Keywords: Learning
Abstract: The transformation of the transport sector is continuously in motion. Through advances in sensing, connectivity, computing, and electrification, the control community has been, and will continue to be, actively engaged in shaping a sustainable and efficient infrastructure for moving people and goods. While self-driving technologies have garnered significant attention, achieving widespread, safe deployment remains a challenge. Meanwhile, innovations in optimizing and enhancing the resilience of transport systems continue to advance, highlighting the broader impact of control technology on mobility. This lecture will explore the emerging field of learning-enabled cyber-physical-human systems and discuss some specific examples in intelligent transport. We will show how connected vehicles acting as mobile sensors and actuators can enable traffic predictions and control at a scale never before possible, by learning traffic models using physics-informed machine learning techniques. The complexities of safe interactions between automated and human-driven vehicles will be discussed, emphasizing the integration of formal reasoning methods and the use of tele-operation. The presentation highlights joint work with students, postdocs, and collaborators in academia and industry.

Keywords: Stochastic optimal control, Reinforcement learning, Filtering
Abstract: In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where these constitute weak Feller and Wasserstein regularity and controlled filter stability. These are then utilized to arrive at existence results on optimal policies for both discounted and average cost problems, and regularity of value functions. Then, we study rigorous approximation results involving quantization based finite model approximations as well as finite window approximations under controlled filter stability. Finally, we present several recent reinforcement learning theoretic results which rigorously establish convergence to near optimality under both criteria.

Keywords: Stochastic optimal control, Filtering, Reinforcement learning
Abstract: We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where these constitute weak Feller and Wasserstein regularity and controlled filter stability. These are then utilized to arrive at existence results on optimal policies for both discounted and average cost problems, and regularity of value functions. Then, we study rigorous approximation results involving quantization based finite model approximations as well as finite window approximations under controlled filter stability. Finally, we present several recent reinforcement learning theoretic results which rigorously establish convergence to near optimality under both criteria.

Keywords: Stochastic optimal control, Markov processes, Reinforcement learning
Abstract: The traditional approach to POMDPs is to convert them into fully observed MDPs by considering a belief state as an information state. However, a belief-state based approach requires perfect knowledge of the system dynamics and is therefore not applicable in the learning setting where the system model is unknown. Various approaches to circumvent this limitation have been proposed in the literature. We present a unified treatment of some of these approaches by viewing them as models where the agent maintains a local recursively updateable ``agent state'' and chooses actions based on the agent state. We highlight the different classes of agent-state based policies and the various approaches that have been proposed in the literature to find good policies within each class. These include the designer's approach to find optimal non-stationary agent-state based policies, policy search approaches to find a locally optimal stationary agent-state based policies, and the approximate information state to find approximately optimal stationary agent-state based policies. We then present how ideas from the approximate information state approach have been used to improve Q-learning and actor-critic algorithms for learning in POMDPs.

Keywords: Stochastic optimal control, Filtering, Reinforcement learning
Abstract: In this talk, we present reinforcement learning for agent-state based policies: these include agent-state based Q-learning (ASQL) and agent-state based actor critic (ASAC). We show how to analyze the convergence of these algorithms and characterize the suboptimality of the converged solution. We illustrate that these suboptimality bounds can be used to add a novel “AIS block” in the standard Q-learning and action-critic pipelines, where the AIS block learns a model to minimize a proxy for the suboptimality bounds. Experiments on large-scale POMDPs demonstrate that adding such an AIS block improves performance of RL algorithms. We conclude by a discussion of various practical considerations including choice of predicting state vs predicting observations, the choice of metric, the relationship with representation learning, and others.

Keywords: Data driven control, Distributed control, Cooperative control
Abstract: This paper presents novel solutions of the data-based synchronization problem for continuous-time multiagent systems. We consider the cases of homogeneous and heterogeneous systems. First, we obtain a data-based representation of the synchronization error dynamics for homogeneous systems and show how to extend existing data-based stabilization results to stabilize such error dynamics. The proposed method relies on the solution of a set of linear matrix inequalities that are shown to be feasible. Then, we solve the synchronization problem for heterogeneous systems by means of dynamic controllers. Different from existing results, we do not require model knowledge for the followers and the leader. The theoretical results are finally validated using a numerical simulation.

Keywords: Data driven control, Machine learning, Nonlinear systems identification
Abstract: Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit kernel representation of the system trajectories while keeping the requirements on persistency of excitation. We show that this representation is equivalent to the solution of a specific kernel regression problem. We explore the possible structures of the underlying kernel as well as the system classes to which they correspond.

Keywords: Data driven control, Time-varying systems, Learning
Abstract: Many systems are subject to periodic disturbances and exhibit repetitive behaviour. Model-based repetitive control employs knowledge of such periodicity to attenuate periodic disturbances and has seen a wide range of successful industrial implementations. The aim of this paper is to develop a data-driven repetitive control method. In the developed framework, linear periodically time-varying (LPTV) behaviour is lifted to linear time-invariant (LTI) behaviour. Periodic disturbance mitigation is enabled by developing an extension of Willems’ fundamental lemma for systems with exogenous disturbances. The resulting Data-enabled Predictive Repetitive Control (DeePRC) technique accounts for periodic system behaviour to perform attenuation of a periodic disturbance. Simulations demonstrate the ability of DeePRC to effectively mitigate periodic disturbances in the presence of noise.

Keywords: Data driven control, Predictive control for linear systems
Abstract: Recently, several direct Data-Driven Predictive Control (DDPC) methods have been proposed, advocating the possibility of designing predictive controllers from historical input-output trajectories without the need to identify a model. In this work, we show their equivalence to a (relaxed) indirect approach, allowing us to reformulate direct methods in terms of estimated parameters and covariance matrices. This allows us to provide further insights into how these direct predictive control methods work, showing that, for unconstrained problems, the direct methods are equivalent to subspace predictive control with a reduced weight on the tracking cost, and analyzing the impact of the data length on tuning strategies. Via a numerical experiment, we also illustrate why the performance of direct DDPC methods with fixed regularization tends to degrade as the number of training samples increases.

Keywords: Data driven control, Linear parameter-varying systems
Abstract: A promising step from linear towards nonlinear data-driven control is via the design of controllers for linear parameter-varying (LPV) systems, which are linear systems whose parameters are varying along a measurable scheduling signal. However, the interplay between uncertainty arising from corrupted data and the parameter-varying nature of these systems impacts the stability analysis and limits the generalization of well-understood data-driven methods available for linear time-invariant systems. In this work, we decouple this interplay using a recently developed variant of the Fundamental Lemma for LPV systems and the concept of data-informativity, in combination with biquadratic Lyapunov forms. Together, these allow us to develop novel linear matrix inequality conditions for the existence of scheduling-dependent Lyapunov functions, incorporating the intrinsic nonlinearity. Appealingly, these results are stated purely in terms of the collected data and bounds on the noise, and they are computationally favorable to check.

Keywords: Data driven control, Predictive control for linear systems, Estimation
Abstract: Data-driven control uses a past signal trajectory to characterise the input-output behaviour of a system. Willems’ lemma provides a data-based prediction model allowing a control designer to bypass the step of identifying a state- space or transfer function model. This paper derives a more parsimonious formulation of Willems’ lemma that separates the model into initial condition matching and predictive control design parts. This avoids the need for regularisers in the predictive control problem that are found in other data-driven predictive control methods. In the noise-free model data case it also gives a closed form expression for the optimal (minimum variance) unbiased predictor of the future output trajectory. When used for predictive control the resulting controller is equivalent to Subspace Predictive Control in some cases. Simulation comparisons illustrate very good control performance even in the non-idealised case of noisy model data trajectories.

Keywords: Nonlinear systems, Game theory
Abstract: The well-known replicator equation in evolutionary game theory describes how population-level behaviors change over time when individuals make decisions using simple imitation learning rules. In this paper, we study evolutionary dynamics based on a fundamentally different class of learning rules known as logit learning. Numerous previous studies on logit dynamics provide numerical evidence of bifurcations of multiple fixed points for several types of games. Our results here provide a more explicit analysis of the logit fixed points and their stability properties for the entire class of two-strategy population games -- by way of the r-Lambert function. We find that for Prisoner's Dilemma and anti-coordination games, there is only a single fixed point for all rationality levels. However, coordination games exhibit a pitchfork bifurcation: there is a single fixed point in a low-rationality regime, and three fixed points in a high-rationality regime. We provide an implicit characterization for the level of rationality where this bifurcation occurs. In all cases, the set of logit fixed points converges to the full set of Nash equilibria in the high rationality limit.

Keywords: Game theory, Reinforcement learning
Abstract: Asymmetric information stochastic games (AISGs) arise in many complex socio-technical systems, such as cyber-physical systems and IT infrastructures. Existing computational methods for AISGs are primarily offline and can not adapt to equilibrium deviations. Further, current methods are limited to particular information structures to avoid belief hierarchies. Considering these limitations, we propose conjectural online learning (COL), an online learning method under generic information structures in AISGs. COL uses a forecaster-actor-critic (FAC) architecture, where subjective forecasts are used to conjecture the opponents' strategies within a lookahead horizon, and Bayesian learning is used to calibrate the conjectures. To adapt strategies to nonstationary environments based on information feedback, COL uses online rollout with cost function approximation (actor-critic). We prove that the conjectures produced by COL are asymptotically consistent with the information feedback in the sense of a relaxed Bayesian consistency. We also prove that the empirical strategy profile induced by COL converges to the Berk-Nash equilibrium, a solution concept characterizing rationality under subjectivity. Experimental results from an intrusion response use case demonstrate COL's faster convergence over state-of-the-art reinforcement learning methods against nonstationary attacks.

Keywords: Mean field games, Game theory, Markov processes
Abstract: In many real-world large-scale decision problems, self-interested agents have individual dynamics and optimize their own long-term payoffs. Important examples include the competitive access to shared resources (e.g., roads, energy, or bandwidth) but also non-engineering domains like epidemic propagation and control. These problems are natural to model as mean-field games. Existing mathematical formulations of mean field games have had limited applicability in practice, since they require solving non-standard initial-terminal value problems that are tractable only in limited special cases. In this letter, we propose a novel formulation, along with computational tools, for a practically relevant class of Dynamic Population Games (DPGs), which correspond to discrete-time, finite-state-and-action, stationary mean-field games. Our main contribution is a mathematical reduction of Stationary Nash Equilibria (SNE) in DPGs to standard Nash Equilibria (NE) in static population games. This reduction is leveraged to guarantee the existence of a SNE, develop an evolutionary dynamics-based SNE computation algorithm, and derive simple conditions that guarantee stability and uniqueness of the SNE. We provide two examples of applications: fair resource allocation with heterogeneous agents and control of epidemic propagation.

