. Compared to existing methods, the proposed scheme gives more freedom to select a dynamic controller and relies only on output feedback. As a result, it offers better formation tracking and containment performance and advantages when full-state measurements are unavailable. Finally, a real-time flight experiment was conducted on networked Crazyflie quadcopters to examine the control performance in both healthy and faulty (e.g. a sudden loss of agents, communication failure, hardware faults, etc.) operating conditions.

Keywords: Linear systems, Identification, Stability of linear systems
Abstract: In this paper, we consider the problem of robust stabilization of linear time-invariant systems with respect to unmodeled dynamics and structure uncertainties. To that end, we first present a methodology to find the nearest negative imaginary system for a given non- negative imaginary system. Then, we employ this result to construct a near optimal linear quadratic Gaussian controller achieving desired performance measures. The problem is formulated using port-Hamiltonian method and the required conditions are defined in terms of linear matrix inequalities. The technique is presented using fast gradient method to solve the problem systematically. The designed controller satisfies a negative imaginary property and guarantees a robust feedback loop. The effectiveness of the approach is demonstrated by simulation on a numerical example

Keywords: Robust control, Stability of linear systems
Abstract: Rate limitation on the control input is ubiquitous in numerous mechanical actuators and demands special care in control systems design. Since several mechanical systems are known to satisfy negative imaginary (NI) system properties, this paper addresses the problem of finding suitable strictly negative imaginary (SNI) controllers for robustly stabilizing such linear time-invariant (LTI) NI plants, with no pole at origin, constrained by rate-limited actuation. The proposed design method relies on a dissipative characterization of NI systems and on a particular structure of a stabilizing SNI controller to effectively address the input rate constraint. It is shown that the stabilizing controller can be represented as an interconnection of an integrator preceded by strictly positive real (SPR) dynamics in the forward path and a positive definite gain matrix in negative feedback. This parameterization facilitates synthesis of SNI controllers guaranteeing rate-bounded control. In addition to satisfying the DC gain condition for closed-loop stability, a suitable design of the positive definite matrix, a part of the controller, ensures the magnitude shaping of the control input and impacts the closed-loop control performance. Moreover, by employing the existing technique of dynamical forward action to make a system NI, the proposed framework can be extended to design robust controllers for a larger family of non-NI systems with rate limits as well. The results are demonstrated through numerical examples.

Keywords: Emerging control applications, Cooperative control, Autonomous systems
Abstract: This paper develops a cooperative controller for a fleet of multi-tilt tricopter drones modelled as Negative Imaginary (NI) systems via closed-loop linearisation exploiting Sliding-Mode Control (SMC) technique. The multi-tilt tricopter model is derived from the first principles, and the SMC method is invoked to obtain a closed-loop linear model of the tricopter plant with six outputs and six inputs. A subspace-based system identification algorithm is developed to identify the linearised drone model enforcing the NI property. The primary control objective is to design a distributed `mixed' NI and strictly Passive control protocol so that the tricopter agents asymptotically reach the desired formation and keep tracking the target. Instead of the Lyapunov approach, the characteristic loci method is used to prove the asymptotic convergence of the trajectory tracking error. Finally, an exhaustive simulation case study is carried out on a fleet of six multi-tilt tricopter drones to demonstrate the feasibility of the cooperative controller presented in this work.

Keywords: Emerging control theory, Robust control, Stability of linear systems
Abstract: This brief addresses the frequency-domain dissipativity problem of a broader class of Output Negative Imaginary systems, termed as the time-domain ONI (or TD-ONI) systems, which have been defined in the time domain w.r.t. an abstract energy supply rate function. This definition encompasses the existing strict/non-strict NI subsets, including those having imaginary-axis poles. This paper introduces the idea of a "shifted (Q_{sigma}(omega), S_{sigma}(omega), R_{sigma}(omega))-dissipativity", as an alternative to the conventional (Q(omega), S(omega), R(omega))-dissipativity, to capture the TD-ONI systems, particularly the ones having imaginary-axis poles. The shifted (Q_{sigma}(omega), S_{sigma}(omega), R_{sigma}(omega))-dissipativity is defined w.r.t. a shifted imaginary axis (sigma + jomega, ; sigma > 0) and thereby, it overcomes the limitation of earlier frequency-domain dissipative frameworks to capture systems with imaginary-axis poles. The paper has also established the relationship between the time-domain and frequency-domain dissipativity of TD-ONI systems. Finally, a closed-loop stability theorem is also given for a positive feedback interconnection of two TD-ONI systems.

Keywords: Linear systems
Abstract: This paper studies the operator-valued irrational complex symmetric negative imaginary (CSNI) systems. The complex symmetric negative imaginary function is defined using the complex symmetric operator. In this case, a matrix-valued symmetric negative imaginary transfer function G(s):mathbb{C}longrightarrow mathbb{C}^{mtimes m} is identical to an operator-valued CSNI transfer function defined on a finite dimensional Hilbert space. A necessary and sufficient condition for operator-valued CSNI transfer functions is given by using the frequency-domain properties. A specific illustration of an operator-valued CSNI function is shown.

Keywords: Biomedical systems, Modeling, Optimization
Abstract: Mathematical models of cancer growth and evolution of cancer cell characteristics, aka phenotypes, together with optimisation and optimal control methods to contain them, in the framework of adaptive dynamics of cell populations, are presented, that take into ac- count the heterogeneity of cancer cell populations, i.e., their biological variability, and their intrinsic plasticity, i.e., their nongenetic instability that allows them to quickly adapt to changing environments. The presented vision of the cancer disease, which is specific to multicellular organisms, relies on a relatively novel vision, consistent with a billion-year evolutionary perspective. Based on recent contributions from philosophy of cancer, these mathematical models aim at designing theoretical therapeutic strategies to simultaneously contain tumour progression and limit adverse events of drugs to healthy cell populations.

