Keywords: Optimal control, Iterative learning control, Game theoretical methods
Abstract: The interplay between Pontryagin’s Minimum Principle and Bellman’s Principle of Optimality is exploited to revisit optimal control problems. This interplay allows characterizing the optimal feedback as the fixed point of a nonlinear static map and, in the finite horizon case, it allows a similar characterization for the optimal costate. The interplay also reveals that the underlying Hamiltonian system can be externally stabilized to reliably compute approximate optimal feedback strategies. Applications of these ideas and tools to the design of novel algorithm for the solution of AREs, to iterative learning, and to differential game theory are also discussed.

Keywords: Nonlinear system identification, Identification for control, Predictive control for nonlinear systems
Abstract: A simple yet expressive prediction model is an essential ingredient in model-based control and estimation. Models derived from fundamental physical principles may fail to capture the complexity of the actual system dynamics. A potential solution is the use of a physics-informed, or gray-box model that extends a physics-based model with a data-driven part. Learning the latter might be challenging, due to noisy measurements and lack of full state information. This work presents a method based on Moving Horizon Estimation (MHE) for simultaneous state estimation and training of a neural network submodel. The method can be used in offline training or applied online for adaptation without any prior knowledge than the white-box submodel. We analyze the capabilities of the method in a two degree of freedom robotic manipulator case study, also showing how it can be used for online adaptation to cope with a time-varying model mismatch.

Keywords: Optimal control, Machine learning, Optimization algorithms
Abstract: The combination of Reinforcement Learning (RL) and Model Predictive Control (MPC) has gained a lot of interest in the recent literature as a way of producing optimal policies from MPC schemes based on inaccurate models. In that context, Deterministic Policy Gradient (DPG) methods are often observed to be the most reliable class of RL methods to improve the MPC closed-loop performance. DPG methods are fairly easy to formulate when used with compatible function approximation as an advantage function. However, this formulation requires an additional value function approximation, often carried out using Deep Neural Networks (DNNs). In this paper, we propose to estimate the required value function approximation as a first-order expansion of the value function estimate from the MPC scheme providing the policy. The proposed approach drastically simplifies the use of DPG methods for learning-based MPC because no additional structure for approximating the value function needs to be constructed. We illustrate the proposed approach with two numerical examples of varying complexity.

Keywords: Predictive control for nonlinear systems, Computational methods, Uncertain systems
Abstract: By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to i) the increased number of augmented states in the optimization problem, as well as ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach, and combine it with ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension n_x for each SQP iteration from mathcal{O}(n_x^6) to mathcal{O}(n_x^3), and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.

Keywords: Neural networks, Nonlinear system identification, Automotive
Abstract: The aim of this work is to investigate the use of Incrementally Input-to-State Stable (δISS) deep Long Short Term Memory networks (LSTMs) for the identification of nonlinear dynamical systems. We show that suitable sufficient conditions on the weights of the network can be leveraged to setup a training procedure able to learn provenly-δISS LSTM models from data. The proposed approach is tested on a real brake-by-wire apparatus to identify a model of the system from input-output experimentally collected data. Results show satisfactory modeling performances.

Keywords: Optimization, Optimization algorithms, Identification
Abstract: Multivariate polynomial optimization is a prevalent model for a number of engineering problems. From a mathematical viewpoint, polynomial optimization is challenging because it is non-convex. The Lasserre's theory, based on semidefinite relaxations, provides an effective tool to overcome this issue and to achieve the global optimum. However, this approach can be computationally complex for medium and large scale problems. For this motivation, in this work, we investigate a local minimization approach, based on the alternating direction method of multipliers, which is low-complex, straightforward to implement, and prone to decentralization. The core of the work is the development of the algorithm tailored to polynomial optimization, along with the proof of its convergence. Through a numerical example we show a practical implementation and test the effectiveness of the proposed algorithm with respect to state-of-the-art methodologies.

Keywords: Iterative learning control, Optimal control
Abstract: Within the Iterative Learning Control (ILC) framework, damping is often introduced as a heuristic to facilitate convergence of the ILC iterates. We analyze how two simple damping approaches affect the local convergence behaviour of a zero-order optimization-based ILC method and prove that the condition for local convergence, which is given in terms of the eigenvalues of an iteration matrix, can be relaxed if damping is introduced. Leveraging a simple example, we illustrate the effects of damping, which might be (1) convergence of an initially diverging iteration or (2) acceleration or deceleration of a converging iteration.

Keywords: Game theoretical methods, Optimization algorithms, Output feedback
Abstract: This paper extends recent work in feedback-based, game-theoretic optimization. We first identify limitations of existing approaches to this problem, often requiring a priori knowledge to construct a nominal sensitivity model. Leveraging zero-order optimization techniques inspired by stochastic perturbation, we develop a model-free algorithm that allows agents to estimate these sensitivities during runtime, rather than a priori. We outline the convergence properties of this algorithm as a forward-backward operator-splitting technique. Finally, we compare this model-free algorithm's performance to existing approaches, outlining its benefits and drawbacks.

Keywords: Game theoretical methods, Agents and autonomous systems
Abstract: In this work, we consider the problem of autonomous racing with multiple agents where agents must interact closely and influence each other to compete. We model interactions among agents through a game-theoretical framework and propose an efficient algorithm for tractably solving the resulting game in real time. More specifically, we capture interactions among multiple agents through a constrained dynamic game. We show that the resulting dynamic game is an instance of a simple-to-analyze class of games. Namely, we show that our racing game is an instance of a constrained dynamic potential game. An important and appealing property of dynamic potential games is that a generalized Nash equilibrium of the underlying game can be computed by solving a single constrained optimal control problem instead of multiple coupled constrained optimal control problems. Leveraging this property, we show that the problem of autonomous racing is greatly simplified and develop RAPID (autonomous multi-agent RAcing using constrained PotentIal Dynamic games), a racing algorithm that can be solved tractably in real-time. Through simulation studies, we demonstrate that our algorithm outperforms the state-of-the-art approach. We further show the real-time capabilities of our algorithm in hardware experiments.

Keywords: Game theoretical methods, Optimization, Control over networks
Abstract: We consider generalized Nash equilibrium problems (GNEPs) with linear coupling constraints affected by both local (i.e., agent-wise) and global (i.e., shared resources) disturbances taking values in polyhedral uncertainty sets. By making use of traditional tools borrowed from robust optimization, for this class of problems we derive a tractable, finite-dimensional reformulation leading to a deterministic "extended game", and we show that this latter still amounts to a GNEP featuring generalized Nash equilibria "in the worst-case". We then design a fully-distributed, accelerated algorithm based on monotone operator theory, which enjoys convergence towards a Nash equilibrium of the original, uncertain game under weak struc- tural assumptions. Finally, we illustrate the effectiveness of the proposed distributed scheme through numerical simulations.

Keywords: Game theoretical methods, Optimization, Energy systems
Abstract: We consider a peer-to-peer electricity market modeled as a network game, where End Users (EUs) minimize their cost by computing their demand and generation while satisfying a set of local and coupling constraints. Their nominal demand constitutes sensitive information, that they might want to keep private. We prove that the network game admits a unique Variational Equilibrium, which depends on the private information of all the EUs. A data aggregator is introduced, which aims to learn the EUs' private information. The EUs might have incentives to report biased and noisy readings to preserve their privacy, which creates shifts in their strategies. Relying on performative prediction, we define a decision-dependent game G^stoch to couple the network game with a data market. Two variants of the Repeated Stochastic Gradient Method (RSGM) are proposed to compute the Performatively Stable Equilibrium solution of G^stoch, that outperform RSGM with respect to efficiency gap minimization, privacy preservation, and convergence rates in numerical simulations.

Keywords: Game theoretical methods
Abstract: This paper analyzes a class of Stackelberg games where different actors compete for shared resources and a central authority tries to balance the demand through a pricing mechanism. Situations like this can for instance occur when fleet owners of electric taxi services compete about charging spots. In this paper, we model the competition between the followers as an aggregative game, i.e., each player's decision only depends on the aggregate strategy of the others. While it has previously been shown that there exist dynamic pricing strategies to achieve the central authority's objective, we in this paper present a method to compute optimal static prices. Proof of convergence of the method is presented, together with a numerical study showcasing the benefits and the speed of convergence of the proposed method.

Keywords: Game theoretical methods, Optimal control, Optimization algorithms
Abstract: In this paper, the suitability of decision tree/random forest classifiers for learning the feedback solutions to time-optimal control problems and pursuit evasion games involving Dubins vehicles, is investigated through several numerical experiments. Recent results have shown that feedback solutions to the game of two cars are bang-bang with the pursuer and evader controls switching between extreme values based on the relative geometry of the players. However no explicit formula for the feedback laws exist. This article demonstrates that this geometry-based logic can be learnt by decision trees/forests quite efficiently, resulting in relatively simple implementations of the feedback laws. The laws thus learned matches with analytical solutions for the variants of the game where these are known. For the cases where such closed form solutions are unknown, the decision tree/forest based laws match with optimal trajectories computed according to other available numerical methods.

Keywords: Agents and autonomous systems, Machine learning, Predictive control for nonlinear systems
Abstract: We present an approach for safe trajectory planning, where a strategic task related to autonomous racing is learned sample efficiently within a simulation environment. A high-level policy, represented as a neural network, outputs a reward specification that is used within the function of a parametric nonlinear model predictive controller. By including constraints and vehicle kinematics in the nonlinear program, we can guarantee safe and feasible trajectories related to the used model. Compared to classical reinforcement learning, our approach restricts the exploration to safe trajectories, starts with an excellent prior performance and yields complete trajectories that can be passed to a tracking lowest-level controller. We do not address the lowest-level controller in this work and assume perfect tracking of feasible trajectories. We show the superior performance of our algorithm on simulated racing tasks that include high-level decision-making. The vehicle learns to efficiently overtake slower vehicles and avoids getting overtaken by blocking faster ones.

Keywords: Autonomous robots, Autonomous systems, Robotics
Abstract: We investigate the problem of risk averse robot path planning using the deep reinforcement learning and distributionally robust optimization perspectives. Our problem formulation involves modelling the robot as a stochastic linear dynamical system, assuming that a collection of process noise samples is available. We cast the risk averse motion planning problem as a Markov decision process and propose a continuous reward function design that explicitly takes into account the risk of collision with obstacles while encouraging the robot's motion towards the goal. We learn the risk-averse robot control actions through Lipschitz approximated Wasserstein distributionally robust deep Q-learning to hedge against the noise uncertainty. The learned control actions result in a safe and risk averse trajectory from the source to the goal, avoiding all the obstacles. Various supporting numerical simulations are presented to demonstrate our proposed approach.

Keywords: Computer aided control design, Computational methods, Aerospace
Abstract: Computing the exact area of the union of an arbitrary number of circles is a challenging problem, since the union is generally non-convex and may be composed of multiple non-overlapping regions. In this paper, we propose tackling this problem by using graph-theoretical concepts and Green's Theorem for exact area computation. Moreover, we show the implementation of this method for a rapid area coverage application with unmanned aerial vehicles (UAVs). Maximizing the area covered using multiple agents is difficult because fast solutions to large-scale optimization problems are sought. In our solution method, we present a hierarchical control framework. On the upper layer, a high-level controller performs centralised computation to determine the optimal UAV locations to maximize the area covered. On the bottom level, we adopt a decentralised approach by implementing multiple local controllers to tackle the trajectory planning and collision avoidance for each agent individually using Nonlinear Model Predictive Control (NMPC). Numerical experiments show that our method for computing the covered area can reduce the computational time required to solve the optimal positioning problem by more than two orders of magnitude when compared to a Monte-Carlo method. The trajectory planning problem was tested for up to 13 agents and the run-time was on the order of milliseconds, demonstrating the suitability for real-time implementation of the presented framework.

Keywords: Predictive control for nonlinear systems, Agents and autonomous systems, Adaptive systems
Abstract: Path planning for Unmanned Aerial Vehicles (UAVs) is a challenging and important problem that received significant attention in recent years. In this paper we focus on Partially Observable Markov Decision Processes (POMDP), a powerful and popular model for planning and control that has several applications on UAVs (e.g search & rescue, surveillance, or automatic warehouse). In particular, we propose a methodology to plan trajectories that allow UAVs to reach a target while avoiding no-fly zones, optimizing, e.g, fuel consumption, flight time, or constraining the approaching angle. The fixed-wing aircraft dynamic is considered in the problem formulation and an uncertainty model error is added to take into account the approximations. The sensing system providing observations of the aircraft state consists of a GPS sensor, an Inertial Navigation System (INS), and other onboard sensors. Considering the complexity of the domain and following the recent literature, we propose an online solution approach based on Monte Carlo Tree Search (MCTS). The online nature of the approach mitigates the complexity typically associated with POMDP models by avoiding the computation of the whole policy. This approach has been validated and tested in simulation on different scenarios and with different cost functions.

Keywords: UAV's, Cooperative autonomous systems, Emerging control applications
Abstract: Aerial package transportation often requires complex spatial and temporal specifications to be satisfied in order to ensure safe and timely delivery from one point to another. It is usually efficient to transport versatile payloads using multiple UAVs that can work collaboratively to achieve the desired task. The complex temporal specifications can be handled coherently by applying Signal Temporal Logic (STL) to dynamical systems. This paper addresses the problem of waypoint navigation of a multi-UAV payload system under temporal specifications using higher-order time-varying control barrier functions (HOCBFs). The complex nonlinear system of relative degree two is transformed into a simple linear system using input-output feedback linearization. An optimization-based control law is then derived to achieve the temporal waypoint navigation of the payload. The controller's efficacy and real-time implementability are demonstrated by simulating a package delivery scenario inside a high-fidelity Gazebo simulation environment.

Keywords: Electrical power systems, Optimal control, Constrained control
Abstract: Modern power systems are characterized by a low inertia and fast voltage dynamics due to the increase of sources connecting via power electronics and the removal of large traditional thermal generators. Power electronics are commonly equipped with fast controllers that are able to reach a desired voltage setpoint within seconds. In this paper, we propose and compare two approaches using Model Predictive Control (MPC) to compute optimal voltage references for the power electronic devices in order to minimize the losses in a DC microgrid: i) the design of a traditional setpoint-tracking MPC which receives a previously computed optimal setpoint; ii) the design of an economic MPC which does not require a priori computed setpoints. We show that the economic MPC outperforms the setpoint-tracking MPC in simulations with the CIGRE benchmark system when multiple load disturbances occur. Some insights and discussions related to the stability of the closed-loop system using its dissipativity properties are highlighted for both approaches.