Open source software for SNE computation: https://gitlab. ethz.ch/elokdae/dynamic-population-games

Keywords: Mean field games, Stochastic optimal control, Game theory
Abstract: In a regular mean field game (MFG), the agents are assumed to be insignificant, they do not realize their effect on the population level and this may result in a phenomenon coined as the Tragedy of the Commons by the economists. However, in real life this phenomenon is often avoided thanks to the underlying altruistic behavior of (all or some of the) agents. Motivated by this observation, we introduce and analyze two different mean field models to include altruism in the decision making of agents. In the first model, mixed individual MFGs, there are infinitely many agents who are partially altruistic (i.e., they behave partially cooperatively) and partially non-cooperative. In the second model, mixed population MFGs, one part of the population behaves cooperatively and the remaining agents behave non-cooperatively. Both models are introduced in a general linear quadratic framework for which we characterize the equilibrium via forward backward stochastic differential equations. Furthermore, we give explicit solutions in terms of ordinary differential equations, and prove the existence and uniqueness results.

Keywords: Game theory, Learning, Optimal control
Abstract: Mirror play (MP) is a well-accepted primal-dual multi-agent learning algorithm where all agents simultaneously implement mirror descent in a distributed fashion. The advantage of MP over vanilla gradient play lies in its usage of mirror maps that better exploit the geometry of decision domains. Despite extensive literature dedicated to the asymptotic convergence of MP to equilibria, the understanding of the finite-time behavior of MP before reaching equilibria is still rudimentary. To facilitate the study of MP's non-equilibrium performance, this work establishes an equivalence between MP's finite-time primal-dual path (mirror path) in monotone games and the closed-loop Nash equilibrium path of a finite-horizon differential game, referred to as mirror differential game (MDG). Our construction of MDG rests on the Brezis-Ekeland variational principle, and the stage cost functional for MDG is Fenchel coupling between MP's iterates and associated gradient updates. The variational interpretation of the mirror path in static games as the equilibrium path in MDG holds in deterministic and stochastic cases. Such a variational interpretation translates the non-equilibrium studies of learning dynamics into a more tractable equilibrium analysis of dynamic games, as demonstrated in a case study on the Cournot game, where MP dynamics corresponds to a linear quadratic game.

Keywords: Game theory, Agents-based systems, Randomized algorithms
Abstract: This paper constructs an algorithmic framework for adaptively achieving the mechanism design objective, finding a mechanism inducing socially optimal Nash equilibria, without knowledge of the utility functions of the agents. We consider a probing scheme where the designer can iteratively enact mechanisms and observe Nash equilibria responses. We first derive necessary and sufficient conditions, taking the form of linear program feasibility, for the existence of utility functions under which the empirical Nash equilibria responses are socially optimal. Then we utilize this to construct a loss function with respect to the mechanism, and show that its global minimization occurs at mechanisms under which Nash equilibria system responses are also socially optimal. We develop a simulated annealing-based gradient algorithm and prove that it converges in probability to this set of global minima, thus achieving adaptive mechanism design.

Keywords: Data driven control, Observers for Linear systems, Linear systems
Abstract: In this paper we investigate the existence and the design of delayed unknown-input observers (d-UIOs) via a data- driven approach, by extending some recent results obtained in (Disaro' and Valcher, 2023) and (Turan and Ferrari-Trecate, 2022). Necessary and sufficient conditions for the existence of such observers are also related to the concept of data informativity introduced by van Waarde, Eising and co-authors in (vanWaarde et al., 2020) and subsequent works, thus providing a clear overall picture of how several concepts and conditions available in the literature and pertaining UIO design are mutually related.

Keywords: Automata, Data driven control, Hybrid systems
Abstract: In this paper, we introduce a data-driven frame-work for synthesizing controllers that enforce properties expressed by so-called ℓ universal co-Büchi automata (ℓ-UCA) over control systems with finite input sets and unknown mathematical models. The proposed framework leverages the notion of co-Büchi control barrier certificates (CBC). These certificates, together with their corresponding controllers, guarantee that a region in the state set is visited finitely often as the system evolves, limiting visits to at most ℓ times. The CBC is defined over a domain that augments the system and the ℓ-UCA, incorporating a counter variable to track the number of visits to the accepting states of ℓ-UCA. However, constructing these CBCs typically requires precise knowledge of the dynamics of the system, which is often unavailable in real-world applications. Therefore, we propose a data-driven scheme where we initially formulate the CBC conditions as a robust optimization program (ROP). Since the unknown model appears in some of the ROP constraints, we employ sampled data points collected from the system’s trajectories to formulate a scenario optimization program (SOP) associated with the ROP. By solving the corresponding SOP, we construct CBCs and controllers that enforce ℓ-UCA properties for the unknown system with a formal correctness guarantee. The efficacy of our data-driven approach is demonstrated by applying it to a three-tank system whose dynamics is assumed to be unknown.

Keywords: Variable-structure/sliding-mode control, Data driven control
Abstract: In this paper, in light of the recent advances in direct data-driven control, a novel approach for the design of integral sliding mode control (ISMC) in the case of unknown model of the plant is devised. The proposed data-driven integral sliding mode control (DD-ISMC) relies on the so-called virtual reference feedback tuning (VRFT) approach to select the ideal control component of the classical ISMC law. The VRFT enables the selection of the ideal controller by exclusively exploiting data from experiments, through the solution of a global model-reference optimization problem. Then, the reference model exploited by the VRFT approach is employed in the design of the integral sliding variable, in place of the unknown nominal model of the plant. In the paper, the proposal is theoretically analyzed, and its effectiveness is illustrated in simulation.

Keywords: Data driven control, Fault detection, Observers for Linear systems
Abstract: In this paper we propose a data-driven approach to the design of a residual generator, based on a dead-beat unknown-input observer, for linear time-invariant discrete-time state-space models, whose state equation is affected both by disturbances and by actuator faults. We first review the model-based conditions for the existence of such a residual generator, and then prove that under suitable assumptions on the collected historical data, we are both able to determine if the problem is solvable and to identify the matrices of a possible residual generator. We propose an algorithm that, based only on the collected data (and not on the system description), is able to perform both tasks. An illustrating example concludes the paper.

Keywords: Robust control, Data driven control, Predictive control for linear systems
Abstract: This work proposes a robust data-driven tube-based zonotopic predictive control (TZPC) approach for discrete-time linear systems, designed to ensure stability and recursive feasibility in the presence of bounded noise. The proposed approach consists of two phases. In an initial learning phase, we provide an over-approximation of all models consistent with past input and noisy state data using zonotope properties. Subsequently, in a control phase, we formulate an optimization problem, which by integrating terminal ingredients is proven to be recursively feasible. Moreover, we prove that implementing this data-driven predictive control approach guarantees robust exponential stability of the closed-loop system. The effectiveness and competitive performance of the proposed control strategy, compared to recent data-driven predictive control methods, are illustrated through numerical simulations.

Keywords: Formal Verification/Synthesis, Data driven control, Stochastic systems
Abstract: This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates. The first step is learning the dynamics of the system via Gaussian process (GP) regression and obtaining probabilistic errors for this estimate. Then, we develop an algorithm for constructing piecewise stochastic barrier functions to find a maximal permissible strategy set using the learned GP model, which is based on sequentially pruning the worst controls until a maximal set is identified. The permissible strategies are guaranteed to maintain probabilistic safety for the true system. This is especially important for learning-enabled systems, because a rich strategy space enables additional data collection and complex behaviors while remaining safe. Case studies on linear and nonlinear systems demonstrate that increasing the size of the dataset for learning the system grows the permissible strategy set.

Keywords: Delay systems, Agents-based systems, Stability of linear systems
Abstract: In this paper, we study a Proportional-Retarded (PR) consensus protocol in a multiagent system (MAS) with single integrator dynamics where the communication network is described by a mixed graph. As previous work on this problem focused on particular systems that generate either real or complex eigenvalues of the graph Laplacian, the main contribution of this paper is providing analytical PR tuning rules for the general case, where complex and real eigenvalues originate together from the mixed graph. Validations through simulations and experiments in a robotic application are also presented.

Keywords: Delay systems, Linear systems, Extremum seeking
Abstract: We propose a novel stability analysis for linear systems with unknown control directions, focusing on stabilization through extremum seeking to minimize a Lyapunov function. Our approach draws inspiration from Lie bracket systems, employing a transformation using time-delay analysis to convert the closed-loop system into a nominal time-delay system. Leveraging techniques from Input-to-State Stability (ISS), we provide a proof of semiglobal practical asymptotic stability. Compared to the preceding analysis based on Lie bracket systems, the use of time-delay methods transforms intricate mathematical discussions and proofs into a structured computational framework, facilitating a more intuitive understanding. Also, we propose a method for selecting controller parameters and can provide a more comprehensive explanation for the current high-gain parameter choices. Finally, we present a new control parameter to reduce the requirements of the frequency of the sinusoidal signals.

Keywords: Delay systems, Optimal control, Stability of linear systems
Abstract: We characterize the turnpike property of optimal control constrained by delay equations by means of two verifiable algebraic conditions, which are equivalent to the exponential stabilizability and detectability of the delay system. Our work extends the existing finite dimensional results to delay equations. Numerical simulations validate the theoretical findings of the paper.

Keywords: Delay systems, Nonlinear output feedback, Sampled-data control
Abstract: In this paper, the stabilization problem of nonlinear systems with state delays by means of event-triggered observer-based quantized sampled-data controllers is studied. By exploiting an emulation approach, sufficient conditions are provided ensuring the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that the related digital closed-loop system, exploiting an event-triggered mechanism to update the control law only when necessary, is semi-globally practically stable with arbitrarily small neighbourhood of the origin. The theory of the stabilization in the sample-and-hold sense is used to prove the results. In the theory here developed, time-varying sampling periods and the non-uniform quantization of both input/output channels are allowed. An application concerning a continuous stirred tank reactor with recycle is studied to show the potential of the approach.