Keywords: Biomedical systems, Modeling, Optimization
Abstract: Blood cell formation (hematopoiesis) is a paradigmatic example of tissue homeostasis and regeneration. It is driven by hematopoietic stem cells (HSCs). To adapt the blood cell production to the current need of the organism, the hematopoietic system is subjected to complex non-linear control loops. Stem cell function (proliferation, self-renewal, differentiation) is dependent on and regulated by the micro-environment, the so-called stem cell niche. Without close contact to the niche HSCs lose their stem cell phenotype. This is exploited by blood cancer cells which out-compete healthy hematopoiesis. Acute myeloid leukemia (AML) is a malignancy of the hematopoietic system and belongs to the most aggressive cancers. All malignant cells are derived from a small population of leukemic stem cells (LSCs) which resist to treatment. Recent findings suggest that LSCs invade the hematopoietic stem cell niche where they expand at the expense of HSCs. This results in life-threatening symptoms due to impaired healthy blood cell production. Due to its limited experimental accessibility the role of the human stem cell niche in AML is not well understood. We propose different nonlinear ordinary differential equation models of the stem cell niche. The models account for important processes such as proliferation, self-renewal and differentiation of stem cells, attachment and detachment of stem cells to the niche and competition of HSCs and LSCs for spaces in the stem cell niche. We use model analysis, computer simulations and clinical data to provide insights in the following questions: Which mechanisms allow malignant stem cells to expand at the expense of healthy stem cells ? What are potential targets for AML therapy? How do processes in the stem cell niche impact on disease progression ? Which clinically accessible parameters can be used to infer the malignant cell burden in the stem cell niche? How does chemotherapy interfere with the stem cell niche?

Keywords: Biological systems, Modeling, Optimization
Abstract: Cancers are heterogeneous diseases, notably in terms of development times. While some malignancies arise and develop quickly, others might take decades. Myeloproliferative Neoplasms (MPNs) belong to the latter. MPNs are hematological malignancies due to the acquisition of a driver mutation in hematopoietic stem cells. While MPNs are often detec- ted at advanced ages (about 65-70), it has recently been shown that the driver mutations might have been acquired decades before the disease onset and potentially during fetal life. A slow development for cancer gives the opportunity to intercept it early and further control its development using adequate treatments. In this tutorial, we present a mathematical methodology to estimate the optimal age at which the population should be tested for a particular mutation. Here, we focus on the case of the two most prevalent MPN driver mutations, for which we recently published the results of our methods (Hermange et al. PNAS, 2022). Yet, the methodology might be generalized to other driver mutations of slowly developing cancers. Our mathematical methodology is based on different steps that we will detail in the tutorial : 1) Construct a mathematical model of the mutation acquisition and the subsequent cancer development, 2) Infer the model parameters using a likelihood-free method, namely ABC-SMC, 3) Validate the robustness of the results using a leave-one-out method, and evaluate the capacity to predict the disease onset for a new patient, 4) Use the calibrated and validated model to estimate the optimal age at which early screening should be done. This talk addresses the thematics of stochastic models, Bayesian inference, numerical computation, model validation, and uncertainty propagation.

Keywords: Biological systems, Modeling, Optimization
Abstract: Medical research is looking for new combined targeted therapies against cancer. Hematopoiesis provides a paradigm for studying all the mammalian stem cells, as well as all the mechanisms involved in the cell cycle. In this talk we address multiple issues related to the modeling and analysis of the cell cycle, with particular insights into the hematopoietic systems. Stability features of some classical models are highlighted, since systems trajectories reflect the most prominent healthy or unhealthy behaviors of the biological process under study. We perform stability analysis of systems describing healthy and unhealthy situations, with a particular interest in the case of acute myeloblastic leukemia (AML). We pursue the objectives of understanding the interactions between the various parameters and functions involved in the mechanisms of interest. For that purpose, an advanced stability analysis of the cell fate in treated or untreated leukemia is performed in several modeling frameworks, in order to suggest new anti-leukemic combined chemotherapy. In this talk, we cover many biological evidences that are currently undergoing intensive biological research, such as: cell plasticity, mutations accumulation, cohabitation between ordinary and mutated cells, control or eradication of cancer cells, cancer dormancy, etc. An age-structured model describing the coexistence between cancer and ordinary stem cells is also discussed. This model is transformed into a nonlinear time-delay system that describes the dynamics of healthy cells, coupled to a nonlinear differential-difference system governing the dynamics of unhealthy cells. We pursue an analysis that provides a theoretical treatment framework following different medical orientations.

Keywords: Biological systems, Modeling, Optimization
Abstract: The region of attraction (RoA) of a dynamical system is the set of initial conditions for which there exist a control such that the states are driven to a stable equilibrium. In the context of cancer treatments, this set represents the set of initial health indicators (tumor volume, immune cells density..) for which there exist a treatment protocol such that the pa- tient is healed. Therefore, the determination of such sets is interesting for tumor dynamics. The complexity of determination of RoAs rises when considering stochastic uncertainties. The latter being important to consider, since cancer systems are known to be highly uncer- tain. Some frameworks that have already been proposed in the literature can be adapted to the problem of RoA estimation under stochastic uncertainties, such as polynomial optimi- zation and probabilistic certification. This presentation will address the problem of RoA estimation in the presence of parametric uncertainties using different frameworks, by fo- cusing on validated mathematical models describing tumor immune dynamics, in presence of chemotherapy and immunotherapy.

Keywords: Machine learning, Intelligent systems
Abstract: Powered by advances in deep neural networks, reinforcement learning (RL) has made great strides in the past decade, and its impact in control is increasingly being felt. This talk will begin by introducing the RL framework and some key algorithms. Afterwards, some recent applications of RL in active robotic mapping will be presented, in which the robot is controlled so as to obtain information about the map as quickly as possible. The map is represented either as an occupancy grid or a function defined over the robot’s operating area. A simpler variation of such a technique that only aims to find the maximum of the function will allow analysis of the convergence rate to the optimum. Time permitting, the talk will conclude with a model-based, planning framework counterpart for RL, with strong converge nce guarantees to the optimal control of general nonlinear systems with general costs.