Keywords: Predictive control for nonlinear systems, Robotics, Optimization
Abstract: The sum function notion allows one to define a continuous, piecewise affine over a polyhedral support, surface which accurately penalizes the closeness to polyhedral obstacles. This, in turn, leads to a continuous and piecewise description of the potential field surface further used into an NMPC (Nonlinear Model Predictive Control) motion planning problem.

We introduce and analyze their smooth versions to show significant computational speedup. We analyze the links between the piecewise and smooth surfaces (magnitude and location of critical points). The results are validated in simulation and shown to compare favourably with previous mixed-integer based formulations.

Keywords: Predictive control for nonlinear systems, Machine learning, Safety critical systems
Abstract: In this paper, we introduce a novel approach to safe learning-based Model Predictive Control (MPC) for nonlinear systems. This approach, which we call the “compatible model approach”, relies on computing two models of the given unknown system using data generated from the system. The first model is a set-valued over-approximation guaranteed to contain the system’s dynamics. This model is used to find a set of provably safe controller actions at every state. The second model is a single-valued estimation of the system’s dynamics used to find a controller that minimises a cost function. If the two models are compatible, in the sense that the estimation is included in the over-approximation, we show that we can use the set of safe controller actions to constrain the minimisation problem and guarantee the feasibility and safety of the learning-based MPC controller at all times. We present a method to build an over-approximation for nonlinear systems with bounded derivatives on a partition of the states and inputs spaces. Then, we use piecewise multi-affine functions (defined on the same partition) to calculate a system’s dynamics estimation that is compatible with the previous over-approximation. Finally, we show the effectiveness of the approach by considering a path-planning problem with obstacle avoidance.

Keywords: Linear systems, Optimization, Predictive control for linear systems
Abstract: This paper provides a combinatorial interpretation for the explicit solution of the quadratic cost, linear-constrained MPC (model predictive control) problem. We link the Hasse diagram of the lifted feasible domain with the critical regions which partition the parameter space and serve as polyhedral support for the piecewise affine explicit MPC solution.

Keywords: Predictive control for linear systems, Robust control
Abstract: Based on a convex lifting approach for the state partitions, the present paper studies the sensitivity of piecewise affine (PWA) control laws for linear discrete-time systems with state and input constraints. In particular, the goal is to study the impact of perturbations on the state space partitions. Unlike the current results, which concentrate on the local disturbance of vertex or hyperplane representations, each state partition in this work is considered to be potentially affected. The aim is to characterize the admissible perturbation. Practically, a collection of maximal admissible regions (CMAR) is defined to characterize the maximum perturbation for each set within the original state partition. Based on CMAR, which guarantees the positive invariance of the original controller, and using the in- duced fragility margin for the associated convex lifting (FMCL) is proposed to realize a PWA control in an implicit (region-free) form. A numerical example illustrates the effectiveness of the new PWA controller.

Keywords: Predictive control for nonlinear systems, UAV's, Optimal control
Abstract: This paper presents a novel recovery technique for a fixed-wing UAV (Unmanned Aerial Vehicle) based on constrained optimization: i) we propose a trajectory generation for landing the UAV where it first reduces its altitude by deep stalling, then perches on a recovery net, ii) we design an NMPC (Nonlinear Model Predictive Control) tracking controller with terminal constraints for the optimal generated trajectory under disturbances. Compared to nominal net recovery procedures, this technique greatly reduces the landing time and the final airspeed of the UAV. Simulation results for various wind conditions demonstrate the feasibility of the idea.

Keywords: Biomedical systems, Medical signal processing
Abstract: This paper aims to investigate the effects of an event-based Proportional-Integral-Derivative control system for propofol and remifentanil coadministration on hemodynamics variables in general anesthesia. The validity of the considered control system with respect the anesthetic variables has already been proven in previous works. Here hemodynamic variables are also analyzed by using a specifically devised simulator. In general anesthesia, the balance between propofol and remifentanil is a key factor to optimize the automatic infusion of anesthesia during long and invasive surgical procedures. Indeed, the possibility given by the control system to change the ratio between the infusion rates of the two drugs during the surgery allows the anesthesiologist to handle the patient's hemodynamics in each situation, thus, providing an improved healthcare. Results obtained from simulations suggest that the devised control solution can provide a suitable depth of hypnosis of the patients by always keeping the hemodynamic variables inside their recommended values.

Keywords: Emerging control applications, Robust control, Biomedical systems
Abstract: Computer-based control of anesthesia is a puzzle requiring multiple other states to be suitably monitored and controlled. Among these, hemodynamic stabilization is a must. Very few studies have been reported regarding the automatic control of the combined anesthesia-hemodynamic systems. Hemodynamic states are strongly affected by hypnotic drugs. At the same time, drugs used for hemodynamic control influence the depth of hypnosis. In this paper, a solution to maintain anesthetic and hemodynamic variables within safe operating ranges is presented and consists in a multivariable fractional order controller. The robustness of the proposed solution is analysed by considering a benchmark patient model and data from 24 patients.

Keywords: Biomedical systems, Modeling, Safety critical systems
Abstract: Falls during sit-to-stand are a common cause of injury. The ability to perform this movement with ease is itself correlated with a lower likelihood of falling. However, a rigorous mathematical understanding of stability during sit-to-stand does not currently exist, particularly in different environments and under different movement control strategies. Having the means to isolate the different factors contributing to instability during sit-to-stand could have great clinical utility, guiding the treatment of fall-prone individuals. In this work, we show that the region of stable human movement during sit-to-stand can be formulated as the backward reachable set of a controlled invariant target, even under state-dependent input constraints representing variability in the environment. This region represents the 'best-case' boundaries of stable sit-to-stand motion. We call this the stabilizable region and show that it can be easily computed using existing backward reachability tools. Using a dataset of humans performing sit-to-stand under perturbations, we also demonstrate that the controlled invariance and backward reachability approach is better able to differentiate between a true loss of stability versus a change in control strategy, as compared with other methods.

Keywords: Process control, Biomedical systems, Uncertain systems
Abstract: We propose a model-free artificial pancreas (AP) for people with type 1 diabetes. The algorithmic parameters are tuned to a virtual population of 1,000,000 individuals, and the AP repeatedly estimates the basal and bolus insulin requirements necessary for maintaining normal blood glucose levels. Therefore, the AP can be used without healthcare personnel or engineers customizing the algorithm to each user. The estimates are based on bodyweight, measurements from a continuous glucose monitor (CGM), and estimates of the meal carbohydrate contents. In a virtual clinical trial with all 1,000,000 individuals (i.e., a Monte Carlo closed-loop simulation), the AP achieves a mean time in range of more than 87% and over 88% of the participants satisfy several glycemic targets.

Keywords: Biomedical systems, Optimal control, Identification for control
Abstract: In this article, we present the design of a smart electrostimulator for muscle rehabilitation or reinforcement, using fast computations, in order to control the muscular force. The Ding and al. model allows to predict and to optimize the muscular force response to functional electrical stimulation. We analyze the estimation of the Ding and al. parameters using an approximation of the force response which depends upon the 6 parameters of the Ding's model and we derive optimization scheme which bypass the time computational expensive integration of the dynamics of the Ding and al. equations.

Keywords: Mechatronics, Metabolic systems, Biomedical systems
Abstract: Treatment of type 1 diabetes mellitus is significantly improved by using commercially available hybrid closed-loop systems to deliver insulin. These systems, also called artificial pancreas (AP), use the subcutaneous (SC) route to deliver insulin. However, meal announcements are necessary due to the slow insulin absorption from the SC tissue. Thus due to the need for human intervention, it is called ``hybrid closed loop'' AP.

In this work, a bi-hormonal AP with intraperitoneal (IP) infusion is designed to increase the time within the range of 3.9--10.0 mmol/l and alleviate the burden of meal announcements. A two-layer controller is designed to provide safe and effective insulin and glucagon delivery. The primary layer is based on classical PID controllers for insulin and glucagon, and the supervisory layer includes four parts: (A) Zone-based control settings, (B) Extrapolation of sensor data to compensate for sensor delay in SC tissue, (C) Auto-tuning of the PID parameters in the primary layer through simulation in an animal model, and (D) Safety barriers. The controller is designed to prevent hypoglycemia after meals and during physical activity, as well as prevent postprandial hyperglycemia.

The designed AP achieved 92.5% of the time within the range of 3.9--10.0 mmol/l on a simulator trained on data from animal experiments.

The results indicate that this two-layer control structure with IP infusions makes it feasible to achieve a fully automated artificial pancreas without the need for meal announcements, i.e. without human intervention.

Keywords: Flexible structures, Modeling
Abstract: The article presents the initial attempts to provide a geometric framework for modelling and control of flexible link robotic manipulators whose end-effector interacts with a compliant surface. The case study presented here restricts itself to planar flexible link manipulators. Ideas from Lie groups and Lie algebras have been employed to derive the forward and inverse kinematic maps, and their associated Jacobian. Finally we employ the geodesic equation to write down the comprehensive dynamical equations of the system. A geometrical interpretation of the Jacobian is presented and a velocity-level control law proposed earlier in literature is recast in the geometric language. Lastly we incorporate Christoffel symbols in the dynamic model of the flexible manipulator highlighting the underlying geometry. Using this framework, an existing velocity based control law is synthesized and simulated. Results demonstrate that the geometric framework yields a smoother and faster error convergence.

Keywords: Flexible structures, Observers for linear systems, Lyapunov methods
Abstract: Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain coefficients. Sufficient conditions for the convergence of the constructed observer are obtained on the basis of the invariance principle. This result is applied to a flexible beam model attached to a mass-spring system with lumped and distributed actuators. The estimation error decay is illustrated with numerical simulations of finite-dimensional approximations of the observer dynamics.

Keywords: Mechatronics
Abstract: Exploiting the relation between systems and signals, the dynamics of the supposedly known flexible motion system is given a voice in the making process of the desired trajectory signals it has to follow. In doing so, and according to the herein proposed approach, a singularly perturbed version of the system dynamics is obtained which allows the system to be treated as time-invariant despite any existing time dependency. Based on the nature of the system assigned task, the trajectory making process is subdivided into several intervals, where each interval has its own boundary conditions that need to be assigned by the motion designer. In this sense, the boundary conditions act as way-points that govern the smooth states evolution over time, and are used to build internal and self-driven optimal reference trajectories to fulfill the desired actual system motion profile. Despite its simplicity, the superiority of the proposed technique is compared to the 2^nd-order, 3rd-order, and Sine standard motion trajectories, and its performance is evaluated through simulation.

Keywords: Robust adaptive control, Robotics, Uncertain systems
Abstract: A prescribed-time robust nonlinear controller for multi-link robotic manipulators with flexible joints and uncertain input unmodeled dynamics is considered. The controller achieves regulation of the tracking error to within an arbitrarily specified neighborhood of zero (i.e., "practical" tracking) within an arbitrary time interval specified by the control designer. The controller is robust to disturbance torques as well as uncertainties in parameters of the robotic manipulator in addition to uncertain actuator dynamics in the form of input unmodeled dynamics. Time-varying control gains in a vector backstepping approach along with a dynamic scaling based approach to handle input unmodeled dynamics are used to enforce convergence of the tracking error to within the specified neighborhood within the specified time interval. Simulation studies for a two-link manipulator with flexible joints and input unmodeled dynamics are presented to demonstrate the efficacy of the proposed controller design.

Keywords: Flexible structures, Reduced order modeling
Abstract: The paper presents a novel method for deriving approximated finite dimensional models for infinite-dimensional transfer functions that describe the dynamic behavior of flexible structures. The exact transfer function from a point force excitation to a point displacement or velocity, which is derived directly from the wave equation contains delays, corresponding to the traveling waves. The standard and convenient form for analysis and control is a rational transfer function. To overcome this discrepancy, an approximate, rational, finite dimensional model is sought. One approach is spatial discretization where the most common way is the well-known finite element method (FEM). In this work we introduce an alternative method that starts from the exact model and uses Padé approximation for the delay terms. The Padé based approximation (PBA) method is conceptually and technically completely different than FEM. It is shown that it preserves fundamental properties of the exact model and yields better approximations of the time and frequency responses.

Keywords: Flexible structures, Delay systems, Linear systems
Abstract: This paper addresses the problem of active vibration control of a flexible axisymmetric membrane. This mechanical system is equipped with two piezoelectric circular chips where one of them works as an actuator, whereas the other is used as a sensor. Both are glued on the membrane, one on each side, and centered according to its axis of symmetry. The design of the proposed controller is based on delayed proportional actions. We exploit a property called Coexisting Real Roots inducing Dominancy to an assignment of spectral values in an appropriate region of the complex plane, corresponding to a desired damping. The aim of this work is to examine the performances of the proposed output feedback controller in terms of vibration damping of the main observable and controllable vibrating modes.

Keywords: Energy systems, Observers for nonlinear systems, Sliding mode control
Abstract: This paper addresses the problem of achieving current sharing and voltage balancing in DC microgrids in the scenario where filter’s parasitic resistances of Distributed Generation Units (DGUs), based on Buck converters, are unknown and potentially time-varying. Assuming to measure the generated current and voltage, we propose two schemes to estimate the value of the DGUs filter’s parasitic resistance. The first scheme is a novel and suitably tailored, distributed adaptive control approach that solves the aforementioned problem in the case of constant parasitic resistances whilst guaranteeing closed-loop stability. Inspired by the Super-Twisting Sliding Mode Algorithm (STA), the second scheme estimates the resistance in finite time and tracks its evolution. Moreover, this second estimator is coupled with a previously reported control algorithm for achieving current sharing and voltage balancing.

Keywords: Energy systems, Electrical power systems, Predictive control for linear systems
Abstract: This paper contributes to the current trend of development of model-based predictive controls for the operation of sub-transmission grids with storage devices and significant distributed generation. As a main contribution of the current work, it is shown that a receding horizon optimization is able to not only automatically handle the curtailment levels but also to indicate the levels of relaxation for the curtailments, whenever they are admissible. The major difficulty in this process resides in the fact that a reduction of the curtailment implies potential increase of the generation power and can lead to transmission line congestions. To avoid the ensuing safety constraint violations, an upper bound is used for the available power to cope with the lack of information when the curtailment is active. The controller's performance is evaluated via simulations through a case study of a real sub-transmission area in the French power grid.