Keywords: Delay systems, Stability of linear systems, Computer-aided control design
Abstract: Systems governed by delay differential equations (DDEs) are distinguished by having infinite-dimensional dynamics. This key feature in the context of linear time-delayed systems reflects itself in the associated operator eigenvalue problem. Moreover, in numerous applications including power systems and machining, an accurate description leads to time-periodic models. To address the stabilization problem of such systems, we minimize the spectral radius of the discretized monodromy operator. We propose two approaches to impose smoothness on the designed periodic feedback gain. In our first approach, we limit the total variation of the feedback gain and impose approximate periodicity of the controller gain by adding regularization terms to the cost function. Conversely, in the second approach, the feedback gain is constrained to be characterized by a finite number of harmonics of its Fourier series representation; hence, smoothness and periodicity are explicitly encoded in the controller parametrization. We develop computationally tractable formulations for the derivative of the spectral radius with respect to the controller parameters, which are employed by the optimization algorithm. Finally, through a case study involving a milling machine, we validate the efficacy and applicability of the presented work.

Keywords: Robust control, Delay systems, Networked control systems
Abstract: With increasing control applications in large-scale distributed and networked systems, the impact of uncertain time delay is ever-increasing. This paper proposes the use of a novel non-parametric Integral Quadratic Constraint (IQC) to achieve robustness against uncertain time delays. The proposed IQC is then integrated into a frequency-domain controller synthesis approach for robustness guarantees. Numerical simulation of an active suspension system within an intra-car network shows the effectiveness of the proposed method.

Keywords: Networked control systems, Output regulation, Hierarchical control
Abstract: In this article, we propose a data-driven solution to the output containment control problem of multiagent systems characterized by heterogeneous and unknown dynamics. The proposed data-driven scheme is hierarchical, which includes a network layer and a physical layer, bypassing the traditional modeling exercise and eliminating the need for explicit state-space models. In the network layer, a fully distributed observer without knowing the dynamics of leaders is designed to generate a containment trajectory. A data-driven approach based on data sampled from an auxiliary system is developed to overcome the dependence on the explicit state-space models for design of control gains. This paves the way for deriving a data-driven solution to the regulator equation, which is derived by employing the data informativity condition and relevant data in the physical layer. The results demonstrate that the closed-loop system is asymptotically stable, and the regulated output containment converges to zero. Compared to generic model-based hierarchical schemes, the assumptions that the system matrices are completely known and homogeneous on system dynamics can be relaxed.

Keywords: Networked control systems, Predictive control for linear systems, Robust control
Abstract: Robustly compensating network constraints such as delays and packet dropouts in networked control systems is crucial for remotely controlling dynamical systems. This work proposes a novel prediction consistent method to cope with delays and packet losses as encountered in UDP-type communication systems. The augmented control system preserves all properties of the original model predictive control method under the network constraints. Furthermore, we propose to use linear tube MPC with the novel method and show that the system converges robustly to the origin under mild conditions. We illustrate this with simulation examples of a cart pole and a continuous stirred tank reactor.

Keywords: Networked control systems, Robust adaptive control, Stochastic systems
Abstract: We propose a unified framework for robustly and adaptively stabilizing large-scale networked uncertain Markovian jump linear systems (MJLS) under external disturbances and mode switches that can change the network's topology. Adaptation is achieved by using minimal information on the disturbance to identify modes that are consistent with observable data. Robust control is achieved by extending the system level synthesis (SLS) approach, which allows us to pose the problem of simultaneously stabilizing multiple plants as a two-step convex optimization procedure. Our control pipeline computes a likelihood distribution of the system's current mode, uses them as probabilistic weights during simultaneous stabilization, then updates the likelihood via Bayesian inference. Because of this ``softer’’ probabilistic approach to robust stabilization, our control pipeline does not suffer from abrupt destabilization issues due to changes in the system's true mode, which were observed in a previous method. Separability of SLS also lets us compute localized robust controllers for each subsystem, allowing for network scalability; we use several information consensus methods so that mode estimation can also be done locally. We apply our algorithms to disturbance-rejection on two sample dynamic power grid networks for numerical validation.

Keywords: Networked control systems, Uncertain systems, Nonlinear systems
Abstract: For a class of nonlinear networked control systems (NCSs), we consider designing a control architecture to render controllers constructed via the prescribed performance control (PPC) methodology robust, against the presence of control input data losses, while preserving, to a large extend, the performance attributes achieved in their absence. To succeed the aforementioned, the PPC designed controller is smoothly reconfigured to a safe mode of operation, whenever the NCS states evolve close to the user-defined performance bounds. The latter scheme effectively permits performance bounds crossing, thus avoiding the appearance of PPC-instability, attributed to its operational philosophy that resembles barrier functions in constraint optimization. Performance bounds crossing is undoubtedly highly expected, as during the data loss phenomenon the NCS practically operates in open-loop. Even though the duration of the data loss phenomenon and its appearance are unknown, no detection mechanism is incorporated to acquire such knowledge. Simulation studiesclarify and verify the theoretical findings.

Keywords: Networked control systems
Abstract: This paper presents a distinct framework for the design of an observer-based feedback control strategy for networked control systems (NCS) affected by unknown time-varying transmission delays larger than the sampling time Td. The pivotal element of the proposed strategy lies in the configuration of network nodes and a buffering mechanism which enable state estimation at the controller's side using observer strategies not initially designed for NCS. Consequently, the Luenberger-type observer can be designed independently from the utilized network, thus leading to a substantial reduction in the complexity typically associated with uncertain and time-varying NCS. Furthermore, the proposed framework allows the strategic incorporation of predicted state estimates in the controller design. This mitigates the effect of the network delay by reducing it by Td, which can significantly improve the system performance, as demonstrated in a simulation example.

Keywords: Networked control systems
Abstract: In this paper, we address remote state estimation of a continuous-time multi-output linear time-invariant system over power-constrained parallel Gaussian channels with feedback from decoder to encoder. We establish necessary and sufficient conditions on power constraints for designing a mean square stable remote estimator, considering both individual subchannel and total channel power constraints. The conditions involve the interplay between the topological entropies of cyclic subsystems of the plant and the communication channels. We also give design method of mean square stable remote estimator.

Keywords: Distributed control, Control system architecture
Abstract: Many multiagent system applications necessitate each agent to separately visit a specific location in space at a particular moment in time (i.e., spatiotemporal points). To this end, we propose a finite-time distributed control protocol over directed acyclic graphs that addresses the problem of multiagent placement at spatiotemporal points. In particular, we demonstrate that the proposed protocol can drive the trajectories of agents to their spatiotemporal points at different user-defined times by employing methods ranging from time transformation to input-to-state stability and Lyapunov stability. To show the efficacy of the proposed protocol, we also give two illustrative numerical examples.

Keywords: Distributed control, Optimization, Linear systems
Abstract: In this paper, we investigate the distributed optimization problem for heterogeneous linear multi-agent systems with unknown disturbances. By applying the primal-dual method and the time-scale separation technique, a distributed dynamic controller without using any disturbance information is proposed. Based on the optimal condition, the relationship between the optimal solution and the equilibrium point of the system is established, and it is shown that the distributed optimization problem is solved provided that the closed-loop system is stable. Then, inspired by the nonsingular perturbation analysis, it is proved that the closed-loop system is exponential input-to-state stable with respect to the derivative of the disturbance. Numerical examples are provided to illustrate the theoretical results.

Keywords: Distributed control, Cooperative control, Networked control systems
Abstract: This paper exploits the Negative Imaginary systems theory to develop a novel affine formation manoeuvre control framework for multi-agent systems using dynamic output feedback. The framework begins by deriving affine transformation matrices for leader agents, enabling dynamic adjustments from the nominal formation to the target formation. An output-feedback distributed Strictly Negative Imaginary control law is then proposed for follower agents to achieve affine formation manoeuvres. Unlike existing affine formation manoeuvre control schemes, which typically rely on full-state feedback (including both position and velocity measurements), the proposed approach requires only relative position measurements. In addition, it offers more freedom in choosing a dynamic controller transfer function, thereby improving formation tracking performance. A comprehensive simulation case study is provided to test the effectiveness of the proposed output-feedback-based affine formation manoeuvre control framework.

Keywords: Distributed control, Cooperative control, Constrained control
Abstract: This paper studies the zone allocation and preservation problem in multiagent systems. Specifically, a new state transformation method predicated on a diffeomorphic map is first proposed to make the solution to this problem feasible. Building upon the transformed multiagent system, a new distributed adaptive control protocol is then presented to ensure that an agent approaches a command available to the leader agent(s) when this command enters its zone and otherwise the same agent maintains proximity to this command while preserving its own zone. In addition to the presented system-theoretical results, two illustrative numerical examples are also given to demonstrate the efficacy of the overall architecture.

Keywords: Distributed control, Network analysis and control, Resilient Control Systems
Abstract: A critical edge is an edge whose removal results in the associated undirected network becoming disconnected. Identifying these critical edges and enhancing the corresponding edge connectivity is critical for achieving robustness in network connectivity. While existing methodologies are effective, they are centralized and rely on global information, which makes them not scalable with respect to the network size or its implementation. To address these shortcomings, a fully distributed approach is introduced in this paper to identify all the critical edges within an undirected network without requiring a central coordinating authority. Computationally, the proposed method has a complexity of mathcal{O}(n), where n is the number of nodes, which is more efficient when compared to the centralized approaches. Furthermore, the proposed method can be used to incrementally increase the network's edge connectivity to 2, thus addressing the network's most vulnerable edges.

Keywords: Distributed control, Optimal control, Networked control systems
Abstract: This paper focuses on the optimal design of a high-order consensus protocol applied to agents modeled with multiple integrators. Concretely, the problem addressed amounts to determining the optimal values for the coupling gains and for the weights of the directed graph edges, considering a given communication topology. An LQR-based cost function is proposed, which is obtained from the typical LQR cost function by taking the expectation over the initial system state, and a second-order method is then applied to determine the optimal parameters for the high-order consensus protocol. To that end, the evaluation of the cost and its derivatives is first described, to account for the particularities of the consensus problem, and the application of a truncated Newton method to the considered problem is then presented. Finally, the efficacy of the proposed approach is illustrated with examples.