Keywords: Neural networks, Servo control
Abstract: Currently, there is a growing interest in merging physics–based models and artificial intelligence to increase control performance for systems with complex dynamics. In this talk we will present a systematic method for embedding a known (or identified) physical model within a neural network and we will provide regularized training cost functions that address two key issues: competition among black-box and physics-based neural network layers, and robustness to non-training data. We will show that the developed physics-based neural networks (PNNs) model class is able to achieve improved accuracy with the same reliability as physical models. The relation of PNNs with physics-informed neural networks will also be discussed. To demonstrate the impact of PNNs on control performance, we will consider the problem of feedforward control design for precision motion control. Experimental results will be shown for two real-life applications: a coreless linear motor used in lithography machines and a hybrid stepper motor used in industrial printing machines. Such applications are indeed characterized by known physics-based motion dynamics and complex, partially unknown dynamics, e.g., due to electromagnetic forces or nonlinear friction. The PNN-based feedforward controllers achieve a factor 2 improvement with respect to conventional industrial feedforward controllers, while their design and tuning can be largely automated.

Keywords: Constrained control, Emerging control theory
Abstract: Constraints handling and uncertainty characterization for dynamical systems represent a continuous interest in the control literature. In the first part of this talk, classic definitions of constraint satisfaction and set invariance will be reviewed, pointing to the latest developments with respect to some specific classes of dynamics as for example the time-delay ones. In the second part of the talk, the aim is to go beyond the rigid concepts by characterizing the intermittent constraint satisfaction along the evolution of the trajectories of a dynamical system. Two relaxed notions are introduced in this sense, one characterizing the validation of constraints within a given finite window and the other imposing the validation after a fixed number of time-steps following a violation. The constraint satisfaction with respect to a trajectory will then be extended to a set of constraints and tubes of trajectories. It is shown that all these notions can be accordingly anchored to the well-known positive set invariance thus offering a generalized framework for the analysis of dynamical systems in a set-theoretic framework.

Keywords: Computational methods, Large-scale systems, Fluid flow systems
Abstract: In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method solves a reduced order linear system in order to compute the Newton step. This reduced system is derived using a projection matrix, obtained using proper orthogonal decomposition, which is updated in each time step of the numerical method. We demonstrate that the method can be used together with Euler's implicit method to simulate CO2 injection into an oil reservoir, and we compare with using Newton's method. The Newton-like method achieves a speedup of between 39% and 84% for systems with between 4,800 and 52,800 state variables.

Keywords: Computational methods, Linear systems
Abstract: Motivated by the distance to uncontrollability problem, we define a distance between finite-length linear time-invariant systems. The method proposed in this paper for computing the distance exploits the principal angles associated with structured matrices representing the systems.

Keywords: Fault detection and identification, Linear parameter-varying systems, Uncertain systems
Abstract: In this work, a novel and simple technique to detect the formation of frost in a commercial refrigerator evaporator is presented. The technique relies on the change of the dynamic behaviour of the valve opening to evaporator outlet temperature, which in turn effectively modifies the corresponding transfer function and can be easily implemented without additional hardware on the controlling unit.

Keywords: Optimal control, Modeling
Abstract: Efficiently solving optimal control problems (OCP) is a prerequisite for using methods such as model predictive control (MPC) for real-time control of complex robotic systems. For many applications, it is mandatory to guarantee that the OCP solutions correspond to collision-free motions. However, establishing appropriate constraints for OCP is not straightforward. A main reason is that the function determining the Euclidean distance between two arbitrary convex shapes is often non-differentiable and non-convex. Moreover, this function can generally only be defined implicitly, for example, by an optimization problem. Recently, it was proposed to derive collision constraints by utilizing duality theory of convex optimization as the resulting constraints are differentiable and allow to check the exact distance between arbitrary compact convex sets. These constraints naturally depend on the chosen representation of the sets for which collision avoidance should be established. In this paper, we show that the computational effort of solving OCP including the proposed constraints can be reduced by explicitly considering the type of sets involved and choosing their representation properly. To this end, we consider the two prominent cases where collision avoidance has to be established between two polytopic sets or between a polytopic and an ellipsoidal set. The claim that our proposed constraints allow improved computational performance is supported by numerical experiments with a car model.

Keywords: Linear parameter-varying systems, Predictive control for linear systems, Computational methods
Abstract: Missing values in multivariate time series introduces challenges when conducting different activities, such as data processing or analysis. Numerous methods have been developed to address the issue of gap filling, but each of these techniques exhibits shortcomings under different circumstances. This paper proposes a strategy that leverages the interdependencies between the series and employs machine learning algorithms to capture these connections, thereby inferring the missing values within the series. The experimental outcomes illustrate that, provided such interdependencies exist, the proposed solution proves to be a dependable approach to tackle the gap filling problem.

Keywords: Reduced order modeling, Signal processing, Computational methods
Abstract: This paper presents a model reduction approach to find the optimal simulation model in the presence of finite word-length computing. The optimal simulation model refers to a simulation model with minimum errors from modeling and computing. The problem is formulated by putting the computational errors into the dynamics to minimize the output error to the dynamic system one wants to simulate. An algorithm is proposed to find the threshold of the optimal model size at which the total simulation error is minimized. A tensegrity example is studied to demonstrate this approach. Results show that one may intentionally introduce dynamics error for a smaller total simulation error. The proposed algorithm in this paper can also be applied to other high-dimensional dynamical systems to find the optimal model size and the least necessary computing resources.