Keywords: Energy systems, Predictive control for linear systems, Neural networks
Abstract: In this paper we present a learning-based Model Predictive Control (MPC) algorithm based on differentiable optimisation layers. Recent works show that it is possible to include an optimisation problem as a network layer in a Neural Network (NN) architecture. Here the MPC optimisation problem is integrated on the last layer of a NN which is used to estimate the uncertain parameters of the objective function. The NN is then trained online, end-to-end (E2E), based on previous control actions performance. We show that directly targeting the optimality of the control actions leads to improved control results with respect to the standard method of estimating the uncertain parameters and then perform the optimisation. The effectiveness of the proposed method is illustrated on a microgrid energy management problem where the future profile of the electricity price is not known.

Keywords: Optimal control, Optimization, Energy systems
Abstract: This paper proposes a new approach for the optimal operation and control of a Proton Exchange Membrane Fuel Cell (PEMFC) in a microgrid. This approach is based on a bi-level optimization architecture: an economic optimization for the operational management at the higher level, and a control-oriented optimization problem, based on a Reference Governor (RG) approach, at the lower level. The economic optimization imposes flexibility in the power production of the PEMFC. This operating behavior may cause violation of the equipment operating limits when switching from one power level to another, thus provoking the premature aging phenomena that leads to poor performance of the system. With the RG real-time control approach, the operating limits of the system are being respected despite the forced variability and better performances are obtained compared to the classical Proportional-Integer (PI) controller. This work focuses on the stack’s temperature as the key process variable to control. The effectiveness of the control approach is proved by a significant reduction in the sudden changes of the PEMFC stack temperature by up to 85% via a real case study.

Keywords: Optimization, Distributed control, Energy systems
Abstract: Within the concept of Micro-Grids, the day ahead energy management plays an important role where the principal objective is to minimize the cost of the operation. Adequate strategies are required to find an optimal solution for the scheduling of energy flows, that can be formulated as centralized or distributed optimization problems. Energy storage systems are becoming an essential component of Micro-Grids due to their contribution to reducing the peak load and mitigating the intermittency of renewable resources. However, battery aging is a latent problem that is not usually considered in energy management systems. Consequently, this paper presents a day-ahead dispatch strategy for a set of Micro-Grids, solvable by centralized and ADMM distributed approaches, and with the inclusion of battery degradation costs. A detailed simulation was executed to verify the behavior of the proposed approaches. It is shown that both, centralized and distributed solutions, converge to the same minimum with a difference of less than 1%. A Pareto analysis with the ε constraint method evidences that the operative costs can increase up to a 11.7% if the aging cost of the battery is constrained below its nominal level.

Keywords: Nonlinear system theory, Linear systems
Abstract: In this paper, we provide some extension results for systems with counterclockwise input-output dynamics and give their relationship with negative imaginary systems. We give a method of characterizing systems with counterclockwise input-output dynamics in terms of the state vectors of the system. We do this by using the dissipative property of the systems. We provide conditions under which local counterclockwise input-output dynamics of a nonlinear system can be inferred from the negative imaginary property of the linearized system. Furthermore, we show that if a system has the counterclockwise input-output dynamics, then the linearized system will be a negative imaginary system. Finally, we provide a numerical example where we use some of the developed result to show that there are nonlinear systems which do not possess the counterclockwise input-output property, but the linearized system is negative imaginary.

Keywords: Nonlinear system theory, Stability of nonlinear systems, Decentralized control
Abstract: We generalize the principle of extension and controller design using this principle for nonlinear systems. We first define principles of inclusion and extension for nonlinear time-invariant (NLTI) systems. Thereafter, we present the necessary and sufficient conditions for a system to be an extension of another and show that when the expanded system is an extension of the original system, any controller designed for the expanded system can be contracted for implementation on the original system. Subsequently, we demonstrate how an overlappingly decomposed NLTI system can be expanded so that the expanded system is an extension of the original system, how decentralized controllers can be designed for the expanded system, and how these controllers can be contracted for implementation on the original system. An example is also provided to illustrate the extension and contraction concepts and show controller design using the proposed principles.

Keywords: Modeling, Switched systems, Nonlinear system theory
Abstract: The price/demand curve in a scenario characterized by the so-called Veblen effect is analytically identified as a modification, due to a variable that we call hankering, of the classical monotonic (price/demand) curve. Differentiating this function with respect to price and using a classical time variation of price, we obtain a control dynamical system. We exploit this model to analyse the possible trajectories and the equilibrium points. Based on these results, we design a strategy that maximizes the earnings of the seller.

Keywords: Optimal control, Nonlinear system theory, Constrained control
Abstract: Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form q'' = f(t, q, q'). While simulation methods tailored to these equations have been studied, using them in direct optimal control methods is rare. Indeed, the standard approach is to perform a state augmentation, adding the velocities to the state. The main drawback of this approach is that the number of decision variables is doubled, which could harm the performance of the resulting optimization problem. In this paper, we present an approach tailored to second-order ODE. We compare it with the standard one, both on theoretical aspects and in a numerical example. Notably, we show that the tailored formulation is likely to improve the performance of a direct collocation method, for solving optimal control problems with second-order ODE of the more restrictive form q'' = f(t, q).

Keywords: Algebraic/geometric methods, Stability of nonlinear systems, Nonlinear system theory
Abstract: A non-linear Euler-Lagrange (EL) controller is proposed for underactuated mechanical Euler-Lagrange systems. The rationale is that mimicking the process structure in the controller will lead to improved performance. The tuning of the controller can be rather intuitive as it can be seen as an auxiliary mechanical system that is connected to the process, also called the main system. The tuning methodology used here finds its roots in the vibration absorber technology: transfer the energy from the main to the auxiliary system and dissipate the energy in the additional structure. Energy, in the form of the Hamiltonian, is used to examine stability of the compound system using Lyapunov's direct method. To evaluate the performance of the controller, the Hamiltonian of the main system is used. A planar manipulator with two and three degrees-of-freedom (DOF) shows the effectivity of the proposed tuning method.

Keywords: Nonlinear system theory, Identification for control, Nonlinear system identification
Abstract: We present a method for identifying equilibria maps in asymptotically stable nonlinear dynamical systems whose equilibria maps are monotonic. This information can be used to improve the effectiveness of linear schemes for controlling nonlinear systems. The method consists of two stages: a "static" design of experiments problem and a "dynamic" one. The first stage finds the specific steady-state input u_star that leads to the corresponding steady-state output x_star with the highest information content by balancing exploration and exploitation trade-offs using a Gaussian Processes-Lower Confidence Bounds (GP-LCB) framework. The second stage considers the current state of the system and the estimated u_star and x_star to find the control signal profile that brings the system to the specific equilibrium as fast as possible. The capabilities of the method are demonstrated using a scalar synthetic nonlinear dynamic system.

Keywords: Electrical power systems, Robust control, Optimal control
Abstract: The new concept of the Dynamic Virtual Power Plant is explained along with the control objectives and challenges, both at grid and generator levels. Architectures of controls and synthesis methodologies are presented to ensure participation of the DVPP generators to system ancillary services. They are based on time and space separation of control actions according to the natural dynamics of the DVPP. This allows both (a) Participation of the DVPP to classic primary and secondary (voltage and frequency) control levels (b) Centralized and decentralized implementations of the controls.

Keywords: Electrical power systems, Robust control, Optimal control
Abstract: This talk compares two model‐based design methods for solar PV and wind power plants formally represented by multivariable LPV systems. The goal of the control system is to design control dynamics for local generation units that can be integrated into a higher‐level DVPP scheme. Examined are two design methods in which the desired characteristic of the decentralized control loops are specified by either a parameterized pole region or by model matching, which results in different LMI formulations for LPV systems. In particular, the various LMI‐based criteria are discussed, and illustrative examples demonstrate their applicability.

Keywords: Electrical power systems, Robust control, Optimal control
Abstract: We address the problem of designing decentralized controllers for DVPPs. The key idea is to design local feedback controllers for a collection of devices such that in aggregate they provide fast ancillary services including primary frequency and voltage control. First, a general overview of the DVPP control design as a coordinated model matching is presented, where the goal is to match the actual aggregate behavior as closely as possible to some desired dynamic behavior (by means of fully decentralized control) while at the same satisfying the local device limitations. To do so, the initial focus is refined to a DVPP with all devices at one common bus bar in the transmission grid. Moreover, the initial control setup considers a grid‐following signal causality, where power injection is controlled as a function of a bus voltage measurement. A decentralized control design method is proposed to solve the control design problem at hand. It decomposes the problem into two steps: (i) disaggregating the desired dynamic behavior among the individual devices, and (ii) local model matching for each individual device. The theory behind this design approach is presented, and its excellent performance is demonstrated on modified IEEE 9 bus system illustrative examples. Finally, extensions of the initial control design method towards a grid‐forming signal causality, as well as spatially distributed device arrangements are discussed.

Keywords: Large-scale systems, Robust control, Optimal control
Abstract: The talk will address potential modeling, simulation and control challenges and opportunities that renewable energy‐based DVPPs can bring into modern power networks. We will discuss which are the most relevant simulation tools available for such future grids, exposing the key options to be used for different scenarios and contingencies. Additionally, how different possible DVPP control roles can impact the power system stability will be explained.

Keywords: Electrical power systems, Robust control, Optimal control
Abstract: For the real‐time operation of DVPP, a real‐time simulation tool is utilized to describe the dynamics of the system. A fast, scalable, rolling‐time horizon redispatch optimization algorithm implemented and executed through GAMS+Simulink in a real‐time simulation environment is prompted when internal or external deviations occur in the system. The tool is integrated within an automatic Frequency Restoration Reserve regulation scheme for DVPPs, and the performance of such controller is illustrated and discussed.

Keywords: Predictive control for nonlinear systems, Predictive control for linear systems, Emerging control theory
Abstract: While recent years have shown rapid progress of learning-based and data-driven methods to effectively utilize data for control tasks, providing rigorous theoretical guarantees for such methods is challenging and an active field of research. This talk will give an overview of the state of the art of the recently developed framework for data-driven model predictive control (MPC) of unknown systems. In this framework no mathematical model is required for the MPC controller and only input-output data is needed. As a big advantageous feature, this framework admits rigorous theoretical guarantees for the closed loop. The proposed approach relies on the Fundamental Lemma of Willems et al. which parametrizes trajectories of unknown linear systems using data. First, we cover MPC schemes for linear systems with a focus on theoretical guarantees for the closed loop, which can be derived even if the data are noisy. Building on these results, we then move towards the general, nonlinear case. Specifically, we present a data-driven MPC approach which updates the data used for prediction online at every time step and, thereby, stabilizes unknown nonlinear systems using only input-output data. In addition to introducing the framework and the theoretical results, we also discuss successful applications of the proposed framework in simulation and real-world experiments.

Keywords: Optimization, Optimization algorithms, Computational methods
Abstract: We investigate proximal ε-subdifferentials and derive sum rules that hold for weakly convex function, by incorporating the corresponding moduli of weak convexity into the respective formulas. As an application, we analyse inexact proximity operators for weakly convex functions in terms of proximal ε-subdifferentials and the related notion of criticality.

Keywords: Optimization, Optimization algorithms
Abstract: We propose a unifying framework for the automated computer-assisted worst-case analysis of cyclic block coordinate algorithms in the unconstrained smooth convex optimization setup. We compute exact worst-case bounds for the cyclic coordinate descent and the alternating minimization algorithms over the class of smooth convex functions, and provide sublinear upper and lower bounds on the worst-case rate for the standard class of functions with coordinate-wise Lipschitz gradients. We obtain in particular a new upper bound for cyclic coordinate descent that outperforms the best available ones by an order of magnitude. We also demonstrate the flexibility of our approach by providing new numerical bounds using simpler and more natural assumptions than those normally made for the analysis of block coordinate algorithms. Finally, we provide numerical evidence for the fact that a standard scheme that provably accelerates random coordinate descent is actually inefficient when used in a (deterministic) cyclic algorithm.

Keywords: Optimization algorithms, Optimization, Electrical power systems
Abstract: In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple closed convex set. We formulate the nonlinear least-squares problem as an optimization problem using the Euclidean norm as a merit function. In our method, at each iteration we linearize the functional constraints inside the merit function at the current point and add a quadratic regularization, yielding a strongly convex subproblem that is easy to solve, whose solution is the next iterate. We present global convergence guarantees for the proposed method under mild assumptions. In particular, we prove stationary point convergence guarantees and under Kurdyka-Lojasiewicz (KL) property for the objective function we derive convergence rates depending on the KL parameter. Finally, we show the efficiency of this method on the power flow analysis problem using several IEEE bus test cases.

Keywords: Machine learning, Optimization, Iterative learning control
Abstract: Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with regularizers which are only convex. In this setting, the dual problem is non smooth, and dual gradient descent cannot be used. In this paper, we study the regularization properties of a subgradient dual flow, and we show that the proposed procedure achieves the same recovery accuracy as penalization methods, while being more efficient from the computational perspective.

Keywords: Optimization algorithms, Optimization, Statistical learning
Abstract: In this paper, we present a new method for solving optimization problems involving the sum of two proper, convex, lower semicontinuous functions, one of which has Lipschitz continuous gradient. The proposed method has a hybrid nature that combines the usual forward-backward and the generalized conditional gradient method. We establish a convergence rate of o(k^{-1/3}) under mild assumptions with a specific step-size rule and show an application to a total variation parameter learning problem, which demonstrates its benefits in the context of nonsmooth convex optimization.

Keywords: Randomized algorithms, Optimization, Linear systems
Abstract: In this paper we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain acceleration we build on the fact that the Kaczmarz method is dual to a coordinate descent method. We use a recently proposed acceleration method for the randomized coordinate descent and transfer it the primal space. This method inherits many of the attractive features of the accelerated coordinate descent method, including its worst-case convergence rates. Theoretical analysis of the convergence of the proposed method is given. Numerical experiments show that the proposed method is more efficient and faster than the existing methods for solving the same problem.

Keywords: Sampled data control, Stochastic control, Optimal control
Abstract: In this paper, we address the continuous-time chance-constrained nonlinear Stochastic Model Predictive Control (SMPC) problem using Conditional Value at Risk (CVaR). Chance constraint directly enforces a user-specified upper bound for the probability of constraint violation. However, it is known that a chance constraint may be non-convex and intractable in general. CVaR is a risk measure that provides a convex approximation of chance constraints. In this paper, we first use the multiple shooting method for the stochastic systems in order to represent a continuous-time Optimal Control Problem (OCP) in a Nonlinear Programming (NLP) form. Then we use scenario tree sampling to deal with the disturbances. Wheeled Mobile Robot (WMR) path planning with obstacle avoidance will be considered to illustrate the efficiency of the method.