Keywords: Optimization, Optimization algorithms
Abstract: We consider the mirror-prox algorithm for solving monotone Variational Inequality (VI) problems. As the mirror-prox algorithm is not practically implementable, except in special instances of VIs (such as affine VIs), we consider its implementation with Popov method updates. We provide convergence rate analysis of our proposed method for a monotone VI with a Lipschitz continuous mapping. We establish a convergence rate of O(1/t), in terms of the number t of iterations, for the dual gap function. Simulations on a two player matrix game corroborate our findings.

Keywords: Optimization, Stochastic systems, LMIs
Abstract: Recently a moment-sum-of-squares hierarchy for exit location estimation of stochastic processes has been presented. When restricting to the special case of the unit ball, we show that the solutions approach the optimal value by a super-polynomial rate. To show this result we state a new effective Positivstellensatz on the sphere with quadratic degree bound based on a recent Positivstellensatz for trigonometric polynomials on the hypercube and pair it with a recent effective Positivstellensatz on the unit ball. At the present example, we aim to highlight the effectiveness of specialized Positivstellensätze for the moment-SoS hierarchy and their interplay with problem intrinsic properties.

Keywords: Optimization, Transportation networks, Identification
Abstract: The behavior of cyclists when choosing the path to follow along a road network is not uniform. Some of them are mostly interested in minimizing the travelled distance, but some others may also take into account other features such as safety of the roads or level of pollution, including carbon dioxide emission by the cars or even the noise pollution. Identifying the different groups of users, estimating the numerical consistency of each of these groups, and reporting the weights assigned by each group to different characteristics of the road network, is quite relevant. Indeed, when decision makers need to assign some budget for infrastructural interventions, they need to know the impact of their decisions, and this is strictly related to the way users perceive different features of the road network. In this paper, we propose an optimization approach to detect the weights assigned to different road features by various user groups, leveraging knowledge of the true paths followed by them, accessible, for example, through data collected by bike-sharing services.

Keywords: Algebraic/geometric methods, Optimization, Data driven control
Abstract: We propose a new geometric-optimization framework for maximum likelihood estimation of moving-average models. Instead of optimizing directly over the moving average parameters, we formulate the estimation problem over the reflection coefficients and show how to perform gradient descent over a reflection-coefficient manifold. This choice leads to simpler expressions in the objective function and in the constraints, which can yield more convenient expressions for theoretical analysis. Finally, we numerically implement and compare the proposed estimation schemes in the reflection coefficients to those based on moving-average parmeterizations. We show that our novel formulation works in practice and yields equivalent solutions to currently employed formulations.

Keywords: Finance, Identification, Optimization
Abstract: This study considers a practically important financial transactions allocation problem originated from interbank market. To achieve fairness and sparsity at the same time, we formulate the problem as a non-linear sparse optimization problem. A novel two-step algorithm that (1) finds the most sparse but not necessarily fair solution, (2) then utilizes iterative local adjustments to cope with non-linear fairness constraint is proposed. An adaptive parameter selection method to improve efficiency, avoiding time-consuming parameter search is devised. We provide theoretical guarantees that the two-step algorithm along with the adaptive parameter selection can always find a feasible solution with as much sparsity as possible. The effectiveness and efficiency of the algorithm is demonstrated by conducting empirical analysis on a real dataset from financial industry.

Keywords: Optimization algorithms, Variational methods, Distributed control
Abstract: Distributed decision problems feature a group of agents that can only communicate over a peer-to-peer network, without a central memory. In applications such as network control and data ranking, each agent is only affected by a small portion of the decision vector: this sparsity is typically ignored in distributed algorithms, while it could be leveraged to improve efficiency and scalability. To address this issue, our recent paper introduces Estimate Network Design (END), a graph theoretical language for analysis and design of distributed iterations. END methods can be tuned to exploit the sparsity of specific problem instances, reducing communication overhead and minimizing redundancy, yet without requiring case-by-case convergence analysis. In this paper, we showcase the flexibility of END in the context of distributed optimization. In particular, we study the sparsity-aware version of many established algorithms, including ADMM, AugDGM and Push-Sum DGD. Simulations on an estimation problem in sensor networks demonstrate that END algorithms can boost convergence speed and greatly reduce the communication cost.

Keywords: Observers for nonlinear systems, Estimation, Nonlinear systems
Abstract: This work presents a triangular form that is shown to be canonical for constructible discrete-time systems. For this form, we propose an observer that resembles the well-known high-gain observer in continuous time. This discrete-time observer exhibits exponential stability if its dynamics are picked sufficiently fast, as well as robustness against disturbances and measurement noise. We also study how to transform general discrete-time systems into this constructible form, under constructibility and backward distinguishability, and recover convergence in the given coordinates. Application to an electrical machine with comparison to the discretized version of the continuous-time high-gain observer illustrates our methods.

Keywords: Observers for nonlinear systems, Nonlinear systems, Estimation
Abstract: This paper introduces the concept of theta-invariant systems, which can be regarded as a generalization of symmetry-preserving systems. This new property enables the re-scaling of time coordinates while dilating the solutions. We discuss some of the implications of this concept for observer design and adapt the results about the existence of a canonical representation for an observer obtained in the context of invariant systems. Furthermore, we demonstrate how our generalization can be used to construct an observer design framework for homogeneous systems with arbitrary degrees.

Keywords: Observers for nonlinear systems, Lyapunov methods, Stability of nonlinear systems
Abstract: This paper addresses the design of nonlinear quasi-unknown input observers for systems that can be interpreted as an interconnection of a linear dynamical subsystem with a static nonlinear feedback subject to additive perturbations. As assumed classically an exosystem is considered describing the dynamics of the perturbation, meaning that the dynamical mechanisms giving rise to the perturbation are sufficiently well known but the underlying initial condition is unknown. Extending classical results based on the Sylvester equation, and combining them with well-established dissipativity concepts and design methods, a new approach for quasi-unknown input observer design is obtained. It simplifies previous work on general unknown input observer design by exploiting the structural knowledge about the exosystem, without extending the state dimension. The approach is illustrated with numerical case examples.

Keywords: Observers for nonlinear systems, Lyapunov methods, Stability of hybrid systems
Abstract: This paper examines the dynamic properties of a hybrid momentum observer for mechanical systems, extending the previously-reported results. The observer estimates the momentum vector from measurements of the configuration vector and is shown to be input-to-state stable with respect to external perturbations. In the absence of external perturbation the observer is shown to be globally exponentially stable, converging at a user-controlled rate. The observer is constructed from a port-Hamiltonian representation of mechanical systems and exhibits a passivity property with respect to an input-output port that can be utilised for subsequent control design. The theoretical results are demonstrated via numerical simulation on a 2-link vertical manipulator.

Keywords: Observers for nonlinear systems
Abstract: This paper discusses input properties allowing observer design for a class of nonlinear systems which are not uniformly observable. This refines the notion of {em locally regular inputs} for which an observer solution is already available, based on combined Kalman and high gain techniques. In particular, a link with standard regularly persistent inputs is highligthed. Simulation examples are provided as an illustration.

Keywords: Observers for nonlinear systems, Uncertain systems, Estimation
Abstract: This paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to propagate CZs through nonlinear functions, which is normally done using conservative linearization techniques. The new propagation method provides better approximations than those resulting from linearization procedures, leading to significant improvements in the computation of reachable sets in comparison to other CZ methods from the literature. Numerical examples highlight the advantages of the proposed algorithm.

Keywords: Systems biology, Hybrid systems, Biological systems
Abstract: This contribution explores mechanisms that regulate the dynamics of single-cell size, maintaining equilibrium around a target set point. Using the formalism of Stochastic Hybrid Systems (SHS), we consider continuous exponential growth in cell size (as determined by volume/mass/surface area). This continuous-time evolution is interspersed by cell division events that occur randomly as per a given size-dependent rate, and upon division, only one of the two daughter cells is tracked. We show that a size-independent division rate does not provide cell size homeostasis, in the sense that the variance in cell size increases unboundedly over time. Next, we consider a division rate proportional to cell size that yields the adder size control observed in several bacteria in which a constant size is added on average between birth and division regardless of the newborn size. For this scenario, we obtain exact formulas for the steady-state moments (mean, variance, and skewness) of cell size. Expanding the SHS model, we explore a biologically relevant scenario where the time between successive division events is further divided into multiple discrete stages with size-dependent stage transitions. Exact moment computations demonstrate that increasing the number of stages reduces cell size variability (noise). We also find formulas considering uneven size partitioning between daughters during division, and where the division rate follows a power law of the cell size leading to deviations from adder size control. This work provides a method for estimating model parameters from observed cell size distributions and enhances our understanding of mechanisms underlying cell size regulation.

Keywords: Game theory, Biological systems, Cellular dynamics
Abstract: Stackelberg Evolutionary Game (SEG) theory models the interacting dynamics between a rational leader and a population of evolving followers, merging classical and evolutionary game theory. Although both methods are well-developed individually, the potential of SEG itself has not been appropriately recognized. Thus, in this paper we propose a novel eco-evolutionary model with resource mutualism and competition and we introduce a control framework based on SEGs, to steer the eco-evolutionary dynamics of followers at will. As a case study, we consider the treatment of cancer, where tumour cells are the followers that evolve in response to changes in the tumour micro-environment (and thus on available resources) and to the medical therapy, where the physician is the leader. An interesting aspect of this approach is that the objective function can be tailored according to the goal, e.g. jointly balancing tumour size, developed resistance, and toxicity of therapy, to ensure maximum quality of life for the patient. Simulations confirm the effectiveness and the potential of the proposed approach.

Keywords: Biological systems, Systems biology, Switched systems
Abstract: The evolution of antibiotic resistance in bacteria is a significant public health risk influenced by several factors. Switched systems can abstract the evolutionary aspects driven by antibiotic use in a given population. However, mathematical models are not perfect, and uncertain dynamics remain. Based on a set theory approach, our main result is the development of an algorithm to demonstrate the stabilizability of a robust invariant set for the uncertain switched system. The algorithm also provides a characterization of invariant regions for switched systems under perturbations. Our findings provide insights into how to incorporate uncertainties in switched systems. This paves the way for selecting antibiotics to tackle drug-resistant infections.