Keywords: Automotive, Autonomous systems, Optimal control
Abstract: A reference governor approach based on model predictive control (MPC-RG) for an autonomous racing vehicle is developed in this work. This control strategy avoids constraint violations and includes online health management capabilities by solving a multi-objective optimization problem. In this case, a trade-off between the maximization of the state of charge of the battery and the longitudinal velocity, even the minimization of the control actions variation is carried out. In turn, the invariant zonotopic sets analysis ensures the convergence of states to a stable region. On the other hand, the proposed control scheme also combines a robust states feedback linear quadratic regulator (LQR) with a Kalman filter (KF) estimator to compensate for model uncertainty and exogenous disturbances, as well as, to estimate the unmeasured lateral velocity. Moreover, to represent the non-linear behaviour of the vehicle, a data-driven neuro-fuzzy Takagi-Sugeno (TS) model is employed. The developed approach is tested and evaluated in realistic environments by means of a simulated 1/10 Scale RC car.

Keywords: Emerging control applications, Predictive control for nonlinear systems, Transportation systems
Abstract: A critical operational challenge in Mobility-on-demand systems is the problem of imbalance between vehicle supply and passenger demand. However, conventional model-based methods require accurate parametric system models with complex nonlinear dynamics that are non-trivial to build or identify. In this paper, we implement a novel data-enabled predictive control algorithm for empty vehicle rebalancing (DeePC-VR) to instruct the repositioning policy between regions. Constructed by collected historical data from the considered unknown system, a non-parametric representation is used to predict future behavior and obtain optimal control actions, circumventing the costly system modeling process. The effectiveness of the proposed method is verified by an agent-based simulator modeling the real road network of Shenzhen, China. The proposed methods can serve more passengers with less waiting time compared to other policies, improving system efficiency and quality of service.

Keywords: Linear parameter-varying systems, Optimization, Automotive
Abstract: This paper deals with the problem of robust stability analysis of Moving Horizon Estimator~(MHE) for Linear Parameter Varying~(LPV) systems. We introduced novel stability analysis tools which guarantee exponential robust convergence of the MHE under the incremental Exponential Input-Output-to-State Stability~(i-EIOSS) assumption without observability condition. An application of the proposed estimation scheme on a steering-controlled lateral vehicle model is provided to show the effectiveness of the proposed estimation scheme.

Keywords: Machine learning, Agents and autonomous systems, Stochastic systems
Abstract: We study the problem of distributed stochastic multi-arm contextual bandit with unknown contexts, in which M agents work collaboratively to choose optimal actions under the coordination of a central server to minimize the total regret. In our model, an adversary chooses a distribution on the set of possible contexts and the agents observe only the context distribution and the exact context is unknown to the agents. Such a situation arises, for instance, when the context itself is a noisy measurement or based on a prediction mechanism as in weather forecasting or stock market prediction. Our goal is to develop a distributed algorithm that selects a sequence of optimal actions to maximize the cumulative reward. By performing a feature vector transformation and by leveraging the UCB algorithm, we propose a UCB algorithm for stochastic bandits with context distribution and prove the regret and communications bounds for linearly parametrized reward functions. Finally, we validated the performance of our algorithm using synthetic data and real-world Movielens dataset.

Keywords: Predictive control for linear systems, Stochastic control, Stochastic filtering
Abstract: We present an output feedback stochastic model predictive control (SMPC) approach for linear systems subject to Gaussian disturbances and measurement noise and probabilistic constraints on system states and inputs. The presented approach combines a linear Kalman filter for state estimation with an indirect feedback SMPC, which is initialized with a predicted nominal state, while feedback of the current state estimate enters through the objective of the SMPC problem. For this combination, we establish recursive feasibility of the SMPC problem due to the chosen initialization, and closed-loop chance constraint satisfaction thanks to an appropriate tightening of the constraints in the SMPC problem also considering the state estimation uncertainty. Additionally, we show that for specific design choices in the SMPC problem, the unconstrained linear-quadratic-Gaussian (LQG) solution is recovered if it is feasible for a given initial condition and the considered constraints. We demonstrate this fact for a numerical example, and show that the resulting output feedback controller can provide non-conservative constraint satisfaction.

Keywords: Predictive control for nonlinear systems, Neural networks, Robust control
Abstract: This work addresses robust offset-free output constrained Model Predictive Control with a Long Short-Term Memory neural network model. Offset-free tracking of asymptotically constant references is obtained by augmenting the model with a disturbance, to be estimated together with the states of the Long Short-Term Memory network. Then, a constraint tightening based on the observer estimation error and a time variant terminal constraint for the Model Predictive Control optimization are proposed, guaranteeing recursive feasibility and robust satisfaction of the output constraints.

Keywords: Signal processing, Autonomous systems, Stability of nonlinear systems
Abstract: In the present work, we consider a second-order phase-locked loop with a lead-lag loop filter and a piecewise-linear phase detector characteristic. Developing ideas of Charles R. Cahn, we offer an effective analytical-numerical method for determination of the global stability boundary and the pull-in range. Due to piecewise-linearity of the corresponding nonlinear system, we can analytically integrate the trajectories on the linear segments and provide necessary and sufficient conditions of global stability. The results are compared with the Cahn pull-in range estimate, which relies on approximations.

Keywords: Agents networks, Distributed control, Sliding mode control
Abstract: We explore the use of set-valued coupling laws for the design of robust synchronized behaviors in networks of dynamical systems. Under an incremental dissipativity context, it is shown that coupling systems via maximal monotone mappings leads to synchronization that is robust against matched disturbances. Additionally, it is shown that perfect synchronization of heterogeneous networks with persistent matched disturbances is attained with finite coupling strength but infinite incremental gain on the coupling maps. The real-life implementation of the proposed controllers is studied under the context of practical synchronization via Yosida regularizations. Simulations illustrate the effectiveness of the proposed methods.