Keywords: Sampled data control, Linear time-varying systems, Lyapunov methods
Abstract: This paper presents an event-triggered boundary control strategy for a class of reaction-diffusion PDEs with time-varying reactivity under Robin actuation. The control approach consists of a backstepping full-state feedback boundary controller and a dynamic event-triggering condition, which determines the time instants when the control input needs to be updated. It is proved that under the proposed event-triggered boundary control approach, there is a uniform minimal dwell-time between two event times. Furthermore, the well-posedness and the global exponential convergence of the closed-loop system to zero in L^2-sense are established. A simulation is conducted to validate the theoretical developments.

Keywords: Sampled data control, Optimization, Markov processes
Abstract: This paper deals with the output regulation problem (ORP) of a linear time-invariant (LTI) system in the presence of sporadically sampled measurement streams with the inter-sampling intervals following a stochastic process. Under such sporadically available measurement streams, a regulator consisting of a hybrid observer, continuous-time post-processing internal model, and stabilizer are proposed, which resets with the arrival of new measurements. The resulting system exhibits a deterministic behavior except for the jumps that occur at random sampling times and therefore the overall closed-loop system can be categorized as a piecewise deterministic Markov process (PDMP). In existing works on ORPs with aperiodic sampling, the requirement of boundedness on inter-sampling intervals precludes extending the solution to the random sampling intervals with possibly unbounded support. Using the Lyapunov-like theorem for the stability analysis of stochastic systems, we offer sufficient conditions to ensure that the overall closed-loop system is mean exponentially stable (MES) and the objectives of the ORP are achieved under stochastic sampling of measurement streams. The resulting LMI conditions lead to a numerically tractable design of the hybrid regulator. Finally, with the help of an illustrative example, the effectiveness of the theoretical results are verified.

Keywords: Traffic control, Sampled data control, Lyapunov methods
Abstract: Autonomous vehicles (AVs) enable more efficient and sustainable transportation systems. Ample studies have shown that controlling a small fraction of AVs can smooth traffic flow and mitigate traffic congestion. However, deploying AVs to real-world systems is challenging due to transparency and safety concerns. An alternative approach deployable in the imminent future is human-compatible driving, where human drivers are guided by real-time instructions to stabilize the traffic. To respect human drivers' reaction time Delta, a class of piecewise-constant policies is considered, where periodic instructions are given at every Delta seconds to human drivers, who hold the instructed action constant until the next instruction. While previous work provides a basic theoretical analysis by considering a single driver setting in the absence of traffic, a principled control theoretic analysis that takes into account the full traffic system is lacking. This work uses Lyapunov stability theory to analyze piecewise-constant policies in a traffic system governed by the Optimal Velocity Model (OVM). We provide sufficient conditions for piecewise-constant controls with hold-length Delta to stabilize the system. Numerical simulations demonstrate that our theoretical analyses closely follow simulated results, and can be used to interpret meaningful relationships between system parameters and maximum stable hold lengths.

Keywords: Observers for linear systems, LMI's/BMI's/SOS's, Sampled data control
Abstract: This paper addresses the Unknown Input Observer (UIO) design problem for sampled-data linear time invariant systems with time-varying sampling intervals. A discrete-time modeling approach is used. Based on convex optimization techniques, tractable design conditions are proposed and illustrated on a simple model representative of the thermal behavior of a two room house.

Keywords: Concensus control and estimation, Network analysis and control, Agents networks
Abstract: We consider a coupled Kuramoto system composed of agents that anticipate the future states of their neighbors based on past data and try to align their states accordingly. We show that this anticipatory behavior results in multiple synchronized solutions at different collective frequencies and different stability characteristics. We derive an exact condition for the stability of the synchronized states. We show that the system can exhibit multistability, converging to different synchronized solutions depending on the initial conditions.

Keywords: Control over networks, Network analysis and control, Concensus control and estimation
Abstract: When steering the dynamics of network systems, the control design needs to cope with constraints on actuation and sensing, which often imply that the same control input is injected to each node in a given subset, and this input signal is a function of the state of this node subset. This common situation cannot be modeled in terms of standard pairwise interactions on digraphs, and we propose to use directed hypergraphs as the mathematical object suitable to describe this kind of directed, multibody interactions. We apply this framework to the pinning control problem in networks of coupled linear systems, and derive necessary and sufficient conditions for convergence onto the target trajectory set by the pinner. Furthermore, we provide a dedicated control algorithm to identify the interconnections that are critical for network control.

Keywords: Linear systems, Concensus control and estimation, Network analysis and control
Abstract: In this paper, a new distributed protocol is proposed to force consensus in a discrete-time network of scalar agents with an arbitrarily assignable convergence rate. Several simulations validate the performances and the improvements with respect to more standard protocols.

Keywords: Network analysis and control, Concensus control and estimation, Quantized systems
Abstract: We consider the problems of computing the average degree and the size of a given network in a distributed fashion and under quantized communication. More specifically, we present two distributed algorithms, which rely on quantized operation (i.e., nodes process and transmit quantized messages) and are able to obtain the exact solutions in a finite number of steps. During the operation of our algorithms, each node can determine in a distributed manner whether convergence has been achieved and correspondingly terminate its operation. To the best of the authors' knowledge these algorithms are the first to find exact solutions (i.e., with no error in the final result) under quantized communication. Note that our network size calculation algorithm is the first in the literature to calculate the exact size of a network in a finite number of steps without introducing a final error; in other algorithms, this error can be either due to quantization or asymptotic convergence. In our case, no error is introduced since the desired result is calculated in the form of a fraction involving a quantized numerator and a quantized denominator. We demonstrate the operation of our algorithms and their potential advantages through simulations.

Keywords: Concensus control and estimation, H2/H-infinity methods, Agents and autonomous systems
Abstract: In the literature pertaining to opinion dynamics, stubbornness of agents has been accounted for in the Taylor's model. Although stubbornness may potentially slow down the convergence to consensus or agreement, it may not necessarily be an undesirable feature in the evolution of collective opinions, particularly when noise may corrupt the dynamics of each agent's opinion. Having few stubborn agents in the group can, in fact, make a network more resilient to misinterpretation and miscommunications, which may be viewed as additive noise. In this paper, we study the effect of stubborn agents and their locations in a cycle graph, on noise rejection, using H_2 performance measures. It is analytically proved that in case of two stubborn agents, placing them farthest apart will be better than placing them side by side, for noise rejection.

Keywords: Autonomous systems, Intelligent systems, Concensus control and estimation
Abstract: The present work addresses the problem of leader-follower consensus based on a bioinspired sensorymotor approach. The herein presented learning scheme entails two levels: (i) a supervised offline babbling training, where babbling generates a preliminary inference of the unknown environment, and (ii) during the consensus the execution (online) stage the cortical map is re-training throughout agents, which simultaneously to the consensus lapse the learning model is refined. The purpose of the proposed strategy is to link the human sensorimotor postural model with the consensus problem to endow of natural plasticity to the MAS. In order to fullfil the leader-follower control objective a controller based Lyapunov stability theory is synthesized. A set of numerical simulations are conducted to evaluate the MAS performance while following the cortical-mapped leader trajectory.

Keywords: Hybrid systems, Safety critical systems, Autonomous systems
Abstract: In this work we consider the control problem of systems that are subject to disjunctions of Signal Temporal Logic (STL) tasks. Motivated by existing approaches encoding the STL tasks utilizing time-varying control barrier functions (CBFs), we propose a continuously differentiable function for encoding the STL constraints that is defined as the composition of a smooth approximator of the max operator and a set of functions ensuring the satisfaction of the corresponding STL tasks with a desired robustness, and derive conditions for the choice of the class K function (when the latter is considered to be linear) to ensure that the proposed function is a CBF. Then, a control law ensuring the satisfaction of the STL task is found as a solution to a computationally efficient QP.

Keywords: Computational methods, Computer aided control design, V&V of control algorithms
Abstract: For the implementations of controllers on digital processors, certain limitations, e.g. in the instruction set and register length, need to be taken into account, especially for safety-critical applications. This work aims to provide a computer-certified inductive definition for the control functions that are implemented on such processors accompanied with the fixed-point data type in a proof assistant. Using these inductive definitions we formally ensure correct realization of the controllers on a digital processor. Our results guarantee overflow-free computations of the implemented control algorithm. The method presented in this paper currently supports functions that are defined as polynomials within an arbitrary fixed-point structure. We demonstrate the verification process in the case study on an example with different scenarios of fixed-point type implementations.

Keywords: Traffic control, Robust control, Predictive control for nonlinear systems
Abstract: For reliable traffic control at signalized crossings, this study examines the traffic signal optimization problem using formal methods. Our earlier research considered model predictive control (MPC) with signal spatio-temporal logic constraints to optimize traffic signals at an intersection. However, this approach has a restrictive assumption that the number of vehicles arriving at the intersection from unmodeled streets, termed as the disturbance, is known a priori. Moreover, it has a limitation that the control law is suboptimal if any constraint is not feasible. To relax the assumption and overcome the limitation, this article derives satisfaction and minimal-violation requirements for MPC, which takes into account a disturbance set, to fulfill an optimization constraint if it is feasible; otherwise, the constraint is violated as little as possible. In this way, the MPC is robust against all realizations of additive bounded disturbances.

Keywords: V&V of control algorithms, Hybrid systems, Robotics
Abstract: This work presents partial satisfaction control synthesis over an extension of Weighted Signal Temporal Logic wSTL called wSTL+. The new specification language wSTL+ enables the definition of preferences and importance of subformulae as weights over inclusive (soft) operators (i.e., standard Boolean and temporal operators from wSTL). Furthermore, it includes exclusive operators that impose hard constraints to disallow specific subformulas to be partially satisfied. For conjunctive operators (conjunction and always), all subformulae must be fully satisfied or all violated. In the case of disjunctive operators (disjunction and eventually), mutual exclusive satisfaction is imposed, i.e., exactly one subformula holds. The weights in the specification capture the preferences and importance over fully satisfiable specifications and modulate the solution over conflicting or infeasible specifications. We formulate the partial satisfaction problem over wSTL+ specifications as a bilevel optimization problem. The inner level is modeled as a MILP and captures the customized satisfaction of the wSTL+ specification. The outer level is a linear program that maximizes the robustness of the satisfiable solution found in the inner level. Finally, we show the performance of our method in different case studies involving robot navigation in planar environments.

Keywords: Computational methods, V&V of control algorithms, Safety critical systems
Abstract: We present an effective procedure for solving of the so-called delta-satisfiability modulo theory (SMT) problem over the reals. Our methods are supported by the special approach to the exact real arithmetic: constructive analysis. First, we present an alternative proof of the decidability of the bounded delta-SMT problem within our framework and an efficient branch-and-bound algorithm, which is based on the rational interval arithmetic. We provide some initial experiments to demonstrate the applicability of the derived solver. Finally, we discuss potential extensions and possible optimizations of the suggested algorithm.

Keywords: Agents networks, Cooperative autonomous systems, Markov processes
Abstract: We address multi-robot safe mission planning in uncertain dynamic environments. This problem arises in safety-critical exploration, surveillance, and emergency rescue missions. The multi-robot optimal control problem is challenging because of the dynamic uncertainties and the exponentially increasing problem size with the number of robots. Leveraging recent works obtaining a tractable safety maximizing plan for a single robot, we propose a scalable two-stage framework. Specifically, the problem is split into a low-level single-agent problem and a high-level task allocation problem. The low-level problem uses an efficient approximation of stochastic reachability for a Markov decision process to derive the optimal control policy under dynamic uncertainty. The task allocation is solved using forward and reverse greedy heuristics and in a distributed auction-based manner. Properties of our safety objective enable provable performance bounds on the safety of the approximate solutions of the two heuristics.

Keywords: Biomedical systems, Modeling, Machine learning
Abstract: In this paper, a data-based approach is used to predict the effect of Propofol and Remifentanil on Bispectral Index (BIS) and Mean Arterial Pressure (MAP) during total intravenous anesthesia. In particular, we aim to reproduce the measured data by identifying the pharmacodynamic function using machine-learning techniques. Features from the output of classic pharmacokinetic models and patient information are considered. Five learning methods are tested including linear models, support vector machine, Kernel, k-neighbors regressors, and neural-network. Learning and testing are performed on a particular subset of 150 surgery cases extracted from the VitalDB database. Results show that this approach improves the classic surface-response methods for BIS and MAP prediction and can be used for anesthesia control applications.

Keywords: Biomedical systems, LMI's/BMI's/SOS's, Medical signal processing
Abstract: Objective: The gold standard technique for measuring postprandial glucose fluxes is the triple tracer technique that requires a large number of blood samples and the use of infused tracers with specific infusion patterns. The present work proposes a simple method for estimating plausible postprandial glucose fluxes and other state variables for type 1 diabetes in a meal test using continuous glucose monitors, amount of insulin infused/injected, amount of meal carbohydrates and one blood sample. Methods: The proposed technique is based on a min-max estimation method that incorporates an uncertainty model description derived from the set of virtual patients in the UVa Padova simulator and a sparse vector space of plausible glucose flux patterns. The new algorithm was tested in simulation and performance was measured using relative root mean squared error (RRMSE) and coefficient of determination (COD). Results: The simulation experiments demonstrate that the min-max estimator is more robust to model uncertainties compared to using an estimator with fixed average parameters: median RRMSE performance was 0.1142 vs. 0.1448 and median COD was 81.4% vs. 73%.

Keywords: Applications in neuroscience, Biomedical systems, Modeling
Abstract: This paper inspects dynamical modelling for brain-electrode interface in the context of StereoElectroEncephaloGraphic (SEEG) recordings using electrodes directly implanted into brain tissue. Considering a physical-based non-integer-order transfer function modelling approach, it is first emphasized how it can be usable for tissue classification (between grey and white matters) near each SEEG contact. In addition, it is shown how the model parameters can also provide more insights on electrical properties in the areas where measurements are collected.Validating identification and classification results are finally presented for clinical data, the former providing estimates of resistivity and capacitivity-related coefficients, and the latter showing more than 70% of accuracy.

Keywords: Biomedical systems, Delay systems, Optimization algorithms
Abstract: We consider a nonlinear system with distributed delays modeling cell population dynamics, where the parameters depend on growth-factor concentrations. A change in one of the growth factor concentrations may lead to a switch in the corresponding model parameter. Our first objective is to achieve a network representation of the switching system involving nodes and edges. Each node stands for a full-fledged nonlinear system with distributed delays where the parameters are constant. For each node, a stable positive steady state may exist. In the network framework, a change in the growth-factor concentration is interpreted as a transition from one node to another. The objective is then to determine the best switching signal steering the biological parameters over time, making the overall dynamic system moving from one operating mode to another, until reaching a desired stable state. Our method provides a (sub)optimal therapeutic strategy, guiding the density of cells from an abnormal state towards a healthy one, through multiple drug infusions. The drug sequence is deduced from the optimal switching signal provided by a classical pathfinding algorithm, associated with the network representation.