Keywords: Biological systems, Systems biology, Optimal control
Abstract: For a general class of epidemiological models with an arbitrary number of infected and non-infected compartments, we formulate an optimal vaccination control problem to minimise the number of infections and the cost of vaccination. We show that the problem can be solved efficiently with the sequential quadratic Hamiltonian (SQH) scheme, which we apply to the optimal control of epidemics for the first time and for which we prove rigorous global convergence guarantees in the case of a smooth cost functional. Our numerical simulations show that SQH outperforms the current state-of-the-art numerical scheme in mathematical epidemiology: its convergence can be guaranteed regardless of the initialisation, it is faster and it is also applicable when the cost functional is non-smooth.

Keywords: Optimal control, Biological systems, Stochastic systems
Abstract: We consider the problem of finding optimal policies that mitigate the effects of an epidemic. We develop computational tools for finding such policies for broad classes of stochastic epidemic models and investigate various features of such policies. In particular, we observe that optimal policies are predominantly constant for epidemics where the mitigation measures are associated with the infected population.

Keywords: Systems biology, Biological systems, Optimal control
Abstract: Agricultural production of annual crops is often hampered by annual weeds, which compete with planted crops and persist through the collection of dormant seeds in the soil called the weed seed bank. Conventional weed management relies heavily on chemical herbicides, which are not sustainable. A complementary method that reduces the need for herbicides is ‘cultural control’, in which the crop rotation is designed in part to manage the weed population. We propose a methodology that optimizes the crop rotation, here defined as periodic crop planting densities, subject to periodic weed dynamics. We adopt a well-established model of discrete-time annual weed seed bank dynamics with crop planting density inputs, and show that any periodic weed seed bank trajectory corresponding to a periodic crop rotation is globally exponentially stable. This guarantees convergence to the optimal periodic trajectory obtained by solving a nonlinear optimal control problem with periodic constraints, which we formulate as a nonlinear program.

Keywords: Hybrid systems, Stability of hybrid systems, Lyapunov methods
Abstract: This note explores the QSR-dissipativity of a class of hybrid dynamical systems. We first revisit and extend some existing definitions of dissipativity for hybrid systems. Subsequently, we explore some results regarding the relations between the QSR-dissipativity property of one open hybrid subsystem and its stability. Next, we shift focus to studying the negative-feedback interconnection of two hybrid subsystems, deriving new results about the existence of storage functions guaranteeing that the interconnection between two individual QSR-dissipative hybrid subsystems remains QSR-dissipative in the presence of external input signals. Analyzing such interconnections of hybrid systems may be intricate due to the possibility of both synchronous and asynchronous jumps occurring among the two subsystems, as previously acknowledged by the existing literature.

Keywords: Hybrid systems, Stability of hybrid systems, Nonlinear systems
Abstract: This paper presents a framework that enables analytically shaping the transient behavior of nonlinear dynamical systems, including those with hybrid dynamics combining continuous-time and discrete-time evolution. Our results hinge on the interconnection of the original system with an exogenous dynamic gain system designed to induce a continuous-time deformation of hybrid time domains. Our approach provides conditions that ensure the original system’s stability properties without the dynamic gain are transferable under the continuous-time deformation to the full interconnected dynamics. We develop these results by leveraging tools from hybrid dynamical systems theory, and formulating an appropriate bijective map that relates the solution sets between the original and interconnected systems. To illustrate the approach, we present applications to gradient flow systems and momentum-based optimization techniques with resets, leveraging the framework to customize convergence rates for strictly convex objective functions.

Keywords: Hybrid systems, Switched systems, Nonlinear systems
Abstract: Many systems occurring in real-world applications, such as controlling the motions of robots or modeling the spread of diseases, are switched impulsive systems. To ensure that the system state stays in a safe region (e.g., to avoid collisions with obstacles), barrier functions are widely utilized. As the system dimension increases, deriving suitable barrier functions becomes extremely complex. Fortunately, many systems consist of multiple subsystems, such as different areas where the disease occurs. In this work, we present sufficient conditions for interconnected switched impulsive systems to maintain safety by constructing local barrier functions for the individual subsystems instead of a global one, allowing for much easier and more efficient derivation. To validate our results, we numerically demonstrate its effectiveness using an epidemiological model.

Keywords: Hybrid systems, Observers for nonlinear systems, Switched systems
Abstract: This work proposes an observer design for general hybrid systems, whose outputs are continuous at jumps, and whose jump times are unknown. Inspired by the gluing approach and the Kravaris-Kazantzis/Luenberger (KKL) paradigm, we present conditions under which the hybrid dynamics can be transformed into continuous-time dynamics that take the form of a filter of the output and for which an observer can be readily designed. The possibility of recovering the estimate in the original coordinates is guaranteed outside of the jump times, under a mild backward distinguishability condition that ensures injectivity away from the jump set, assuming sufficient regularity of the transformation. Contrary to previous gluing results, the design of the gluing transformation and the observer is systematic with a well-identified target form of dynamics. While the theoretical conditions are validated on an academic bouncing ball system, we illustrate our method on an application concerning dry friction parameter estimation in the presence of stick-slip, using neural networks to learn a numerical model of the inverse transformation.

Keywords: Hybrid systems, Stability of hybrid systems, Switched systems
Abstract: This paper addresses stabilization of switched affine systems relying on polytopic Lyapunov functions. Several methods have been developed for this family of systems, most of them based on quadratic Lyapunov functions for an average system. An immediate conjecture is that replacing such a function with one of polytopic type should also achieve stable behavior. We disprove this conjecture on a strategy that employs the hybrid systems formalism, by means of examples. Specifically, we show that for a given switching strategy based on a quadratic Lyapunov function, naïvely replacing this function by its polytopic counterpart does not guarantee the same stability properties, and that this happens even in the case of dwell-time switching. We deeply investigate such a problem, identify the conditions that prevent asymptotic stability, and give some directions on how to avoid them to ensure stability. These results are finally illustrated in simulation.

Keywords: Hybrid systems, Switched systems, Networked control systems
Abstract: This paper addresses the cooperative output regulation via error feedback for a class of switched linear multi-agent systems with asynchronous intermittent transmissions. A leader-follower multi-agent scheme is proposed, where a virtual leader is modeled as an exosystem, and the followers are represented by a class of switched linear systems. A novel hybrid distributed control law is proposed, effectively ensuring leader synchronization. The approach allows heterogeneous agent dynamics, and the switching signal between subsystems is modeled in the hybrid framework. The stability and regulation of the multi-agent system with the hybrid distributed control law are analyzed as a complete system. The effectiveness of the contribution is demonstrated through an illustrative example.

Keywords: Optimal control, Adaptive systems, Machine learning
Abstract: In this paper, the evolution equation that defines the online critic for the approximation of the optimal value function is cast in a general class of reproducing kernel Hilbert spaces (RKHSs). Exploiting some core tools of RKHS theory, this formulation allows deriving explicit bounds on the performance of the critic in terms of the kernel and definition of the RKHS, the number of basis functions, and the location of centers used to define scattered bases. The performance of the critic is precisely measured in terms of the power function of the scattered basis used in approximations, and it can be used either in an a priori evaluation of potential bases or in an a posteriori assessments of value function error for basis enrichment or pruning. The most concise bounds in the paper describe explicitly how the critic performance depends on the placement of centers, as measured by their fill distance in a subset that contains the trajectory of the critic.

Keywords: Optimal control, Machine learning, Optimization
Abstract: This paper brings the concept of ``optimism" to the new and promising framework of online Non-stochastic Control (NSC). Namely, we study how can NSC benefit from a prediction oracle of unknown quality responsible for forecasting future costs. The posed problem is first reduced to an optimistic learning with delayed feedback problem, which is handled through the Optimistic Follow the Regularized Leader (OFTRL) algorithmic family. This reduction enables the design of texttt{OptFTRL-C}, the first Disturbance Action Controller (DAC) with optimistic policy regret bounds. These new bounds are commensurate with the oracle's accuracy, ranging from mathcal{O}(1) for perfect predictions to the order-optimal mathcal{O}(sqrt{T}) even when all predictions fail. By addressing the challenge of incorporating untrusted predictions into online control, this work contributes to the advancement of the NSC framework and paves the way towards effective and robust learning-based controllers.

Keywords: Optimization algorithms, Agents-based systems, Machine learning
Abstract: In this paper, we focus on distributed learning over peer-to-peer networks. In particular, we address the challenge of expensive communications (which arise when e.g. training neural networks), by proposing a novel local training algorithm, LT-ADMM. We extend the distributed ADMM enabling the agents to perform multiple local gradient steps per communication round (local training). We present a preliminary convergence analysis of the algorithm under a graph regularity assumption, and show how the use of local training does not compromise the accuracy of the learned model. We compare the algorithm with the state of the art for a classification task, and in different set-ups. The results are very promising showing a great performance of LT-ADMM, and paving the way for future important theoretical developments.

Keywords: Optimization algorithms, Algebraic/geometric methods, Machine learning
Abstract: We consider direct policy optimization for the linear-quadratic Gaussian (LQG) setting. Over the past few years, it has been recognized that the landscape of dynamic output-feedback controllers of relevance to LQG has an intricate geometry, particularly pertaining to the existence of degenerate stationary points, that hinders gradient methods. In order to address these challenges, in this paper, we adopt a system-theoretic coordinate-invariant Riemannian metric for the space of dynamic output-feedback controllers and develop a Riemannian gradient descent for direct LQG policy optimization. We then proceed to prove that the orbit space of such controllers, modulo the coordinate transformation, admits a Riemannian quotient manifold structure. This geometric structure–that is of independent interest–provides an effective approach to derive direct policy optimization algorithms for LQG with a local linear rate convergence guarantee. Subsequently, we show that the proposed approach exhibits significantly faster and more robust numerical performance as compared with ordinary gradient descent.

Keywords: Optimization algorithms, Game theory, Machine learning
Abstract: This work focuses on the entropy-regularized independent natural policy gradient (NPG) algorithm in multi-agent reinforcement learning. In this work, agents are assumed to have access to an oracle with exact policy evaluation and seek to maximize their respective independent rewards. Each individual's reward is assumed to depend on the actions of all agents in the multi-agent system, leading to a game between agents. All agents make decisions under a policy with bounded rationality, which is enforced by the introduction of entropy regularization. In practice, a smaller regularization implies that agents are more rational and behave closer to Nash policies. On the other hand, with larger regularization agents tend to act randomly, which ensures more exploration. We show that, under sufficient entropy regularization, the dynamics of this system converge at a linear rate to the quantal response equilibrium (QRE). Although regularization assumptions prevent the QRE from approximating a Nash equilibrium (NE), our findings apply to a wide range of games, including cooperative, potential, and two-player matrix games. We also provide extensive empirical results on multiple games (including Markov games) as a verification of our theoretical analysis.