Keywords: Robust adaptive control, Distributed control, Optimal control
Abstract: In this work, an algorithm has been developed for heterogeneous network distributed systems (NDS) communicating over a directed network to solve H∞ optimal distributed tracking control problem of continuous-time systems benefiting off-policy reinforcement learning. It should be noted that recent works on heterogeneous NDS have studied the tracking control problem with decentralized performance functions defined for each subsystem in the network, whereas a global performance function has been defined in this work for the whole NDS. The optimal distributed control problem has been defined as a sequential convex optimization problem benefiting off-policy reinforcement learning with sparsity constraints introduced on the state feedback controller gain. Finally, the efficacy of the proposed algorithm is shown by a numerical simulation on heterogeneous NDS.

Keywords: Agents networks, Network analysis and control, Cooperative control
Abstract: In this contribution we propose an extended version of the Friedkin-Johnsen model whose influence matrix is generated according to a homophily mechanism, by keeping into account only the signs of the agents’ appraisals. In the general case, we have been able to prove that the opinion matrix of a group of n agents on m topics asymptotically converges to a constant solution, that strongly depends on the agents’ initial opinions as well as on the agents’ stubbornness, namely their attitude to stick to their original opinions. On the other hand, the influence matrix (when devoid of zero entries) always converges to a constant solution in a finite number of steps. In the special case when the initial opinions of the agents determine a nonnegative influence matrix, all the subsequent opinion dynamics evolves either in a cooperative set-up involving all the agents, in case the initial graph is connected, or in disjoint groups of agents that are internally cooperative.

Keywords: Game theoretical methods, Distributed control, Agents networks
Abstract: We propose a networked policy gradient play algorithm for solving Markov potential games. In a Markov game, each agent has a reward function that depends on the actions of all the agents and a common dynamic state. A differentiable Markov potential game admits a potential value function that has local gradients equal to the gradients of agents' local value functions. In the proposed algorithm, agents use parameterized policies that depend on the state and other agents' policies. Agents use stochastic gradients and local parameter values received from their neighbors to update their policies. We show that the joint policy parameters converge to a first-order stationary point of a Markov potential game in expectation for general action and state spaces. Numerical results on the lake game exemplify the convergence of the proposed method.

Keywords: Delay systems, Distributed parameter systems, Fluid flow systems
Abstract: We consider a model of a microfluidic process under Zweifach-Fung effect, which gives rise to a second-order nonlinear, non-affine system with control input that affects the plant both without delay and with an input-dependent delay defined implicitly through an integral of the past input values (that arises from a transport process with transport speed being the control input itself). We construct a predictor-feedback control law that exponentially stabilizes the output to a desired reference point. This is the first time that a predictor-feedback design is constructed that achieves complete input delay compensation for such a type of input delay and despite that control input affects the plant also without delay. This is attributed to the particular structure of the nonlinear system considered, which allows to deriving an implementable formula for the predictor state at the proper prediction horizon.

Keywords: Distributed parameter systems, Agents and autonomous systems, Lyapunov methods
Abstract: We study the deployment of a first-order multi-agent system (MAS) onto a curve in mathbb{R}^n. The MAS has a chain topology and two types of agents: leaders and followers. The leaders know their positions relative to the target curve. Neighboring leaders can communicate with one another. Each follower is aware of the intended and existing differences between its state and the states of its two nearest neighbors. To solve the formation control problem, we derive a semi-linear parabolic PDE describing the system when the number of agents is sufficiently large. We derive the stability condition in terms of linear matrix inequalities (LMIs). Using numerical simulations, we demonstrate that increased connectivity between the leaders improves the deployment speed of the MAS.

Keywords: Distributed parameter systems, Power plants, Delay systems
Abstract: It is considered a typical configuration of hydroelectric power plant under water hammer for stability studies. It is shown that while (simple, non-asymptotic) Lyapunov stability can be easily obtained by using an energy-like Lyapunov functional, asymptotic stability is connected to the nature of the assumed hydraulic losses in the model. Three cases are discussed: the conservative case, emph{``fragile''} asymptotic stability and standard asymptotic stability as such; they are in direct connection with the asymptotic stability for the difference operator of an associated system of functional differential equations with deviated argument of neutral type.

Keywords: Distributed cooperative control over networks, Machine learning, Model validation
Abstract: A common approach of system identification and machine learning is to generate a model by using training data to predict the test data instances as accurate as possible. Nonetheless, concerns about data privacy are increasingly raised, but not always addressed. We present a secure protocol for learning a linear model relying on recently described technique called real number secret sharing. We take as our starting point the PAC Bayesian bounds and deduce a closed form for the model parameters which depends on the data and the prior from the PAC Bayesian bounds. To obtain the model parameters one needs to solve a linear system. However, we consider the situation where several parties hold different data instances and they are not willing to give up the privacy of the data. Hence, we suggest to use real number secret sharing and multiparty computation to share the data and solve the linear regression with a secure distributed Gaussian elimination protocol such that privacy of the data is preserved. The benefit of using secret sharing directly on real numbers is reflected in the simplicity of the protocols and the number of rounds needed. However, this comes with the drawback that a share might leak a small amount of information, but in our analysis we argue that the leakage is small.

Keywords: Distributed parameter systems, Observers for nonlinear systems, Chemical process control
Abstract: This paper is concerned with the design of an extended Luenberger-type state observer for a class of one-dimensional multi-state semilinear PDE systems considering distributed in-domain measurements over the spatial domain. A design based on modal assignment is proposed for the stabilization of the estimation error dynamics. The approach uses the Riesz spectral characterization of the system differential state operator and the local Lipschitz constant related to the non-linearity of the mathematical model. Thus, the synthesis conditions are reduced to the feasibility of a set of LMI constraints which can be solved numerically using semi-definite programming (SDP) tools. The performance of the observer is exemplified through numerical experiments which demonstrate the efficiency of the proposed approach. A case study consisting of an isothermal tubular reactor is presented to demonstrate the observer performance which are evaluated through simulation studies.