Keywords: Manufacturing processes, Cooperative control, Robotics
Abstract: In robot-driven manufacturing, physically coupled industrial robots exhibit a higher stiffness to resist process forces than a single robot. However, the internal stress between the coupled robots leads to deformation in the joints, which results in the deviation of the tool from the manufacturing path. As the state-of-the-art accuracy enhancement techniques are not extended to physically coupled industrial robots, this paper proposes a hybrid position-torque compensation method that improves the path tracking accuracy. The method is based on the dynamics of coupled robots where the error propagation towards tool deviation is handled explicitly. In the implementation, the compensation is solved by the quadratic programming and a reduction of tool deviation by 61.6% is achieved w.r.t. the case without compensation.

Keywords: Manufacturing processes, Sensor and signal fusion
Abstract: Industrial motion control systems, e.g. pick-and-place tasks in semiconductor manufacturing equipment, require precise positioning for achieving high machine throughput. Linear encoders are the standard industrial sensors used for position feedback due to their relatively low cost, high resolution, and high operating frequency. The challenge is that the linear encoders measure the positions at the points-of-control of the equipment, e.g. motors, and not at the points-of-interest, e.g. pick-and-place positions. The coupling between a point-of-control and the point-of-interest is affected by external disturbances such as mechanical misalignment of the product, friction, and warping of the material, and linear encoders fail to sense these disturbances. Vision-based sensing is a potential alternative to achieve robust sensing and high-precision control. However, vision processing has a long computational delay and affects the machine throughput.

In this paper, we propose a multi-rate multi-sensor fusion approach to improve the positioning accuracy of industrial motion control systems with different points-of-control and points-of-interest. We present a multi-rate Kalman filter with bias correction to fuse accurate but slow and delayed vision sensor data with fast but less accurate linear encoder data for high-precision position control. We validate the proposed method in an evaluation framework by considering an industrial case study of semiconductor die-bonding machine. A design-space exploration is done to evaluate the performance of the proposed solution with respect to various relevant design parameters. The effectiveness of the proposed solution depends on the type of disturbances and vision processing delay. For the parameter range under consideration, we achieve a positioning accuracy of 1μm.

Keywords: Manufacturing processes, Machine learning, Neural networks
Abstract: Melt pressure is one of the key indicators of melt flow stability and quality in polymer extrusion processes. Often, process operators monitor/observe the melt pressure in real time to ensure the safe operation of industrial polymer extrusion processes. However, there might be situations where the melt pressure could not be measured using a physical sensor due to some constraints. Hence, the accurate prediction of this key extrusion parameter would enable the selection of suitable operating conditions to optimize extrusion processes and then minimize melt pressure instabilities. This paper introduces a data-driven model based on deep learning techniques for estimating melt pressure using extrusion process settings as inputs. A deep autoencoder is developed to extract nonlinear features from the process inputs while reducing the input space dimensions. The extracted features are then fed to a feedforward neural network to predict the melt pressure. No previous works have reported on using deep learning techniques for predicting the melt pressure. The proposed model exhibited good predictive performance with a normalized root mean square error of 0.045±0.003 on an unseen dataset. Moreover, it outperformed a neural network model with no dimensionality reduction techniques as well as a neural network combined with principal component analysis.

Keywords: Manufacturing processes, Nonlinear system identification, Predictive control for nonlinear systems
Abstract: The synthesis of Mesalazine via data-driven modelling and a control scheme for the underlying complex continuous flow chemistry process is presented. The challenges of modelling continuous flow synthesis of Mesalazine are overcome by the usage of Neuro-Fuzzy Models together with the so-called Local Linear Model Tree (NFM-LoLiMoT) training algorithm based on data from a highly detailed simulator for the reactor. A state-space representation of the NFM-LoLiMoT allows the implementation of a Non-linear Model Predictive Control (NMPC) strategy in order to perform output tracking and fulfil all input and output constraints. The NMPC scheme guarantees stability through the approximation of an Infinite Horizon cost function using a terminal cost and terminal state constraints. The proposed method provides a systematic approach that can be applied for different setup configurations and reduces the time-consuming process of first-principles modelling of the chemical processes. Simulations of a hydrogenation reactor for the synthesis of Mesalazine are presented to show the performance of the introduced method.

Keywords: Manufacturing processes, Predictive control for nonlinear systems, Modeling
Abstract: Processes of additive manufacturing by 3D-printing are typically operated by only using constant references for feed motion and laser power. For adapting properties of workpieces to desired geometries, the control towards changing reference signals is an enabling factor, though. With a focus on temperature control, this paper proposes a scheme of model predictive control for 3D-printing with consideration of constraints and arbitrary references. Starting from partial differential equations to model heat propagation over the geometry, prediction models and optimization problems are formulated as a local part of a more detailed simulation model of the complete workpiece. For laser velocity and power as manipulated variables, optimization problems involving integer variables are solved. Simulation results show how spatial temperature profiles can be adjusted by the proposed approach.

Keywords: Optimization, Autonomous systems, Manufacturing processes
Abstract: The rapid increase of earth’s population versus earth’s limited resources forces the industrial community to recycle waste and reduce raw materials consumption. In the shadow of industry 4.0, digitization and automation play a significant role in increasing quality, efficiency and reducing time waste, combined with additive manufacturing techniques which helps in rapid prototyping and manufacturing in wide spectrum of applications such as prosthetics, various plastic products and product development with minimal waste. This paper aims to decrease our plastic footprint by introducing an approach for an automated cycle for easily integrating plastic waste into additive manufacturing using self-optimizing fused deposition modeling (FDM) process for identification of ideal processing parameters. By the means of a thermal infrared camera to monitor the inlaid filament through thermal imaging.

Keywords: Game theoretical methods, Distributed control, Energy systems
Abstract: In this paper, we propose a novel control strategy for the optimal scheduling of an energy community constituted by prosumers and equipped with unidirectional vehicle-to-grid (V1G) and vehicle-to-building (V2B) capabilities. In particular, V2B services are provided by long-term parked electric vehicles (EVs) thus acting as temporary storage systems by prosumers, which in turn offer the V1G service to EVs provisionally plugged into charging stations. To tackle the stochastic nature of the framework, we assume that EVs communicate their parking and recharging time distribution to prosumers, allowing them to improve their energy allocation. Prosumers and EVs interact in a rolling horizon control framework with the aim of achieving an agreement on their operating strategies. The resulting control problem is formulated as a generalized Nash equilibrium problem, addressed through the variational inequality theory, and solved in a distributed fashion leveraging on the accelerated distributed augmented Lagrangian method (ADALM). The convergence and effectiveness of the proposed approach are validated through numerical simulations under realistic scenarios.

Keywords: Identification for control, Nonlinear system identification, Energy systems
Abstract: This article presents an identification benchmark based on data from a public swimming pool in operation. Such a system is both a complex process and easily understandable by all with regard to the stakes. Ultimately, the objective is to reduce the energy bill while maintaining the level of quality of service. This objective is general in scope and is not limited to public swimming pools. This can be done effectively through what is known as economic predictive control. This type of advanced control is based on a process model. It is the aim of this article and the considered benchmark to show that such a dynamic model can be obtained from operating data. For this, operational data is formatted and shared, and model quality indicators are proposed. On this basis, the first identification results illustrate the results obtained by a linear multivariable model on the one hand, and by a neural dynamic model on the other hand. The benchmark calls for other proposals and results from control and data scientists for comparison.

Keywords: Optimal control, Energy systems, Emerging control applications
Abstract: This paper proposes and simulates vertical airborne wind energy (AWE) farms based on multi-aircraft systems with high power density (PD) per ground area. These farms consist of many independently ground located systems that are flying at the same inclination angle, but with different tether lengths, such that all aircraft fly in a large planar elliptical area that is vertical to the tethers. The individual systems are assigned non-overlapping flight cylinders depending on the wind direction. Detailed calculations that take into account Betz' limit, assuming a cubically averaged wind power density of 7 m/s, give a potential yearly average PD of 43 MW/km^2. A conventional wind farm with typical packing density would yield a PD of 2.4 MW/km^2 in the same wind field. More refined simulations using optimal control result in a more modest PD of 6.5 MW/km^2 for practically recommended flight trajectories. This PD can already be achieved with small-scale aircraft with a wing span of 5.5 m. The simulations additionally show that the achievable PD is more than an order of magnitude higher than for a single-aircraft AWE system with the same wing span.

Keywords: Adaptive control, Power plants, Energy systems
Abstract: A model-based, delay-adaptive approach to control the rotational speed of the crankshaft in a gas engine power generation system is presented to provide a robust solution for challenges regarding fuel flexibility and operation flexibility in volatile energy production environments, such as 0-100% Hydrogen and micro-grid applications. The control design procedure based on a nonlinear engine model with parametric uncertainties including unknown transport delays is presented, simulation results provide insights in the functionality and testcell measurements highlight the practical applicability.

Keywords: Energy systems, Modeling, Optimal control
Abstract: This paper presents models for renewable energy systems with storage, and considers its optimal operation. We model and simulate wind and solar power production using stochastic differential equations as well as storage of the produced power using batteries, thermal storage, and water electrolysis. We formulate an economic optimal control problem, with the scope of controlling the system in the most efficient way, while satisfying the power demand from the electric grid. Deploying multiple storage systems allows flexibility and higher reliability of the renewable energy system.

Keywords: Complex systems, Optimal control, Predictive control for nonlinear systems
Abstract: Processes for treating wastewater are used to lessen the amount of harmful elements left behind after industrial or human consumption. After that, the water is released into lakes, rivers, and seas, thus it's critical that these systems operate more efficiently. Because they are complicated and exhibit nonlinear behavior, wastewater treatment processes are challenging to regulate. Thus, it proves to be a challenge to create an optimal control problem or apply model predictive control on such a system. Considering the nonlinear system has only four states, we apply both optimal control and model predictive control on the four differential equations by using ACADO Toolkit. Our main reasons for using the ACADO Toolkit are that it is Open Source, it has a user friendly MATLAB interface and has the advantage of being self - contained (only needs a C++ compiler).

Keywords: Optimal control, Distributed control, Control over networks
Abstract: This paper addresses the problem of optimal control design for distributed control systems with multiple agents, using a Linear Quadratic Regulator (LQR) approach. To effectively control large-scale distributed systems, such as smart-grid and multi-agent robotic systems, it is crucial to design feedback controllers that take into account the various communication constraints, such as limited power, limited energy, or limited communication bandwidth. In this work, we focus on reducing the communication energy in LQR optimal control design on wireless communication networks. Since the Radio Frequency (RF) signal can spread in all directions in a broadcast way, we take advantage of this characteristic to formulate a low-rank LQR optimal control model that can significantly reduce communication energy in distributed feedback control systems. To solve the problem, we propose an algorithm based on the Alternating Direction Method of Multipliers (ADMM). Through numerical experiments, we demonstrate that a feedback controller designed using low-rank structure can outperform the previous work on sparse LQR optimal control design, which only focused on reducing the number of communication links in a network, in terms of energy consumption.

Keywords: Optimal control, Energy systems, Stability of linear systems
Abstract: This work proposes a Linear Quadratic Regulator with Feedforward action (LQR-FF) aiming to improve the performance of optimal controllers applied to control thermal Solar Collector Field (SCF) systems. The proposed strategy advances over the linear quadratic controllers proposed in the literature since it accounts for disturbance compensation and process delays in a combined solution. For this purpose, an augmented state-space model directly considers the inputs and disturbances delays in the control design. Furthermore, the LQR-FF design embeds a robustness analysis of the actual model errors that arise from real scenarios in the control of solar collectors due to, namely, nonlinearities and model parameter uncertainty. The LQR-FF is compared to the Linear Quadratic Gaussian with Loop Transfer Recover (LQG/LTR) in a trustworthy simulated scenario using validated models of the solar thermal plant located in CIESOL (University of Almería, Spain). The results show that, by considering the system delays with no approximation and using the FF action in the optimal control law, the LQR-FF improves the control of SCF compared to the LQG/LTR approach, reducing the reference tracking error by up to 18% in the tested scenarios, which can contribute to enhancing the solar thermal plant efficiency.

Keywords: Modeling, Optimal control, Computer aided control design
Abstract: Direct air capture (DAC) of CO2 can entail mixed integer constrained optimization, when different aspects are simultaneously accounted: optimal electrical power schedule, maximization of captured CO2, satisfaction of predicted DAC load demands and fulfilment of system overall operational constraints. Motivated by the need of driving direct air capture systems via offshore wind-energy, in this paper we investigate how to optimally schedule the DAC system with the aim of capturing maximum CO2 by jointly considering renewable energy generation and the energy buffer states. In particular, the energy storage system is integrated to supply smooth DAC loads during low wind hours. We also propose a lightweight, computationally inexpensive technique based on model predictive control (MPC) where a sequence of relaxed linear programming problems is solved to replace state of the art branch-and-bound or branch-and-cut techniques. Extensive simulations justify the effectiveness of the proposed approach.

Keywords: Optimal control, Optimization, Constrained control
Abstract: In the literature of Economic Model Predictive Control (EMPC) and undiscounted Optimal Control Problem (OCP), the optimal steady-state point is an equilibrium point with the minimum stage cost. If the Economic MPC is discounted, this property does not hold, and the optimal steady-state point is not the same as the one obtained from the undiscounted EMPC. Therefore the discounted steady-state point does not yield minimum stage cost and has a bias with respect to the undiscounted one. In this paper, we propose a computationally inexpensive cost modification in the discounted MPC that results in the undiscounted optimal steady-state point, i.e., the steady-state point that leads to the best stage cost. Moreover, we show that this modification does not affect the closed-loop system behavior. We illustrate the proposed method in a numerical example.

Keywords: Predictive control for nonlinear systems, Machine learning, Emerging control applications
Abstract: After a short presentation of the Tutorial Session, its structure and objectives, the first talk will focus on the use of Recurrent Neural Networks for control system design. The main families of RNN will be considered, namely Neural Nonlinear Auto Regressive exogenous, Echo State Networks, Long Short Term Memory, and Gated Recurrent Units. For these structures, some recent results will be presented concerning their Input-to-State Stability (ISS) and Incremental Input-to-State Stability (𝛿𝛿ISS). Then, attention will be placed on the issues that still hinder the widespread use of RNN for control, namely their robustness, verifiability, and interpretability. The former properties are related to the so-called generalization capabilities of the networks, i.e. their consistency with the underlying real plants, even in presence of unseen or perturbed input trajectories. The latter is instead related to the possibility of providing a clear formal connection between the RNN model and the plant. In this context, it wil be shown how ISS and 𝛿𝛿ISS represent a significant step towards the robustness and verifiability of the RNN models, while the requirement of interpretability paves the way to the use of physics-based networks. The design of model predictive controllers with RNN as plant's model will be also briefly discussed.