Keywords: Optimization algorithms, Optimal control, Machine learning
Abstract: The increasing reliance on numerical methods for controlling dynamical systems and training machine learning models underscores the need to devise algorithms that dependably and efficiently navigate complex optimization landscapes. Classical gradient descent methods offer strong theoretical guarantees for convex problems; however, they demand meticulous hyperparameter tuning for non-convex ones. The emerging paradigm of learning to optimize (L2O) automates the discovery of algorithms with optimized performance leveraging learning models and data -- yet, it lacks a theoretical framework to analyze convergence of the learned algorithms. In this paper, we fill this gap by harnessing nonlinear system theory. Specifically, we propose an unconstrained parametrization of all convergent algorithms for smooth non-convex objective functions. Notably, our framework is directly compatible with automatic differentiation tools, ensuring convergence by design while learning to optimize.

Keywords: Fluid flow systems, Distributed parameter systems, Stability of nonlinear systems
Abstract: Nonlinear convection, the source of turbulence in fluid flows, may hold the key to stabilizing turbulence by solving a specific cubic polynomial equation. We consider the incompressible Navier-Stokes equations in a two-dimensional channel. The tangential and normal velocities are assumed to be periodic in the streamwise direction. The pressure difference between the left and right ends of the channel is constant. Moreover, we consider no-slip boundary conditions, that is, zero tangential velocity, at the top and bottom walls of the channel, and normal velocity actuation at the top and bottom walls. We design the boundary control inputs to achieve global exponential stabilization, in the L2 sense, of a chosen Poiseuille equilibrium profile for an arbitrarily large Reynolds number. The key idea behind our approach is to select the boundary controllers such that they have zero spatial mean (to guarantee mass conservation) but non-zero spatial cubic mean. We reveal that, because of convection, the time derivative of the L2 energy of the regulation error is a cubic polynomial in the cubic mean of the boundary inputs. Regulation is then achieved by solving a specific cubic equation, using the Cardano root formula. The results are illustrated via a numerical example

Keywords: Distributed parameter systems, Traffic control, Lyapunov methods
Abstract: This paper studies the sampled-data distributed control problem for mixed traffic flow described by the Aw-Rascle-Zhang (ARZ) model, which consists of both manual and adaptive cruise control-equipped (ACC-equipped) vehicles. A group of stationary sensing devices provides spatially averaged state measurements over the sampling spatial intervals, and then the sampled-data distributed controller is designed as the time-gap setting of ACC-equipped vehicles based on the state measurements sampled in space and time. The closed-loop system is re-organized into an equivalent system containing a continuous time control loop and spatio-temporal sampling errors. Then sufficient conditions for ensuring exponential stability of the mixed traffic flow system are developed in terms of matrix inequalities, by employing the Lyapunov function method along with Wirtinger’s and Jensen’s inequalities in H1-norm. Finally, the effectiveness of the proposed method is verified by numerical simulations.

Keywords: Agents-based systems, Distributed parameter systems, Backstepping
Abstract: This paper introduces an innovative rotating encirclement control designed for parabolic Partial Differential Equation (PDE)-based multi-agent systems. The derivation of the PDE-based continuum multi-agent system model stems from techniques in flow system theory. The control strategy involves multi-step control within the domain and boundaries consisting of 2 parts. Initially in part 1, a successful target-enclosing control was applied to the system. After successfully achieving enclosing, here in part 2 of the paper, the agents face further challenges, including rotating around targets and adjusting their formation to maintain the encirclement. To address these challenges, in-domain control is applied to the agents, ensuring compliance with all requirements. Employing successive multi-step controls in a distributed manner is crucial for improving tracking and coordination among the agents, thus enhancing the effectiveness of the encirclement control. Stability analysis of the closed-loop system is conducted using the Lyapunov technique. Finally, simulations are conducted to evaluate the effectiveness of our proposed methodology. It is worth mentioning that part 2 stands as an independent outcome, tackling the challenge of rotating encirclement by leveraging a target-enclosing formation.

Keywords: Backstepping, Delay systems, Distributed parameter systems
Abstract: We present an event-triggered delay-compensated boundary control scheme for a class of reaction-diffusion PDEs with actuator dynamics, where a time delay, whose length is arbitrary, exists between the PDE plant and the actuator. After treating the time delay as a transport PDE, the overall plant configuration becomes ODE-PDE-PDE. Combining PDE and ODE backstepping transformations, a three-step backstepping design is adopted to build the continuous-in-time control law. Then, a dynamic event-triggering mechanism is designed, based on the evaluation of the overall ODE-PDE-PDE system, to determine the updating times of the actuation signal. In the resulting event-based closed-loop system, a strictly positive lower bound of the minimal dwell time is found, which is independent of initial conditions. As a result, the absence of a Zeno behavior is guaranteed. Besides, exponential convergence to zero of all signals, including the H^1 norm of the transport PDE state, the L^2 norm of the reaction-diffusion PDE state, the ODE actuator state, the dynamic variable in the event-triggering mechanism, and the control input, is proved via Lyapunov analysis. The effectiveness of the proposed method is illustrated by numerical simulation.

Keywords: Control applications, Optimal control, Robust control
Abstract: Turbocharged engines often suffer from significant intake manifold pressure response delay due to so-called turbo-lag. Many technologies have been investigated to combat this phenomenon, and combinations of them are often utilized together. The addition of these technologies to already complicated modern engines presents a significant control challenge due to significant system nonlinearity, especially when considering the large operating range of engine speeds and loads. In this paper, a model-based gain-scheduling control strategy is developed, utilizing a constrained H2 linear parameter-varying (LPV) control strategy, for the Ford 6.7L 8-cylinder diesel engine equipped with a variable geometry turbocharger (VGT), exhaust gas recirculation (EGR), and added eBoost along with a bypass valve. The nonlinear eBoost air charge system is modeled as a function of two scheduling parameters, engine load and bypass valve position, for this study and controllers are designed for the defined operating range of these parameters. The developed controller selection and interpolation scheme allows this strategy to be implemented onto computationally-limited hardware that cannot solve the controller, requiring matrix inverse calculation, online. The LPV control strategy is validated in both simulation and experimental studies, and the experimental results show a 66% reduction in engine response time in terms of reaching target intake manifold (boost) pressure following a load step-up, compared with the production configuration (without eBoost and bypass valve) with no significant impact on NOx emissions.

Keywords: Fluid flow systems, Distributed parameter systems, Control applications
Abstract: The paper considers the problem of controlling the shape of the moving interface between two fluids contained in a Hele-Shaw cell during its filling. This system is subject to viscous fingering. The interface shape dynamics is described using a modal decomposition where each mode is governed by a non-smooth ordinary differential equation with a random initial condition that is unknown. Once the interface is visibly non circular, a motion planning technique is employed to control the growth of the modes with the goal of approaching a shape of interest. The paper describes the dynamics at stake, studies its reachability property and proposes a constructive method to solve the motion planning problem. Some numerical experiments illustrate the presented methodology.

Keywords: Identification, Identification for control, Adaptive systems
Abstract: Discrete-time input/output models, also called infinite impulse response (IIR) models or autoregressive moving average (ARMA) models, are useful for online identification as they can be efficiently updated using recursive least squares (RLS) as new data is collected. Several works have studied the convergence of the input/output model coefficients identified using RLS under the assumption that the order of the identified model is the same as that of the true system. However, the case of model order mismatch is not as well addressed. This work begins by introducing the notion of textit{equivalence} of input/output models of different orders. Next, this work analyzes online identification of input/output models in the case where the order of the identified model is higher than that of the true system. It is shown that, given persistently exciting data, the higher-order identified model converges to the model equivalent to the true system that minimizes the regularization term of RLS.

Keywords: Identification, Estimation, Nonlinear systems identification
Abstract: In this paper, we study the system identification problem for linear time-invariant dynamics with bilinear observation models. Accordingly, we consider a suitable parametric description for the system model and formulate the identification problem as estimating the parameters characterizing the mathematical representation of the system through input-output measurement data. To this end, we employ a probabilistic framework aiming to obtain the maximum likelihood estimates of the parameters. Accordingly, we propose utilizing the expectation-maximization approach to improve the tractability of the identification procedure. Through the numerical experiments, we verify the efficacy of the proposed scheme and demonstrate its performance.

Keywords: Identification, Nonlinear systems identification
Abstract: Researchers develop new models to explain the unknowns. The developed models typically involve parameters that capture tangible quantities, the estimation of which is desired. However, prior to parameter estimation, the identifiability of the parameters should be investigated. Parameter identifiability investigates the recoverability of the unknown parameters given the error-free outputs, inputs, and the developed equations of the model. Different notions of and methods to test identifiability exist for dynamical systems defined in the continuous state space. Yet little attention was paid to identifiability of discrete-space systems, where variables and parameters are defined in a discrete space. We develop the identifiability framework for discrete space systems and highlight that this is not an immediate extension of the continuous space framework. Unlike the continuous case, a ``neighborhood'' is not uniquely defined in the discrete space, and hence, neither are local identifiability concepts. Moreover, results on algebraic identifiability that proved useful in the continuous space are much less so in their discrete form as the notion of differentiability disappears.

Keywords: Identification, Kalman filtering, Nonlinear systems identification
Abstract: In this paper, we investigate the use of active-learning (AL) strategies to generate the input excitation signal at runtime for system identification of linear and nonlinear autoregressive models. We adapt various existing AL approaches for static model regression to the dynamic context, coupling them with a Kalman filter to update the model recursively, and also cope with the presence of input and output constraints. The increased efficiency in terms of sample usage of the proposed AL approaches with respect to random excitation is evaluated on a few examples.

Keywords: Identification, Optimization, Stochastic systems
Abstract: The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation distance with respect to white noise process is a double-sided autoregressive non-causal graphical model. Then, we generalize the paradigm to a class of graphical autoregressive moving-average models. Finally, we test the performance of the proposed method through some numerical experiments.