Keywords: Distributed parameter systems, Observers for linear systems, Process control
Abstract: This paper investigates the state estimation problem for systems described by the convection-diffusion-reaction partial differential equation, with or without the diffusion term. The analysis of the observability leads to different results for the observability of the system e.g. a time-dependent approximate observability for the convection-reaction equation, this behavior does not occur for the convection-diffusion-reaction equation. To analyze these differences, a quantitative indicator of the unobservability is proposed based on the criterion of exact final observability. For the convection-reaction equation the indicator can be calculated analytically while for the convection-diffusion-reaction equation a numerical lower bound can be calculated using arbitrary precision calculation. For this indicator, the same qualitative behaviour as for the observability of the convection-reaction equation can be observed for the convection dominated convection-diffusion-reaction equation.

Keywords: Distributed estimation over sensor nets, Control over networks
Abstract: This paper proposes a method to navigate a mobile robot by estimating its state over a number of distributed sensor networks (DSNs) such that it can successively accomplish a sequence of tasks, i.e., its state enters each targeted set and stays inside no less than the desired time, under a resource-aware, time-efficient, and computation- and communication-constrained setting. We propose a new robot state estimation and navigation architecture, which integrates an event-triggered task-switching feedback controller for the robot and a two-time-scale distributed state estimator for each sensor. With the controller, the robot is able to accomplish a task by following a reference trajectory and switch to the next task when an event-triggered condition is fulfilled. With the estimator, each active sensor is able to estimate the robot state. We provide conditions to ensure that the state estimation error and the trajectory tracking deviation are upper bounded by two time-varying sequences, respectively. Furthermore, we find a sufficient condition for accomplishing a task and provide an upper bound of running time for the task. Numerical simulations of an indoor robot's localization and navigation are provided to validate the proposed architecture.

Keywords: Observers for nonlinear systems, Energy systems, Hybrid systems
Abstract: Effective management and just-in-time maintenance of lithium-ion batteries require the knowledge of unmeasured (internal) variables that need to be estimated. Observers are thus designed for this purpose using a mathematical model of the battery internal dynamics. It appears that it is often difficult to tune the observers to obtain good estimation performances both in terms of convergence speed and accuracy, while these are essential in practice. In this context, we demonstrate how a recently developed hybrid multi-observer can be used to improve the performance of a given observer designed for an electrochemical model of a lihium-ion battery. Simulation results, obtained with standard parameters values, show the estimation performance improvement using the proposed method.

Keywords: Optimization algorithms, Markov processes, Sensor and signal fusion
Abstract: Incidents where water networks are contaminated with microorganisms or pollutants can result in a large number of infected or ill persons, and it is therefore important to quickly detect, localize and estimate the spread and source of the contamination. In many of today’s water networks only limited measurements are available, but with the current internet of things trend the number of sensors is increasing and there is a need for methods that can utilize this information. Motivated by this fact, we address the problem of estimating the spread of pollution in a water network given measurements from a set of sensors. We model the water flow as a Markov chain, representing the system as a set of states where each state represents the amount of water in a specific part of the network, e.g., a pipe or a part of a pipe. Then we seek the most likely flow of the pollution given the expected water flow and the sensors observations. This is a large-scale optimization problem that can be formulated as a Schrödinger bridge problem with partial information, and we address this by exploiting the connection with the entropy regularized multimarginal optimal transport problem. The software EPANET is used to simulate the spread of pollution in the water network and will be used for testing the performance of the methodology.

Keywords: Observers for nonlinear systems, Power plants
Abstract: A specific moving horizon estimation scheme is proposed for reconstructing the axial xenon concentrations in pressurized water nuclear reactors (PWR). Themodel considered is continuous time, with a parcimonious spatial discretization. The estimation scheme involves continuous time integration while using low frequency sampling of measurements. The results support a sensitivity analysis. The quality of the estimation is shown to be good, even though the model is particularly stiff, and the implementation altogether light.

Keywords: Distributed estimation over sensor nets, Observers for linear systems
Abstract: The problem of distributed state estimation of a linear-time-invariant (LTI) system is addressed in this paper. Given a directed communication network, the full state vector can be reconstructed at an appointed node under the assumption of an open Hamiltonian path. By a suitably designed coordinate transformation, the initial conditions of the subsystems can be estimated successively along the path. Thanks to the Volterra integral operator induced by non-asymptotic kernel functions, the estimation task at each agent can be achieved within a predefined finite time and transmitted to the next node. As such, the instant state vector can be reconstructed at the end node after a finite time interval. Such a scheme is prone to reduce the communication burden. Extensive numerical examples are conducted to verify the effectiveness of the proposed observer in both noise-free and noisy scenarios.

Keywords: Observers for nonlinear systems, Constrained control, Output feedback
Abstract: This paper extends the authors' previous work on Control by Interconnection - Model Predictive Control (CbI-MPC) design for constrained port-Hamiltonian systems to deal with the unmeasurable system states. The first contribution resides in the CbI-oriented formulation of the augmented system, including the plant and the observer. It explicitly supplies observed states as output, which serves to freely design any state-feedback controller. Then, for the second contribution, the CbI-MPC control design is adapted to take into account this augmented PH system. Hence, a new controller input matrix is proposed with corresponding matching conditions. The proposed control method is validated through simulation results for a 3-phase Permanent Magnet Synchronous Motor with input and state constraints.

Keywords: Autonomous robots, Stability of nonlinear systems, Sliding mode control
Abstract: This paper proposes a new sliding mode-based guidance law for mobile robots in the three-dimensional space that offer strong robustness properties and intuitive tuning. The guidance law is proven to guide a vehicle to a boundary region centered in the path particle in finite time. Furthermore, it is proven that for any state inside the boundary region, the guidance law is exponentially stable. Due to its stability properties, the proposed guidance law can guarantee a minimum rate of decay and thus estimate the time of convergence. The stability and robustness properties of the guidance law are analyzed through Lyapunov theory, cascaded system theory, and simulations.