Keywords: Predictive control for nonlinear systems, Machine learning, Emerging control applications
Abstract: The performance and safety of model-based controllers rely heavily on the accuracy of the system model. Robust control provides hard guarantees on safety but can be overly conservative and is limited to linear or input-affine systems. More flexible approaches to deal with model uncertainty involve learning a parametric or non-parametric model description. The parametric approach combines known nonlinear features to form a parameter vector, which is updated iteratively by Bayesian linear regression. This structure can be integrated into a learning-based controller, but feature shaping is not always straightforward. Gaussian processes are a non-parametric approach that bypasses the need for feature shaping by assuming the system dynamics are distributed according to the GP, and non-linearities are described by a kernel function. Although GPs can be integrated into a learning-based controller, they suffer in complexity. The applicability of these learning methods depends on explicitly considering the safety requirements of real-world systems. A framework is explored where the dynamics model is described as a fixed map using flexible kernelized models. This tutorial provides a comprehensive description of these methodologies and reports successful practical applications in autonomous driving and robotic manipulation using GP approximations. Finally, kernel techniques can be formulated as convex programs and are suitable for real-time computation, as demonstrated in a mechatronic example.

Keywords: Predictive control for nonlinear systems, Machine learning, Emerging control applications
Abstract: Most engineering problems can be cast as follows: given prior information and data (models, requirements, experimental data, etc.), estimate or "learn" a vector of parameters (model parameters, system design parameters, controller parameters, etc.) that are optimal according to a suitably defined criterion. The most common approaches to deal with this problem return one parameter vector ("model first"). Quantifying the related uncertainty or robustness is often challenging; yet, in safety-critical applications the uncertainty associated with a solution can be more important than the solution itself. Set Membership methods are a family of approaches designed to compute an uncertainty estimate ("uncertainty first") in the form of a set of admissible parameters, rather than returning a single point. Thus, they provide a systematic way to associate uncertainty to a given parameter vector and to choose, for example, the parameters that minimize uncertainty. This talk will briefly review the main concepts of Set Membership methods and focus on two specific techniques: the estimation of uncertainty tubes associated to multi- step predictions in MPC, and the derivative-free solution of black-box optimization problems, where both the cost and the constraint functions are not tractable analytically.

Keywords: Predictive control for nonlinear systems, Machine learning, Emerging control applications
Abstract: This talk is aimed to discuss several Siemens control engineering solutions for autonomous driving based on data learning. While conventional model-based control methods have been popular in the automotive industry, the recent evolution of autonomous driving bring more control design challenges. For example, how to guarantee and validate safety in various traffic situations, improve vehicle efficiency and enhance driving comfort when human is in passive mode. On the other side, there is more significant sensing data and information becoming available that can be exploited in the control loop. The aim of the talk will be to present several use cases and control architectures where data learning is integrated into the control framework to deal with such challenges: adaptive learning to improve performance, imitation learning based on differentiable MPC, and sim2real reinforcement learning. Moreover, the control developments are validated with industry standard testing process involving simulation, hardware and physical testing in a digital twin fashion resulting in time and cost efficiency.

Keywords: Optimal control, Predictive control for nonlinear systems, Autonomous systems
Abstract: Orthogonal collocation methods are direct approaches for solving optimal control problems (OCP). A high solution accuracy is achieved with few optimization variables, making it more favorable for embedded and real-time NMPC applications. However, collocation approaches lack a guarantee about the safety of the resulting trajectory as inequality constraints are only set on a finite number of collocation points. In this paper we propose a method to efficiently create a convex safety envelope containing the trajectory such that the solution fully satisfies the OCP constraints. We make use of Bernstein approximations of a polynomial’s extrema and span the solution over an orthogonal basis using Legendre polynomials. The tightness of the safety envelope estimation, high accuracy in solving the underlying differential equations, fast rate of convergence and little conservatism are properties of the presented approach making it a suitable method for safe real-time NMPC deployment. We show that our method has comparable computational performance to pseudospectral approaches and can accurately approximate the original OCP up to 9 times more quickly than standard multiple-shooting method in autonomous driving applications, without adding complexity to the formulation.

Keywords: Switched systems, Optimal control
Abstract: This paper proposes an iterative method to solve Mixed-Integer Optimal Control Problems arising from systems with switched dynamics. The so-called relaxed problem plays a central role within this context. Through a numerical example, it is shown why relying on the relaxed problem can lead the solution astray. As an alternative, an iterative Switching Time Optimization method is proposed. The method consists of two components that iteratively interact: a Switching Time Optimization (STO) problem and a sequence optimization. Each component is explained in detail, and the numerical example is resolved, the results of which shows the efficiency of the proposed algorithm. Finally, the advantages and disadvantages of the method are discussed and future lines of research are sketched.

Keywords: Computational methods, Algebraic/geometric methods, Predictive control for nonlinear systems
Abstract: Interpolation and approximation of data provided in terms of a Look-Up Table (LUT) is a common and well-known task, and is especially relevant for industrial applications. When using the function for point-wise evaluation, the method choice only affects the accuracy of the function value itself. However, when the LUT is used as part of an optimization problem formulation, a bad method choice can prevent convergence or alter significantly the outcome of the solver. Moreover, computational efficiency becomes critical due to the much higher number of evaluations required. This work focuses on a variation of Locally Weighted Regression, with approximate derivatives computation. The result is a method that allows one to obtain the function value together with the first n derivatives, at a reduced computational cost. Theoretical properties of the approach are analyzed, and the results of a minimization problem using the proposed method are compared with more traditional ones. The new approach shows promising performance and results, both for computational efficiency and effectiveness when used in optimization.

Keywords: Optimal control, Optimization, Optimization algorithms
Abstract: Efficient integrators with sensitivity propagation are an essential ingredient for the numerical solution of optimal control problems. This paper gives an overview on the acados integrators, their Python interface and presents a workflow that allows using them with their sensitivities within a nonlinear programming (NLP) solver interfaced by CasADi. The implementation is discussed, demonstrated and provided as open-source software. The computation times of the proposed integrator and its sensitivity computation are compared to the native CasADi collocation integrator, CVODES and IDAS on different examples. A speedup of one order of magnitude for simulation and of up to three orders of magnitude for the forward sensitivity propagation is shown for an airborne wind energy system model.

Keywords: Optimization algorithms, Optimization, Predictive control for nonlinear systems
Abstract: In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a linearized augmented Lagrangian method, i.e., we linearize the nonconvex cost function and the functional constraints in the augmented Lagrangian at the current iterate, yielding a strongly convex quadratic subproblem that is easy to solve, whose solution is the next iterate. We show, numerically, the efficiency of the proposed method by using it to solve the nonlinear model predictive control problem of an inverted pendulum on a cart.

Keywords: Optimization
Abstract: Consensus-ADMM (C-ADMM) is devoid of being completely decentralized due to its dependency on star-topology and central coordinator. In this paper, we propose a novel algorithm for simultaneous optimization and consensus, to completely decentralize C-ADMM, and enabling implementation on any connected undirected graph. We present the necessary conditions on the algorithm parameters for it to be stable while proving its convergence. We also highlight the difference between our algorithm and Distributed-ADMM (D-ADMM), existing in literature. We show the way to choose algorithm parameters through simulations for desired results. We also show how our algorithm outperforms D-ADMM through simulations.

Keywords: Optimization algorithms, Predictive control for linear systems, Neural networks
Abstract: Deep learning black-box neural networks have revolutionized many fields, including image processing, inverse problems, text mining and more recently, give very promising results in systems and control. Recently, unfolded deep learning techniques were proposed, which bring the physics of the model and standard optimization techniques into the architecture design, in order to eliminate the disadvantages of the black-box learning. In this paper we design trainable unfolded deep architectures for linear MPC based on two standard iterative optimization algorithms (projected gradient descent - PGD and accelerated projected gradient descent - APGD). Our neural networks are expressed as the combination of weight and activation functions with closed-form expressions and an extra parameter allowing to consider the basic algorithm (PGD) or its accelerated version (APGD). We also study the performance of the proposed networks on a linear MPC application.

Keywords: Statistical learning, Machine learning, Sensor and signal fusion
Abstract: We consider the problem of learning functions by two agents and a fusion center from noisy data. True data comprises of samples of an independent variable (input) and the corresponding value of a dependent variable (output) collectively labeled as (input, output) data. The data received by the agents, both the input and output data, are corrupted by noise. The objective of the agents is to learn a mapping from the true input to the true output. We formulate a general regression problem for the agents followed by the least squares regression (LS) problem. We prove a stochastic representer theorem for the general regression problem and subsequently solve the LS problem. The functions learned by the agents are transmitted to the fusion center where an optimization problem is formulated to fuse the functions together, which is then declared as the mapping. As an example, the methodology developed has been applied to the data generated from a transcendental function.

Keywords: Machine learning, Agents and autonomous systems, Uncertain systems
Abstract: We consider the problem where M agents collaboratively interact with an instance of a stochastic K-armed contextual bandit, where K ≫ M. The goal of the agents is to simultaneously minimize the cumulative regret over all the agents over a time horizon T. We consider a setting where the exact context is observed after a delay and at the time of choosing the action the agents are unaware of the context and only a distribution on the set of contexts is available. Such a situation arises in different applications where at the time of the decision the context needs to be predicted (e.g., weather forecasting or stock market prediction), and the context can be estimated once the reward is obtained. We propose an Upper Confidence Bound (UCB)-based distributed algorithm and prove the regret and communications bounds for linearly parametrized reward functions. We validated the performance of our algorithm via numerical simulations on synthetic data and real-world Movielens data.

Keywords: Machine learning, Intelligent systems, Neural networks
Abstract: This paper presents a reinforcement learning algorithm that enables fast learning of control policies based on a limited amount of training data, by leveraging the attributes of both model-based and model-free algorithms. This is accomplished by using expert demonstrations for initializing the reinforcement learning algorithm, by learning a Gaussian process model and a policy that behaves similar to the expert. The policy is subsequently improved using Bi-poplation Covariance Matrix Adaptation Evolution Strategy (BIPOP-CMA-ES) that exploits the model in a black-box optimizer. Finally, the policy parameters obtained from BIPOP-CMA-ES are refined by a model-free reinforcement learning algorithm. Scalable Variational Gaussian Processes are used in the model to allow high-dimensional state spaces and larger amounts of data; in addition, autoencoders are used for dimensionality reduction of the parameter space in BIPOP-CMA-ES. The algorithm is tested in a cart-pole system as well in a higher-dimensional industrial peg-in-hole task and is compared to state-of-the-art model-free and model-based algorithms. The proposed algorithm solves the peg-in-hole task faster than previous algorithms.

Keywords: Machine learning, Emerging control applications, Decentralized control
Abstract: With the advancement of computational power, it has become easier to approximate a complex policy function using a deep neural network to achieve better accuracy and performance. Hence the policies are formulated as parameterized deep neural networks and the same are trained using state-of-the art policy gradient algorithms. Therefore in recent years, reinforcement learning has gained much attention and its advantages make it ideal for adaptive tuning of PI controllers. This manuscript aims to build an adaptive PI controller using Reinforcement Learning (RL) and Deep Neural Networks (DNN) for 1) nonlinear multivariable systems and 2) non-minimum phase multivariable systems. The main objective is to design a PI controller using RL formulation for nonlinear processes, where nonlinear dynamics may be unknown, by training the agents through interactions with linearized models. Proximal Policy Optimization (PPO) algorithm with dynamic action space is proposed in this manuscript. The proposed PPO based controllers achieve better performance and provide smoother convergence compared to the existing RL based controller. The effectiveness of the proposed RL-based PI controller is demonstrated through a Quadruple-Tank system with nonlinear dynamic behavior. The system exhibits both minimum and non-minimum characteristics based on the multivariable zero location. The reward function is also adapted to aid the control applications and leads to efficient learning and convergence. The results show that the controller performed well on the actual process in both minimum and non-minimum phase cases.

Keywords: Optimal control, Machine learning, Hybrid systems
Abstract: In this paper we present a new approach to determine optimal control sequences for nonlinear systems with imperfect or partial knowledge about their dynamics. In this scenario, classical procedures recommend a more complex analytical modeling design, an effort that may be time consuming due to the acquisition of expertise or possibly not applicable. Our hybrid optimal control design compensates for model errors using Gaussian processes learned from measured system data, thus overcoming the limitations of the classical methodology. The associated hybrid optimal control problem is set up and solved using the unscented transform and the multiple shooting approach, making our developed method flexible, data-efficient, and robust. Relevant practical implementation details are explained and an optimal control is exemplary designed for a fully actuated double pendulum, where we analyze the results and draw a comparison between an application with and without existing prior knowledge.

Keywords: Cooperative control, Agents and autonomous systems, Autonomous systems
Abstract: This paper aims to stabilize agents (or vehicles) on a commonly desired circle with bounded trajectories in an external flow field. We consider the formation in a balanced or synchronized phase pattern. In a balanced phase pattern, all agents symmetrically move on a desired common circle. In contrast, in a synchronized phase pattern, all agents move together with the same phase angle on a desired common circle. We propose the control scheme using the concept of the Barrier Lyapunov Function (BLF), which helps in restricting the agents' trajectories within a predefined boundary. Simulations are provided to support the theoretical developments.

Keywords: Autonomous robots, Control over networks, Concensus control and estimation
Abstract: We address the problem of formation-tracking control of velocity-controlled unicycles in a leader-follower configuration, both with known and unknown leader velocities. The controller design is based on relative measurements: distances and line-of-sight angles. This type of measurements are provided by onboard sensors rather than global positioning systems. We assume that a virtual leader generates a desired reference trajectory for the whole swarm, that is once continuously differentiable, bounded and with bounded derivative. We propose two controllers, one for which it is assumed that the leader velocities are known and one in which they are unknown.

Keywords: Cooperative control, Delay systems, Agents and autonomous systems
Abstract: Consensus tracking problem with constant heterogeneous communication and input delays is studied for double-integrator systems. Contrary to previous works on this topic where the delays are known a priori, this paper studies the convergence of agents to a general desired trajectory when the delays are not known in advance. To solve the tracking problem, we formulate a switching control protocol that consists of a coupled single-integrator estimator and a decentralized tracking controller for an individual agent. We present a delay observer design for each individual agent to determine the respective input delays when these are not known a priori. The communication delays are obtained from the time-stamp on the received data. Exact tracking or bounded tracking with unknown constant delays is possible with the aid of presented autonomous corrective action. Simulation results are performed to validate the efficacy of the proposed autonomous corrective action while guaranteeing consensus tracking.