Keywords: Identification, Optimization algorithms
Abstract: Factor Analysis is about finding a low-rank plus sparse additive decomposition from a noisy estimate of the signal covariance matrix. In order to get such a decomposition, we formulate an optimization problem using the nuclear norm for the low-rank component, the ℓ0 norm for the sparse component, and the Kullback–Leibler divergence to control the residual in the sample covariance matrix. An alternating minimization algorithm is designed for the solution of the optimization problem. The effectiveness of the algorithm is verified via simulations on synthetic and real datasets.

Keywords: Automotive control, Adaptive control, Uncertain systems
Abstract: This paper studies reference tracking control of uncertain lateral vehicle dynamics, using a blending based multiple-model reference adaptive control (MMRAC) approach to overcome the parametric uncertainties and time-variations, including those in the tire force capacities and cornering stiffness. The lateral vehicle dynamics model under consideration is multiple-input, multiple-output, linear, and parameter varying. The design will assume a time-invariant system, such that all uncertain parameter variations lie inside of a known, compact, and convex set. The proposed MMRAC law guarantees perfect tracking of the desired state values generated by a linear reference model representing ideal driving conditions, and the system parameter estimates asymptotically converge to the unknown true values. We present simulations to show the stability and effectiveness of the proposed MMRAC scheme, even in the presence of slow time variations, as well as a performance comparison with existing lateral vehicle motion controllers.

Keywords: Automotive control, Autonomous vehicles, Estimation
Abstract: The paper presents a combined observer and lateral control design approach for autonomous vehicles. The goal of the observer design is to estimate the front and rear slip angles of the vehicle together with the cornering stiffness. The observer is based on the combination of the polytopic LPV approach and the ultra-local model. The ultra-local model is used to update the cornering stiffness and, in this way, improve the performance level of the LPV observer. Then, the resulted observer is exploited during the LPV-based lateral control design. The improved lateral control can adapt to different circumstances such as low adhesion coefficient. The proposed observer and LPV controller is implemented and tested in MATLAB/Simulink environment and using the high-fidelity simulation software, CarMaker.

Keywords: Automotive control, Control applications, Linear systems
Abstract: This paper provides two main contributions to the field of control systems design. Firstly, an algorithm is proposed for computing digital compensators aimed at stabilizing a specific class of linear time-invariant discrete-time systems. The method leverages pole placement to devise a control system that uses a digital compensator within a closed-loop configuration. The poles crucial to this design are determined as roots of sequences of Schur polynomials, constructed via a linear combination of Laguerre polynomials orthogonal to a modified version of the classical Laguerre measure. This design yields an infinite family of compensators capable of stabilizing strictly proper plants by manipulating parameters within the coefficients of orthogonal polynomials. Secondly, the effectiveness of this approach is demonstrated through configuring a compensator for a real Steer-by-Wire platform using an industrial and embedded vehicle control unit with the CAN communication protocol. Additionally, experimental tests show improved performance compared to traditional tuning for PID controllers. The Error-to-Signal Ratio index is reduced by the novel algorithm by up to 35.5% and 65.6% in contrast with the PID controller against DLC and Fishhook procedures.

Keywords: Automotive control, Cooperative control, Optimization
Abstract: This work addresses the problem of coordinating multiple autonomous vehicles. In particular, an optimal planner based on Model Predictive Control (MPC) is designed for each vehicle, using the linear parameter-varying (LPV) representation of each vehicle model to provide feasible references that ensure constraint satisfaction. Meanwhile, mixed integer linear inequalities are embedded in the optimization problem to ensure collision avoidance. The proposed approach is evaluated in an aggressive driving scenario using a 1/10 scale electric car.

Keywords: Automotive control, Optimal control, Adaptive control
Abstract: This paper presents model predictive control strategies for battery electric endurance race cars accounting for interactions with the competitors. In particular, we devise an optimization framework capturing the impact of the actions of the ego vehicle when interacting with competitors in a probabilistic fashion, jointly accounting for the optimal pit stop decision making, the charge times and the driving style in the course of the race. We showcase our method for a simulated 1h endurance race at the Zandvoort circuit, using real-life data from a previous event. Our results show that optimizing both the race strategy and the decision making during the race is very important, resulting in a significant 21s advantage over an always overtake approach, whilst revealing the competitiveness of e-race cars w.r.t. conventional ones.

Keywords: Automotive systems, Optimal control, Optimization algorithms
Abstract: The authors investigate the problem of generating safe motorcycle trajectories intended to advise novice riders on how to safely navigate commonly-encountered road geometries. The method solves a nonlinear program using Legendre-Gauss- Radau pseudospectral collocation with a cost function designed to penalize trajectories that novices find challenging to follow. Trajectories are generated for three different motorcycles nav- igating the following scenarios: a lane change on a straight at 130 km/h, entry and exit of a constant bend at 50 km/h, and traversing a chicane at 80 km/h. The results are compared with those generated by approaches in previous literature and insights are drawn on safe maneuvering for novice riders.

Keywords: Robust adaptive control, Adaptive control, Robotics
Abstract: Research has been performed for many years regarding the development of nonlinear control techniques. One commonly researched concept in nonlinear control theory is the development of methods that can address unknown disturbances or unmodeled effects in a dynamic system when the terms have constant upper bounds. Continuous and discontinuous nonlinear controllers have evolved over many years to address these unknown terms bounded by constants. Unfortunately, these evolved controllers have either been confined to some classes of nonlinear systems or have shown to be susceptible to the chattering effect. The focus of this work is to construct a control framework that addresses unknown dynamic terms with constant bounds while simultaneously minimizing chatter for nonsmooth or switched Euler-Lagrange dynamic systems. The proposed control framework includes a filtered error signal designed to compensate for the unmodeled effects bounded by constants and an adaptive control law designed to address uncertainties in the Euler-Lagrange dynamic system’s control effectiveness matrix. To ensure the effectiveness of the proposed control law for a nonsmooth Euler-Lagrange dynamic model, a nonsmooth Lyapunov-based stability analysis is performed that proves semi-global exponential tracking to an ultimate bound

Keywords: Robust adaptive control, Control applications, Robotics
Abstract: Faulty joints in a robot manipulator adversely affect the tracking control performance and compromise the system's stability; therefore, it is necessary to design a control system capable of compensating for the effects of actuator faults to maintain control efficacy. To this end, this paper presents new amendments to the dynamical formulation of robot manipulators to account for latent actuator faults and over-generated torques mathematically. Subsequently, a novel auto-tuning subsystem-based fault-tolerant control (SBFC) mechanism is designed to force joints' states closely along desired trajectories, while tolerating actuator faults, excessive torques, and unknown modeling errors. Suboptimal SBFC gains are determined by employing the JAYA algorithm (JA), a high-performance swarm intelligence technique, standing out for its capacity to continuously approach optimal control levels without requiring meticulous tuning of algorithm-specific parameters, relying instead on its intrinsic principles. Notably, this control framework ensures uniform exponential stability (UES). The enhancement of accuracy and tracking time for reference trajectories, along with the validation of theoretical assertions, is demonstrated through simulation outcomes.

Keywords: Robust adaptive control, Hierarchical control, Flight control
Abstract: This paper presents a predictor-based adaptive augmentation scheme to recover the designed behavior of a baseline linear controller in presence of parametric uncertainty. Remarkably, the proposed scheme achieves the recovery of the baseline closed-loop performance without the need for explicit knowledge of the baseline controller states and structure; rather, the adaptive mechanism relies solely on the output of the baseline controller and plant states. We showcase how the proposed adaptive design seamlessly integrates into inner-outer loop control architectures, enhancing the overall performance and robustness while simultaneously reducing the control law complexity compared to available solutions.

Keywords: Robust adaptive control, Optimal control, Robotics
Abstract: This work addresses the problem of adaptive control of Euler-Lagrange systems considering unknown parameters without the hypothesis that the persistence of excitation (PE) condition holds. A systematic framework to obtain linear regression equations in accordance with the dynamic regressor extension and mixing (DREM) technique is proposed involving the notion of the Euler-Lagrange first integral. Then, we develop a novel robust nonlinear adaptive H-infinity controller capable of ensuring both convergence of the estimated unknown parameters and trajectory tracking in finite-time under a more relaxed condition than the PE assumption. The effectiveness of the proposed robust nonlinear adaptive H-infinity controller is corroborated through numerical experiments with a simplified CRS-A465 robot manipulator.

Keywords: Uncertain systems, Adaptive control, Stability of nonlinear systems
Abstract: This paper considers the problem of asymptotic stabilization of a class of MIMO control-affine systems with unknown nonlinear terms subject to prescribed transient constraints. We propose a novel control methodology, Barrier Integral Control (BRIC), that achieves asymptotic results while complying with the aforementioned constraints. BRIC relies on a novel integration of reciprocal barrier functions, commonly used in funnel-constrained control, and error-integral terms. The proposed methodology does not use any information from the model’s dynamic terms and, unlike previous works in the related literature, consists of smooth feedback. Theoretical guarantees are provided for three different classes of control-affine nonlinear systems, without adopting boundedness assumptions, growth conditions, or control-gain tuning. Simulation results verify the theoretical findings.

Keywords: Uncertain systems, Adaptive systems, Robotics
Abstract: This paper proposes an observer-based distributed model reference adaptive controller for a networked robotic manipulator system that is able to compensate for anomalies in the system that are unknown non-linear parameters (parametric uncertainties), robot-based uncertainties, and coupled dynamics. Lyapunov stability analysis is provided to show the stability of the closed-loop system. Also, a numerical example is provided to show the efficiency of the designed controller over the networked system that consists of three robot manipulators, each having two degrees of freedom.

Keywords: Model/Controller reduction
Abstract: In this work, we address a model reduction problem in which the resulting reduced-order model simultaneously matches sets of linear and nonlinear moments. We propose a framework for approximating the reduced-order models from time-domain input-output data without requiring knowledge of the state-space representation of the system. The developed theory and the proposed data-driven procedure are demonstrated on a benchmark model showing matching of signals generated by a linear filter and a (nonlinear) Van der Pol oscillator, simultaneously.

Keywords: Modeling, Control applications
Abstract: In this note, we propose a method for describing the dynamics of mechanical systems with velocity-based inputs within the port-Hamiltonian framework. Canonical representations of mechanical systems assume force/torque inputs. Many commonly used actuators, however, have internal dynamics that cause the output velocity to quickly converge to a specified reference velocity. In such cases, it is more meaningful from a modeling and control perspective to define models that admit a velocity input. This is achieved in this work by performing a momentum transformation and state reduction, resulting in a reduced-order model where the relevant velocity is a causal input. The reduced-order model preserves the passivity of the original port-Hamiltonian system. The results are demonstrated by applying a velocity-input control signal to the classical cart-pole system.