Keywords: Optimal control, Computational methods, Adaptive systems
Abstract: An adaptive mesh initialisation algorithm is proposed to compute a collision free trajectory of a robotic manipulator. To this end, we model the problem as a discrete optimal control problem in the joint space. Constraints are imposed on the joint positions and velocities. Moreover, nonlinear geometric collision avoidance constraints account for a detailed obstacle and robot geometry, imposing additional intricacies on the problem. The problem is solved numerically using a backward Semi-Lagrangian dynamic programming method in conjunction with a penalization of the nonconvex collision constraints, as proposed in cite{britzelmeier_decomposition_2021-1}. Further, to adhere to the curse of dimensions an iterative algorithm is proposed to locally refine the initial state space discretisation. The main contribution of this paper is the introduction of a refinement criterion, which is independent of the value function and solely based on a signed distance function estimated from the collision geometry. Optimal trajectories resulting from adaptive and equidistant grid structures are compared and evaluated for the problem of a robotic manipulator operating in a dynamic environment.

Keywords: Randomized algorithms, Stochastic systems, Fault tolerant systems
Abstract: Multiple model adaptive control (MMAC) is an adaptive control method designed for plant parameter uncertainty given both linear and non-linear plant models. For a system subject to varying operating conditions, the number of controllers necessary to guarantee stable control under nominal-plant uncertainty, or under multiple operating conditions, are both unknown. We propose a learning-based controller synthesis approach that can guarantee stability of a system subject to varying operating conditions. We empirically validate this result for a quadcopter, which is subject to faults in rotors and sensors as well as to adverse wind conditions.

Keywords: Safety critical systems, Constrained control, Linear systems
Abstract: Many (semi-)autonomous systems are equipped with mechanisms that provide a window of projecting into the future. Predictions/projections of future exogenous inputs or disturbances, commonly referred to as preview or lookahead, have been widely studied in predictive control systems to yield less conservative controllers that would otherwise have to consider them as worst-case disturbances. However, the incorporation of such preview information has been less studied in the context of safety. Thus, this paper proposes a preview control barrier function (Prev-CBF) that can enforce the controlled invariance of a safe set for a class of linear continuous-time systems with previewable disturbances. Specifically, our approach can leverage future information about external disturbances, e.g., road gradients or predictive trajectories of other agents/vehicles, for a (small) window into the future and can explicitly take input constraints/bounds into consideration to provide strong safety guarantees in a less conservative manner than existing approaches that do not leverage such information.

Keywords: Sliding mode control, Autonomous systems, Robust control
Abstract: The present paper develops an output feedback fixed-time sliding mode control (FxTSMC) approach for lateral trajectory tracking of an autonomous vehicle subject to disturbances. Firstly, a nonsingular terminal sliding manifold is constructed to force the orientation error and lateral deviation to converge to desired values in finite-time. Secondly, a switching control law is proposed to provide fixed-time stability against external disturbances using variable exponent coefficients. One is that by adjusting the control design parameters, the upper bound of the settling time for the closed-loop lateral system can be attained arbitrarily minimal without depending on system’s initial conditions. Although the theoretical studies of autonomous vehicles’ lateral control are typically applied to lane keeping scenarios with asymptotic stabilization, the suggested work studies the fixed-time (FxT) stability. The analyzed lateral system under the suggested controller is fixed-time stable, and the violation of a predetermined output constraint is avoided, according to a rigorous investigation of the strength of the Lyapunov theory. It is shown how quickly and effectively the FxTSMC works by comparing the performances of closed- loop systems with the provided controller and other classical controllers.

Keywords: Hybrid systems
Abstract: Controlling hybrid system is mostly very challenging due to the variety of dynamics that these systems can exhibit. Flat Hybrid Automata (FHA), as a subclass of hybrid systems, offers a solution to deal with such challenge. It is based on the concept of differential flatness and invertibility. In this study, a notation of FHA with discrete output is proposed, including the notation of its variables and the notation of its continuous and discrete subsystems. With the help of the proposed notation, FHA can be formally formulated and its properties can be formally described. Moreover, by using discrete output, the planning of input trajectories can be explicitly described.

Keywords: Optimal control, Switched systems, Predictive control for nonlinear systems
Abstract: We present a new algorithm for addressing nonconvex Mixed-Integer Nonlinear Programs (MINLPs) where the cost function is of nonlinear least squares form. We exploit this structure by leveraging a Gauss-Newton quadratic approximation of the original MINLP, leading to the formulation of a Mixed-Integer Quadratic Program (MIQP), which can be solved efficiently. The integer solution of the MIQP is used to fix the integer variables of the original MINLP, resulting in a standard Nonlinear Program. We introduce an iterative procedure to repeat the optimization of the two programs in order to improve the solution. To guide the iterations towards unexplored regions, we devise a strategy to partition the integer solution space based on Voronoi diagrams. Finally, we first illustrate the algorithm on a simple example of MINLP and then test it on an example of real-world complexity concerning the optimal control of an energy system. Here, the new algorithm outperforms state-of-the-art methods, finding a solution with a lower objective value, at the cost of requiring an increased runtime compared to other approximate methods.

Keywords: Switched systems, Linear systems
Abstract: This article presents the reachability and controllability characterizations for discrete-time linear switched systems under a fixed and known switching signal. A geometric approach is used, and we are able to provide alternative conditions which are more computationally friendly compared to existing results by utilizing the solution formula at switching times. Furthermore, the proposed conditions make it easier to study the dependency of the reachability and controllability on the switching times and the mode sequences; this is a new result currently not investigated in the literature. Some academic examples are provided to illustrate the novel features found in this study.

Keywords: Switched systems, Control over communication, Output regulation
Abstract: Based on the dissipative property, this paper concerns the novel event-triggered output regulation (OR) problem for networked switched systems (NSSs) with severely unstable dynamics (SUDs). First, novel event-triggered mechanisms (ETMs) are proposed combined with the internal dissipative property, which can balance limited network resources and system performance. Secondly, a novel average dwell time (ADT) condition for the switching signal is derived by adding dissipation terms into the Lyapunov function, which loosens the conventional arrangement that the number of stabilizing switchings is more than destabilizing switchings. In addition, sufficient conditions are also given to solve the asynchronous OR of the novel ETMs for NSSs with transmission delay, packet disorders, and packet losses. Finally, the RLC simulation example testifies to the feasibility of the proposed methods.