Keywords: Cooperative control, UAV's, Decentralized control
Abstract: This paper is concerned with the problem of cooperative transportation of payloads by teams of unmanned aerial multirotor vehicles equipped with dexterous robotic arms. In order to increase the autonomy of such systems, a leader-follower setting is implemented. The leader UAV dictates the motion and all other follower UAVs attempt to maintain their desired relative pose with respect to the leader. A fiducial marker structure is attached to the leader, which allows all followers to continuously visually track the leader. Each robotic arm is equipped with force-torque sensors at its end-effector for improving the UAV's flight stability. Specialized controllers are designed for the aerial manipulator systems, in order to ensure a compliant behavior against forces transmitted through the payload. Simulations are provided using the Gazebo environment in order to validate the proposed control methods.

Keywords: Distributed cooperative control over networks, Concensus control and estimation, Machine learning
Abstract: In this paper a new distributed multi-agent Actor-Critic algorithm for reinforcement learning is proposed for solving multi-agent multi-task optimization problems. The Critic algorithm is in the form of the Distributed Emphatic Temporal Difference DETD(lambda) algorithm, while the Actor algorithm is derived as a complementary consensus based policy gradient algorithm, derived from a global objective function having the role of a scalarizing function in the multi-criterion optimization. It is demonstrated that the Feller-Markov properties hold for the newly derived Actor algorithm. The weak convergence of the algorithm to the limit set of an attached ODE is subsequently proved under mild conditions, using decomposition between the Critic and the Actor steps and additional two-time-scale stochastic approximation arguments. An experimental verification of the algorithm's properties is given, showing that it can represent an efficient tool for practice.

Keywords: Distributed control, Switched systems, Concensus control and estimation
Abstract: This paper proposes the distributed observer-based control approach to achieve time-varying formation of second-order autonomous unmanned systems (AUSs) under switching topologies. It is assumed that each AUS has access only to the positions of its neighbouring AUS agents. An observer is then designed to estimate the velocity of neighbouring AUS agents. Furthermore, a distributed control for the AUSs is designed using information of position and estimated velocity. A common Lyapunov function is employed in order to establish sufficient conditions for the stability of closed-loop systems. In order to address the effect of switching topologies, a dwell-time condition is has been considered. Moreover, the observer-based time-varying formation controller satisfies the separation principle. Finally, simulation results are presented to illustrate the effectiveness of the proposed approach.

Keywords: Filtering, Fault detection and identification, Fault estimation
Abstract: This paper presents an attack-free time-distributed UIF approach to solve the secure state estimation (SSE) problem under malicious attacks. In this new approach, the malicious attacks are modeled as unknown inputs. This research investigates the SSE problem as the attack-resilient state estimation problem with sparse actuator and sensor attacks, and with both process and output noises. A sparse solution of the unknown inputs is sought to recast the SSE problem to a standard UIF problem. The existence and stability conditions of the optimal sparse solution are also provided to facilitate the design. An application of this new method to solve the chaotic synchronization problem is also addressed. Simulation results verify the usefulness of the proposed method.

Keywords: Uncertain systems, Sensor and signal fusion, Modeling
Abstract: Classification with incomplete information processing under uncertain circumstance is still an open issue. In this study, the Dempster-Shafer evidence theory is extended to the generalized evidence theory in which this problem is addressed from the perspective of open world assumption. An improved method is proposed to model the incomplete information where the generalized basic probability assignment (GBPA) is generated by using the Gaussian distribution model. First, we constructed the Gaussian distribution based on the mean and variance calculated from the training set. Then, we modeled the potential incomplete information with the GBPA of empty set by matching the test sample with the constructed Gaussian distribution model. Third, we identified and recognized the unknown object by fusing the data with the generalized combination rule. Experiment in classification as well as a comparative study is illustrated to show the superiority and efficiency of this method.

Keywords: Cooperative autonomous systems, Fault tolerant systems, Machine learning
Abstract: Autonomous mobile robots are increasingly used in scenarios where humans cannot be sent due to risk or difficulty, such as exploration or reconnaissance missions in extreme conditions. These missions require multiple agents to communicate and cooperate through a decentralized network. Thus, a successful operation requires a network topology capable of maintaining connectivity between agents and being resilient to failures. The network must also be able to identify and avoid possible threats. Multicriteria missions, in which several activities must be performed simultaneously, are suitable for Machine Learning techniques such as Multi-Agent Deep Reinforcement Learning (MADRL). We applied Proximal Policy Optimization (PPO) and Centralized Training with Decentralized Execution (CTDE) to train a network of 20 agents in learning 4 distinct tasks incrementally: movement and obstacle avoidance, connectivity maintenance, network resilience maintenance, and area coverage enhancement. The resulting model was able to generate such robust network topology and showed promising results for 3 out of 4 tasks.

Keywords: Observers for linear systems, Filtering
Abstract: For large-scale cyber-physical systems, the collaboration of spatially distributed sensors is often needed to perform the state estimation process. Privacy concerns naturally arise from disclosing sensitive measurement signals to a cloud estimator that predicts the system state. To solve this issue, we propose a differentially private set-based estimation protocol that preserves the privacy of the measurement signals. Compared to existing research, our approach achieves less privacy loss and utility loss using a numerically optimized truncated noise distribution. The proposed estimator is perturbed by weaker noise than the analytical approaches in the literature to guarantee the same level of privacy, therefore improving the estimation utility. Numerical and comparison experiments with truncated Laplace noise are presented to support our approach. Zonotopes, a less conservative form of set representation, are used to represent estimation sets, giving set operations a computational advantage. The privacy-preserving noise anonymizes the centers of these estimated zonotopes, concealing the precise positions of the estimated zonotopes.

Keywords: V&V of control algorithms, Safety critical systems, Autonomous systems
Abstract: Simulation-based falsification is a practical testing method to increase confidence that the system will meet safety requirements. Because full-fidelity simulations can be computationally demanding, we investigate the use of simulators with different levels of fidelity. As a first step, we express the overall safety specification in terms of environmental parameters and structure this safety specification as an optimization problem. We propose a multi-fidelity falsification framework using Bayesian optimization, which is able to determine at which level of fidelity we should conduct a safety evaluation in addition to finding possible instances from the environment that cause the system to fail. This method allows us to automatically switch between inexpensive, inaccurate information from a low-fidelity simulator and expensive, accurate information from a high-fidelity simulator in a cost-effective way. Our experiments on various environments in simulation demonstrate that multi-fidelity Bayesian optimization has falsification performance comparable to single-fidelity Bayesian optimization but with much lower cost.

Keywords: Reduced order modeling, Differential algebraic systems, Nonlinear system theory
Abstract: In this work, we propose controllability and observability functions associated with a nonlinear differential-algebraic system. Moreover, we also show that they can be utilized to come up with a balanced realization of the system. Truncation of states based on balanced realization also preserves the constraints associated with the system.

Keywords: Modeling, Optimal control, Biological systems
Abstract: In this paper, we present a novel kinetic growth model for the micro-organism Methylococcus capsulatus(Bath) that couples growth and pH. We apply growth kinetics in a model for single-cell protein production in a laboratory-scale continuous stirred tank reactor inspired by a physical laboratory fermentor. The model contains a set of differential algebraic equations describing growth and pH-dynamics in the system. We present a method of simulation that ensures non-negativity in the state and algebraic variables. Additionally, we introduce linear scaling of the algebraic equations and variables for numerical stability in Newton's method. Finally, we conduct a numerical experiment of economic optimal control for single-cell protein production in the laboratory-scale reactor. The numerical experiment shows non-trivial input profiles for biomass growth and pH tracking.

Keywords: Biological systems, Modeling, Optimal control
Abstract: Mathematical models of cancer growth and evo- lution 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 account 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 organ- isms, 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: Biological systems, Output regulation, Nonlinear system theory
Abstract: Plant–soil negative feedback (PSNF) is the rise in soil of negative conditions for plant performance induced by the plants themselves, limiting the full potential yield and thus representing a loss for the agricultural industry. In this paper we present a control strategy to enhance the production of plant's biomass by limiting the detrimental effects the PSNF has on its growth, and providing a simple yet effective ``recipe'' the human operators have to follow. To control the biomass growth we propose an open-loop, pulse-width modulate periodic control that allows the mean value of the biomass to be regulated by tuning some parameters of the input. Finally, we discuss a promising feedback control scheme that can also take into account economic costs.

Keywords: Genetic regulatory systems, Machine learning
Abstract: We use a learning-based strategy to stabilize a synthetic toggle switch via an external control approach, adopting a sim-to-real paradigm to overcome the data efficiency problem that would render the algorithm unfeasible for practical use in synthetic biology. Here, the policy is learnt via training on a simple model capturing the main dynamical features of a toggle switch and is then validated in-silico using stochastic agent-based simulations. Our in-silico experiments confirm the viability of the approach suggesting its potential use for in-vivo control implementation in microfluidics.

Keywords: Hybrid systems, Servo control, Biological systems
Abstract: Neuromorphic control (NC) is inspired by neuronal systems where signals are encoded into spikes or pulses. Fractional order control extends the classical (integer order) control theory to non-integer orders, which allows the controlled system to achieve more flexible and robust behaviors. This paper explores the combination of neuromorphic and fractional order control in an attempt to maintain their individual benefits. In summary, we propose a fractional order control structure that includes the neuron as an additional element. In order to show the possibilities of this novel strategy, referred to as fractional neuromorphic control (FNC), two types of simulation models are presented: a fast-to-simulate block diagram in Simulink, and a physics-based simulation model, developed using the Simscape toolbox, that includes the electrical behavior of the silicon neuron circuit. A practical step-by-step designing procedure of the analog implementation of the neuron is given.

Keywords: Modeling, Emerging control applications, Decentralized control
Abstract: Improving the efficiency of agriculture is a growing priority due to food security issues, environmental concerns, and economics. Precision agriculture and variable rate application technology could enable increases in yield while maintaining or reducing fertiliser use. However, this requires the development of control algorithms which are suitable for the challenges of agriculture. In this paper, we propose a new mechanistic open model of lettuce growth for use in control of precision agriculture. We demonstrate that our model is cooperative and fits well to experimental data. We use the model to show, via simulations, that a simple proportional distributed control law increases crop uniformity and yield without increasing nitrogen use, even in the presence of sparse actuation and noisy observations.

Keywords: Power plants, Linear parameter-varying systems, Optimization
Abstract: This paper considers the possibility of a direct incorporation of a wind turbine prognostic information in the framework of model predictive control culminating in a Health-aware Economic MPC design. The wind turbine blades, the chosen component of study, is subjected to flapwise edge root moment, as a stress component, to acquire important prognostic information of degradation via the well established stiffness degradation methodology. A series multi-objective optimization problems are solved considering segmented degradation functions based on accumulated stress values on the blades. A two-level control scheme is proposed to allow for wind turbine control at different operating regions of wind and also to circumvent non-linearities in the MPC setup. The controller establishes a trade-off between standard wind turbine control objectives and the mitigation of component degradation in relation to wind turbine blades. A 5 MW benchmark wind turbine is used as a case study for illustrative purposes.

Keywords: Fuzzy systems, Predictive control for nonlinear systems, Robust control
Abstract: Roundabouts are a prevalent form of road infrastructure that effectively control traffic flow and significantly decrease the occurrence of accidents in contrast to traditional intersections. This paper, based on the Multi-Risk Assessment and Management Control Strategy (MRAM-CS) [1] aims to enhance this architecture by considering the obstacle behavior. The MRAM-CS allows autonomous vehicles (called Ego-Vehicles (EVs) in what follows) to determine whether to accelerate or decelerate at the arrival of the roundabout and to enter by applying an appropriate speed profile, determined online, which allows to respect appropriate distances with the vehicles circulating in the roundabout. This is done by using the Predictive Inter-Distance Profile metric (PIDP) and the dynamic progress of the minimum value of PIDP (mPIDP). The proposed control is based on Fuzzy-PID controller, allowing to update the PID gains according to Fuzzy Inference System (FIS) and the behavior feature (calm, aggressive or dangerous) of the other vehicles. Several simulations are performed to demonstrate the reliability and the safety of the proposed approach.

Keywords: Predictive control for nonlinear systems, Autonomous systems, Modeling
Abstract: Recently published nonlinear model-based control approaches achieve impressive performances in complex real-world applications. However, due to model-plant mismatches and unforeseen disturbances, the model-based controller’s performance is limited in full-scale applications. In most applications, low-level control loops mitigate the model-plant mismatch and the sensitivity to disturbances. But what is the influence of these low-level control loops? In this paper, we present the model predictive path integral (MPPI) control of a self-balancing vehicle and investigate the influence of subordinate control loops on closed-loop performance. Therefore, simulation and full-scale experiments are performed and analyzed. Subordinate control loops empower the MPPI controller because they dampen the influence of disturbances, and thus improve the model’s accuracy. This is the basis for the successful application of model-based control approaches in real-world systems. All in all, a model is used to design a low-level controller, then its closed-loop behavior is determined, and this model is used within the superimposed MPPI control loop – modeling for control and vice versa. Videos of the self-balancing vehicle are available at: https://tinyurl.com/mvn8j7vf

Keywords: Predictive control for nonlinear systems
Abstract: This paper investigates the use of relaxed recentered logarithmic barrier functions in the context of nonlinear model predictive control. These functions are a variation of the regular log-barrier functions that are introduced in the objective function of an optimization problem as a penalty for the deviation from the constraint set. The resulting MPC scheme has been studied in the case of linear dynamics, and several interesting results on the global nominal asymptotic stability of the corresponding closed-loop system and constraint satisfaction guarantees have been obtained. Extending them to the case of nonlinear dynamics is non-trivial, and we show in this paper that these properties can still hold locally. The theoretical results are demonstrated by the numerical implementation of a nonlinear benchmark system with four states and two inputs.

Keywords: Predictive control for nonlinear systems, Modeling, Distributed parameter systems
Abstract: We introduce a new inversion-free feedforward hysteresis control using the Preisach model. The feedforward scheme has a high-gain integral loop structure with Preisach hysteresis operator in negative feedback. This allows obtaining a dynamic quantity which corresponds to the inverse hysteresis output, as the loop error tends towards zero for a sufficiently high feedback gain. By analyzing the loop sensitivity function with hysteresis that acts as a state-varying phase lag, we demonstrate the achievable bandwidth and accuracy of the proposed control method. Remarkable fact is that the control bandwidth is theoretically infinite, provided the Preisach operator in feedback can be implemented in a way to ensure the C⁰ continuous hysteresis output. Numerical control examples with the Preisach hysteresis model in differential form are presented.

Keywords: Predictive control for nonlinear systems, Stochastic systems, Uncertain systems
Abstract: This paper presents a parallel Monte Carlo simulation based performance quantification method for nonlinear model predictive control (NMPC) in closed-loop. The method provides distributions for the controller performance in stochastic systems enabling performance quantification. We perform high-performance Monte Carlo simulations in C enabled by a new thread-safe NMPC implementation in combination with an existing high-performance Monte Carlo simulation toolbox in C. We express the NMPC regulator as an optimal control problem (OCP), which we solve with the new thread-safe sequential quadratic programming software NLPSQP. Our results show almost linear scale-up for the NMPC closed-loop on a 32 core CPU. In particular, we get approximately 27 times speed-up on 32 cores. We demonstrate the performance quantification method on a simple continuous stirred tank reactor (CSTR), where we perform 30,000 closed-loop simulations with both an NMPC and a reference proportional-integral (PI) controller. Performance quantification of the stochastic closed-loop system shows that the NMPC outperforms the PI controller in both mean and variance.

Keywords: Predictive control for linear systems, Power electronics, Stability of linear systems
Abstract: Several applications, including power electronics and electrical machines, require a fast system response, which is typically achieved via deadbeat control. Hence, there has been an interest in developing model predictive control (MPC) algorithms with deadbeat control properties, i.e., finite-time convergence to a set-point, for power electronics applications. In this paper, we design a practical deadbeat MPC via controller matching. We make use of an existing result for tuning the weight matrices of the MPC cost function such that the corresponding unconstrained MPC solution matches a desired deadbeat controller. This approach allows for a positive definite input weight matrix and provides stability and recursive feasibility guarantees for the resulting MPC controller. We additionally propose a vertex relaxation of the matching problem, which reduces conservatism, and a method for enlarging the terminal set of the deadbeat MPC controller. Three benchmark examples from the power electronics field are used to show the effectiveness of the proposed MPC design.

Keywords: Electrical machine control, Predictive control for linear systems
Abstract: This paper deals with the design of a predictive safety filter which enables safe learning of optimal operating points for permanent magnet synchronous motors. It is shown that the proposed safety filter can be implemented in real-time on a rapid prototyping hardware using a tailored fast alternating minimization algorithm implementation. The effectiveness of the safety filter is shown when learning optimal operating points for a permanent magnet synchronous motor at the test bench using Bayesian optimization.

Keywords: Predictive control for linear systems, Power electronics, Mechatronics
Abstract: This paper deals with the design of a fast MPC algorithm for the current control of a power amplifier utilized for nanometer precision positioning systems within lithography machines. In order to achieve nanometer precision positioning, the internal power amplifier must accurately track a current reference in a very short time (tens of microseconds). Classical industrial control solutions based on transfer functions do not take duty–cycle limits into account and suffer from limited bandwidth, which in turn limits the achievable positioning precision. We design a fast gradient based MPC algorithm that can accurately track the dynamic current reference while satisfying constraints. Simulations show that the MPC-controlled amplifier results in at least 2x better nanometer positioning precision for specific metrics employed in the lithography industry, compared to an industrial loop-shaping controller and an LQR controller.

Keywords: Power electronics, Robust adaptive control, Electrical power systems
Abstract: Grid-forming (GFM) converters are becoming an inevitable component of AC power systems due to the growing demand for distributed energy resources. However, enhancing their performance is still a critical challenge. Conventional dual-loop proportional-integral (PI) control structures are usually used to control a GFM inverter in a dq reference frame. However, they experience unbalancing in transient and steady-state performance. This paper proposes a sliding-mode control (SMC) based finite control set model predictive control (FCS-MPC) for voltage control of a GFM inverter in a grid-connected mode. The SMC is presented for the adaptive and optimal determination of the weighting factors in FCS-MPC. The proposed strategy's key benefit is the SMC's real-time execution. By doing this, the weighting factors are constantly updated in real-time, which avoids the dependence of the response of the inverter control system under uncertainties and external disturbances. Furthermore, to accurately track power references and deliver the required virtual inertia, a virtual synchronous generator controller is utilized to implement the active power loop. The simulation results demonstrate the effectiveness of the suggested approach when compared to a dual-loop PI control method.

Keywords: Electrical power systems, Power electronics, Hybrid systems
Abstract: Hybrid systems combine both discrete and contin- uous state dynamics. Power electronic inverters are inherently hybrid systems: they are controlled via discrete-valued switch- ing inputs which determine the evolution of the continuous- valued current and voltage state dynamics. Hybrid systems analysis could prove increasingly useful as large numbers of renewable energy sources are incorporated to the grid with inverters as their interface. In this work, we explore a hybrid systems approach for the stability analysis of power and power electronic systems. We provide an analytical proof showing that the use of a hybrid model for the half- bridge inverter allows the derivation of a control law that drives the system states to desired sinusoidal voltage and current references. We derive an analytical expression for a global Lyapunov function for the dynamical system in terms of the system parameters, which proves uniform, global, and asymptotic stability of the origin in error coordinates. Moreover, we demonstrate robustness to parameter changes through this Lyapunov function. We validate these results via simulation. Finally, we present simulation results that combine a droop controller with this hybrid systems approach, and benchmark against the well-studied averaged model and inner current and voltage control loops. In the low-inertia grid community, the juxtaposition of droop control with the hybrid switching control can be considered a grid-forming control strategy using a switched inverter model.

Keywords: Modeling, Nonlinear system theory
Abstract: In this work, we introduce a mathematical framework to study the behavior of networks of memristors. Memristors, originally introduced by L.O. Chua in 1971 are resistors with a memory storage. They can be characterized as a relation between charge and flux. Using this mathematical framework, we show that the port behavior of a network of memristors can be described by a single memristor. Moreover, by using monotonicity properties of the individual memristors in the network, we show how the characteristics of an individual device influence the port behavior of that network.

Keywords: Adaptive systems
Abstract: We show how the recent works on data driven open-loop minimum-energy control for linear systems can be exploited to obtain closed-loop control laws, in the form of linear, dynamic controllers that are relatively optimal. Besides being stabilizing, they achieve the optimal, minimum-energy, trajectory when the initial condition is the same as the open-loop optimal control problem. The order of the controller is N-n, where N is the length of the optimal open-loop trajectory, and n is the order of the system. The same idea can be used for obtaining a relatively optimal controller, entirely based on data, from open-loop trajectories starting from up to n linearly independent initial conditions.

Keywords: Optimal control of communication networks, Predictive control for nonlinear systems, Adaptive control
Abstract: This paper addresses the challenge of control for systems with varying topologies. These changes in topology, which occur during system operation, have a significant impact on the overall system dynamics; hence the control should be adaptive with respect to these topology changes. The paper proposes an approach consisting of efficiently modeling the system and the development of a single model-based controller. For validation of the proposed approach, the paper focuses on a complex air net (pneumatic system). The simulation result and preliminary experimental results show a significant improvement in performance with a limited effort of modeling and controller development, due to the proposed approach, over classic approaches based on limited modeling.

Keywords: Adaptive control, Robust adaptive control, Power electronics
Abstract: The rectifiers and inverters are playing an important role in the integration of green energy sources with the traditional grid. This paradigm shift from the traditional grid operation to the hybrid grid operation provides bidirectional power flow and other benefits. However, in addition, to unpredictable load variations, the uncertain behavior of renewable sources also results in a negative impact on the voltage output and other performance parameters. To mitigate these effects, the paper proposes to use an average model of the rectifier and inverter with a Model Reference Adaptive Controller (MRAC) for improvement in the system performance. Utilizing an average model in the MRAC technique enables better stability and control performance by reducing high-frequency dynamics. The MRAC approach utilizes adaptive controllers that adjust their behavior based on the changing parameters over time. By examining a range of load parameters for rectifier and inverter in a case study, the proposed approach has demonstrated impressive enhancements in voltage output, efficiency, and stability, which positions it as a promising solution for enhancing the performance and reliability of power conversion and regulation systems in practical applications, compared to other control techniques. .

Keywords: Adaptive control
Abstract: The paper explores in detail the use of dynamic adaptation gain/learning rate (DAG) for improving the performance of gradient type adaptation/learning algorithms. The DAG is an ARMA (poles-zeros) filter embedded in the gradient type adaptation/learning algorithms and generalizes the various improved gradient algorithms available in the literature. After presenting the DAG algorithm and its relation with other algorithms, its design is developed. Strictly Positive Real (SPR) conditions play an important role in the design of the DAG. Then the stability issues for adaptive/learning systems using a DAG are discussed for large and low values of the adaptation gains/learning rate. The potential of the DAG is then illustrated by experimental results obtained on a relevant adaptive active noise control system (ANC).

Keywords: Agents and autonomous systems, Adaptive control, Autonomous robots
Abstract: In this paper we design an adaptive motion control scheme for steering a mobile sensory agent in 2D toward the source of a signal field using the signal intensity the agent continuously measures at its current location. The signal field is modeled to be a quadratic function of location, and has its extremum (maximum) at the signal source location. The proposed adaptive control design is based on on-line estimation of the Hessian parameters of the field model and the extremum location. Simulation test results are displayed to verify the established properties of the proposed scheme as well as robustness to signal measurement noise.

Keywords: Control education, Adaptive systems, Optimization
Abstract: Industry 4.0 is one of the emerging technology adopted by many companies in order to cope with the growing demand for a unique product per customer i.e., a flexible production system resulting in a highly efficient production process where the product quality is not compromised. Even though the efficiency in an Industry 4.0 plant is higher, there are certain dynamic parameters of the machine which change over time, decreasing production efficiency. This the problem of the time-varying parameter is tackled with the next level of Industry 4.0 driven through data and intelligence i.e., self-optimizing production systems. This paper describes the optimization potential for the setup of a self-optimizing system in a lab-scale Industry 4.0 benchmark plant which mimics a fluid filling plant. A more innovative approach to framing the system optimisation process diagram (SOP) similar to the Automation pyramid is also discussed along with the hurdles of establishing a standard communication protocol through MODBUS and PyADS to communicate with the various modules present in the plant.

Keywords: Predictive control for linear systems, Predictive control for nonlinear systems
Abstract: This talk recapitulates the main results and recent advances in the theory of explicit MPC. We mostly rest in the linear constraints, quadratic cost case, which is nonetheless rich enough in complexity and which offers the necessary ingredients for more challenging extensions (nonlinearities in the dynamics, mixed integer formulations). We present the main directions of research in the last 20 years with emphasis on the two main elements: computation of the critical regions (offline part) and search of the active solution, i.e., the point location problem (online part). We will interpret these results through the lenses of active set enumeration methods with both geometrical (e.g., face flipping, projection onto the feasible domain) and combi- natorial flavours (enumeration and tree pruning strategies, linear complementarity interpretations). We will unify these equivalent methods under a geometric interpretation. Since classical eMPC wilts under the dimensionality curse quite easily, we also detail various complexity-reduction strategies (partial explicit approaches, regionless storage, approximate solutions, recursive computations, etc.). The talk concludes with an enumeration of successful applications (in process control, robotics and automotive) and of the tools which are employed in the eMPC’s compu- tation (for both critical region enumeration and active region search).

Keywords: Predictive control for linear systems, Predictive control for nonlinear systems
Abstract: Combinatorial methods can be efficient whenever large parts of the combinatorial tree of candidate active sets can be disregarded. The talk focuses on recent progress with methods that combine the analysis of candidate active sets with backward dynamic programming (BDP). While BDP is instrumental for solving the unconstrained linear-quadratic regulator analytically, it did not prove useful for MPC. The talk shows that BDP does indeed prove to be very useful if applied to active sets algebraically, instead of to the PWA laws geometrically. After establishing BDP for active sets, it is easy to see that many features of the geometry of the affine law (e.g., symmetries), are evident from the set of active sets – even if the geometric solution is not available. Furthermore, it can be shown that the behavior of the MPC- controlled system (e.g., the sequence of state space polytopes the closed-loop system evolves along) can more easily be inferred from the BDP set of active sets than from the geometry of the explicit law. The outlook of the talk calls for analyzing generalizations of BDP for active sets. Because the geometric solution is not needed in this approach, it may be easier to generalize BDP to other problem classes than the methods for the determination of the explicit PWA law.

Keywords: Predictive control for linear systems, Predictive control for nonlinear systems
Abstract: Convex liftings (and their dual projection operations) emerged recently as an attractive framework to handle complex nonlinear decision problems. In this presentation the inverse optimality problem is introduced: construct an appropriate optimization problem composed of a set of linear constraints and a cost function such that its optimal solution is equivalent to the a priori given PWA function defined over a polyhedral partition. An algorithm to construct convex liftings of a given convexly liftable cell complex will be put forward to provide the necessary tools. Furthermore, this convex lifting-based method requires at most one sup- plementary dimension. This structural result has interesting connections to control design in constrained linear MPC where it can be shown that: i) any continuous PWA control law can be obtained via a reformulated linear MPC problem with the control horizon at most equal to two prediction steps; and ii) in the evaluation of PWA controllers through a fast positioning mechanism.

Keywords: Predictive control for linear systems, Predictive control for nonlinear systems
Abstract: While explicit MPC may be considered for nonlinear dynamics, the issues afflicting the linear case become expo- nentially more difficult to handle when encountering nonlin- earities. In this talk we show how to partially sidestep these difficulties via a differential flatness reformulation. Specifi- cally, we carry a model inversion procedure for a multicopter dynamics by expressing the input and the states in terms of a flat output. In the new representation, the dynamics become linear, thus allowing to use standard explicit MPC tools (at the price of convoluted constraint formulations). Designing an explicit MPC controller in the new coordinates (with suitable under-approximation of the feasible domain) closes the loop and allows fast control action update. Comparisons with other methods and discussions over experimental testing are provided.

Keywords: Predictive control for linear systems, Predictive control for nonlinear systems
Abstract: Neural networks have recently gained a renewed interest within the nonlinear model predictive control (NMPC) field. Originally, neural networks have been used to learn the system dynamics and they have been employed recursively as one-step predictors in NMPC schemes. Then specialized multi-step or structured neural predictors with improved accuracy have been developed for NMPC. More recently, neural networks have been used to learn explicit model predictive control laws. In this tutorial we will review some of the existing neural network architectures for NMPC and we will illustrate their design, training, validation and implementation.