Keywords: Switched systems, Linear systems, LMI's/BMI's/SOS's
Abstract: In this paper, we consider a new switching L2 gain for evaluating the magnitude of successive system switches, and focus on its upper bound obtained simply as an analysis index. Furthermore, we simultaneously and simply design the initial states of newly-activated controllers at all system switches to establish the potential practicality as a design index of the upper bound. This is a novel approach to initial state design.

Keywords: Switched systems, Nonlinear system theory, Stability of nonlinear systems
Abstract: The solvability of nonlinear nonswitched and switched singular systems in discrete time is studied. We provide necessary and sufficient conditions for solvability. The one-step map that generates equivalent nonlinear (ordinary) systems for solvable nonlinear singular systems under arbitrary switching signals is introduced. Moreover, the stability is studied by utilizing this one-step map. A sufficient condition for stability is provided in terms of (switched) Lyapunov functions.

Keywords: Switched systems, Hybrid systems, Stability of linear systems
Abstract: In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the phase portraits of the switching systems are determined to obtain globally stable limit cycles from simple specifications, such as given amplitudes and frequencies of desired oscillations. As an application, the paper finally shows that an oscillator model can be derived with a small effort from data measured for an unknown oscillating system.

Keywords: Robotics, Machine learning
Abstract: We begin by describing the overall SeaClear robotic system, comprising the concept, system architecture, commu- nication interfaces, operation and evaluation of the system. Within SeaClear, a group of heterogenous unmanned vehicles provide underwater litter cleaning services in ports and coastal areas. A high degree of complexity results from oper- ating in unstructured environments, subject to environmental disturbances (such as tidal currents, winds), marine traffic or legal requirements. The SeaClear systems aims to provide a model workflow for managing fleets of unmanned vehicles for waterborne applications. The system architecture builds upon the envisioned service, which needs to be accessed from anywhere in the world, by various entities, with different roles in the operation. The communication system is de- signed to reduce the throughput requirements for transferring information over broadband wireless communication, while still giving extensive information to all system end-users and, most importantly, to the operative personnel. Lastly, the implementation and performance of SeaClear service are evaluated through sea trials conducted in representative environments.

Keywords: Robotics, Machine learning
Abstract: Having introduced the system, we then delve into detail on the robotic sensing methodology. The fast pace of deep learn-ing breakthroughs has enabled remarkable advancements in computer vision. Contrary to conventional techniques, deep-learning-based computer vision can achieve almost human-level accuracy and at the same time, it can provide flexibility by allowing re-training whenever new data are available. Various sophisticated neural network architectures such as convolutional neural networks and recurrent neural networks have been widely used in computer vision applications. Lately, such state-of-the-art methods are gaining traction in underwater implementations. Enabled by the latest computer vision advancements, novel underwater image processing methods have been developed, which can be utilized in various applications, such as in allowing robots to navigate autonomously under the water and perceive their surround- ing environment. The employment of such underwater au- tonomous robots could provide a novel, effective solution towards targeting water pollution that is alarmingly raising concerns over the last years. The objective of this work is to investigate the advancements of deep learning techniques for computer vision tasks, as well as their potential on underwater, waste-detection applications. More specifically: (a) We present an analysis of the existing deep learning techniques for object detection. (b) We demonstrate the process for data collection and annotation in order to obtain a sufficiently sized and good-quality dataset. (c) We develop and analyze a deep-learning based frame- work to detect and classify underwater litter. The pro- posed framework is demonstrated with real image data from the seabed of different pilot areas.

Keywords: Robotics, Machine learning
Abstract: The second key sensing component of the system deals with robot pose estimation, and moreover with placing the litter detected on an underwater map for subsequent collec- tion. While pose estimation is methodologically straightfor- ward, practical challenges arise that make the application of the method nontrivial. Specifically, positioning the robots underwater is done with acoustic sensors that are unreliable and have large errors, so to compensate for that we rely on position feedback from the UAV, see also Section V below, together with onboard inertial and Doppler velocity sensors. However, since the UUV is not always visible on the UAV image, an interesting intermittent-feedback estimation approach results. For mapping, we build a point-cloud rep- resentation of the seafloor, on which we register the objects detected. Time permitting, in this talk we will also describe a deep reinforcement learning approach for choosing efficient mapping trajectories, shorter than a complete lawnmower.

Keywords: Robotics, Machine learning
Abstract: Next, we focus on the control challenges that arise from operating the SeaClear robots under water, with the concept and challenges being transferable to other robots in extreme environments. In our scenario the strong influence of non- linear hydrodynamics on the motion of underwater robots and (often unpredictable) influences like currents as well as the distorted perception of the environment pose significant challenges for precise control and safe operation. These uncertainties and the variability in operation conditions origi- nating from different demonstration sites require adaptability and robust performance of the closed-loop system. In order to achieve this, we will highlight how a data-augmented model-based control approach can combine known dynamic models of underwater systems with Gaussian processes to capture the unmodeled residuals of the underlying full system dynamics through online learning. Furthermore, we will combine control strategies for the different phases of the pick-up task from the seabed.

Keywords: Robotics, Machine learning
Abstract: The goal of this final talk is to highlight the role of the UAV in the robotic team. Considering the advantages of speed and accurate positioning based on differential GPS, the UAV can be used to detect and map surface and underwater litter, as well as to establish correlations between them. Furthermore, as pointed out in Section III, unavailability of GPS information underwater makes the task of UUV localization a difficult problem that requires deployment of expensive and sometimes unreliable acoustic sensors. This problem can be overcome in shallow water by using the UAV to recover the UUV pose, and we will explain how this is achieved.