Keywords: Modeling, Fuzzy systems, Machine learning
Abstract: This paper proposes a piecewise modeling method based on fuzzy if-then rules using particle swarm optimization. The piecewise model has the shape of a rectangular partition of the state-space; the model can be represented as a fuzzy if-then rule with singleton consequents. The vertex values of the rectangular regions are determined using particle swarm optimization because the optimal solution is a nonlinear programming problem. In order to determine optimal vertex values of the piecewise regions with minimal modeling errors, this paper proposes a learning algorithm based on simplified fuzzy inference reasoning and particle swarm optimization methods. Some numerical simulation results show the effectiveness of the learning algorithm.

Keywords: Modeling, Identification, Robotics
Abstract: The modeling of nonlinear dynamics based on Koopman operator theory, originally applicable only to autonomous systems with no control, is extended to nonautonomous control system without approximation of the input matrix. Prevailing methods using a least square estimate of the input matrix may result in an erroneous input matrix, misinforming the controller. Here, a new method for constructing a Koopman model that yields the exact input matrix is presented. A set of state variables are introduced so that the control inputs are linearly involved in the dynamics of actuators. With these variables, a lifted linear model with the exact input matrix, called a Control-Coherent Koopman Model, is constructed by superposing control input terms, which are linear in local actuator dynamics, to the Koopman operator of the associated autonomous nonlinear system. As an example, the proposed method is applied to multi degree-of-freedom robotic arms, which are controlled with Model Predictive Control (MPC). It is demonstrated that the prevailing Dynamic Mode Decomposition with Control (DMDc) using an approximate input matrix does not provide a satisfactory result, while the Control-Coherent Koopman Model performs well with the correct input matrix, even performing better than the bilinear formulation of the Koopman operator.

Keywords: Modeling, Reduced order modeling, Simulation
Abstract: We study the moment matching problem for linear systems in a discrete-time setting and introduce a family of reduced-order models that can replicate the steady-state response of the underlying system. We show that reduced-order models can be directly computed from input-output data without needing to compute the moment of the underlying system. We then use a benchmark example to highlight performance improvements of the discrete-time algorithm over its continuous-time counterpart.

Keywords: Modeling, Iterative learning control, Mechatronics
Abstract: We study the properties of remnant function, which is a function of output remnant versus amplitude of the input signal, of Preisach hysteresis operators. The remnant behavior (or the leftover memory when the input reaches zero) enables an energy-optimal application of piezoactuator systems where the applied electrical field can be removed when the desired strain/displacement has been attained. We show that when the underlying weight of Preisach operators is positive, the resulting remnant curve is monotonically increasing and accordingly a Newton and Secant update laws for the remnant control are proposed that allows faster convergence to the desired remnant value than the existing iterative remnant control algorithm in literature as validated by numerical simulation.

Keywords: Stability of linear systems, Uncertain systems, Optimization
Abstract: This paper is concerned with the stabilization problem of unstable systems with mixed gain and phase perturbations, thence elaborating on the exact computation of optimal robustness margins. We focus on non-minimum phase and minimum phase plants, both stabilized by proportional and proportional-integral (PI) controllers. Specifically, for non-minimum phase systems with mixed perturbations, we first show that the computation of optimal gain margin constitutes a constrained optimization problem. It is proved that the maximum gain margin is attained at zero integral gain and the boundary value of proportional gain, which can be thus determined exactly. Via the Bilherz criterion, we next demonstrate that the maximal phase margin of non-minimum phase systems subject to mixed perturbations is also achieved at zero integral gain. It turns out that the calculation of optimal phase margin amounts to solving a concave optimization problem. Finally, we find that both for the minimum phase and non-minimum phase plants, proportional-integral control, and proportional control promise the same expressions of optimum robustness margins. Our explicit results clearly characterize the well-established dependence of the maximum robustness margins and/or the optimal controller coefficients on the system’s unstable pole, nonminimum phase zero as well as uncertain perturbations.

Keywords: Stability of linear systems, Lyapunov methods, LMIs
Abstract: This study presents a relaxation method for second-order matrix-valued multivariate polynomial inequalities(SMMPI), with a specific application to the stability analysis of continuous-time linear systems with additive time-varying delays (ATDs). Initially, a general expression of SMMPI is decomposed into a first-order matrix-valued multivariate polynomial and an augmented multivariate vector. By utilizing the orthogonal complement of the augmented multivariate vector, a sufficient condition for the SMMPI is proposed with a newly introduced free matrix, which highly increases the freedom. Subsequently, the proposed relaxation method is employed for the stability analysis of linear systems with ATDs. Introducing a new Lyapunov-Krasovskii functional, the time derivative is formulated as a second-order matrix-valued multivariate polynomial on the two ATDs. The obtained stability criteria have superiority over existing studies since the degree of freedom is significantly increased due to the new relaxation technique. A practical example is presented to illustrate the effectiveness of the proposed technique.

Keywords: Stability of linear systems, Data driven control, Learning
Abstract: This paper proposes a data-driven approach to design a feedforward Neural Network (NN) controller with a stability guarantee for plants with unknown dynamics. We first introduce data-driven representations of stability conditions for Neural Feedback Loops (NFLs) with linear plants, which can be formulated into a semidefinite program (SDP). Subsequently, this SDP constraint is integrated into the NN training process to ensure stability of the feedback loop. The whole NN controller design problem can be solved by an iterative algorithm. Finally, we illustrate the effectiveness of the proposed method compared to model-based methods via numerical examples.

Keywords: Time-varying systems, Stability of linear systems, Numerical algorithms
Abstract: An implicit Euler discretization scheme is given for a linear system driven by the prescribed-time stabilizing control algorithm from [Song, et al.,2017] in the presence of matched disturbances and measurement noise. The discretized version preserves all main properties of the continuous-time counterpart, and can be recursively applied on infinite horizon rather than confined to the prescribed-time interval. In addition, the discretized estimation error is robustly stable with respect to the measurement noise with a linear gain. The efficiency of the suggested discretization is illustrated through numeric experiments.

Keywords: Optimal control, Stability of linear systems, Uncertain systems
Abstract: Model mismatch often presents significant challenges in model-based controller design. This paper investigates model predictive control (MPC) for uncertain linear systems with input constraints, where the uncertainty is characterized by a parametric mismatch between the true system and its estimated model. The main contributions of this work are twofold. First, a theoretical performance bound is derived using relaxed dynamic programming. This bound provides a novel insight into how the prediction horizon and modeling errors affect the suboptimality of the MPC controller to the oracle infinite-horizon optimal controller, which has complete knowledge of the true system. Second, sufficient conditions are established under which the nominal MPC controller, which relies solely on the estimated system model, can stabilize the true system despite model mismatch. Numerical simulations are presented to validate these theoretical results, demonstrating the practical applicability of the derived conditions and bounds. These findings offer practical guidelines for achieving desired modeling accuracy and selecting an appropriate prediction horizon in designing certainty-equivalence MPC controllers for uncertain linear systems.

Keywords: Large-scale systems, Stability of linear systems, Lyapunov methods
Abstract: We consider a two-component coupled system of differential equations with operator coefficients. In contrast to the well-known small-gain approach, we assume the presence of the exponential stability property of only one subsystem. We introduce a condition for the dominance of this subsystem, which allows us to prove new conditions for the exponential stability of a coupled system. An example of infinite networks and coupled ODE+PDE equations is given. The results are compared with a small-gain approach based on the Lyapunov vector function.

Keywords: Output regulation, Lyapunov methods, LMIs
Abstract: This paper deals with the observer-based output feedback control for a class of nonlinear systems with Lipschitz nonlinearities and affected by noises. Stability in the absence of disturbances and input-to-state stability in the presence of disturbances are established under suitable conditions that are given by bilinear matrix inequalities. Since there are no general tools to solve such inequalities, gridding and linear matrix inequalities will be used. A design method is presented to find solutions satisfying such conditions. Numerical tests are reported to illustrate the effectiveness of the resulting regulator as compared to other approaches based on linearized models of the plant.

Keywords: Agents-based systems, Nonlinear systems, Game theory
Abstract: In this paper, a planar herding problem is addressed, where a single superior pursuer herds a flock of noncooperative, inferior evaders around a predefined target point. An inverse square law of repulsion is assumed between the pursuer and each evader. It is demonstrated that a constant velocity, circular trajectory of the pursuer, encompassing all the evaders and centered around the target point, guarantees the herding of the evaders into an arbitrarily small limit cycle around the target point. The conditions for the stability of this limit cycle, as well as the radius of the limiting herd, are derived as functions of the pursuer’s radius, angular velocity, and the strength of pursuer-evader repulsion. Estimates of the region of attraction for this stable limit cycle are computed and are found to lie within a larger unstable limit cycle, which is itself contained within the pursuer’s trajectory.

Keywords: Backstepping, Robust control, Nonlinear systems
Abstract: This paper derives robust, nonparametric backstepping controllers for nonlinear systems that include functional uncertainties known to lie in a reproducing kernel Hilbert spaces (RKHSs) of vector-valued functions. In contrast to the classical backstepping control architecture, including its robust formulations, the derived controllers are defined in terms of the operator kernel underlying the RKHS, and, hence, do not require a regressor vector or other finite-dimensional parameterizations to capture uncertainties. Existing approaches for robust backstepping control assume that uncertainties lie in a known finite-dimensional space; the proposed approach removes this assumption and, hence, leads to robustness for substantially larger classes of uncertainties. Furthermore, the proposed approach relieves the user from seeking bases that provide a parametric representation of the functional uncertainty. The qualitative behavior and validation of performance guarantees for the proposed controllers are shown through numerical examples.

Keywords: Data driven control, Autonomous vehicles, Nonlinear systems
Abstract: This paper proposes a data-driven control (DDC) strategy for nonlinear automated vehicles, employing a multi-description coding (MDC) mechanism based on scalar quantization to address the challenges of data dropouts and limited bandwidth in networked communication environments. The developed MDC-based communication protocol enhances system robustness by reducing the probability of data dropout. It achieves this by transmitting multiple descriptions of source data through diverse channels, incorporating quantization and index reassignment to efficiently alleviate bandwidth constraints. Based on the reconstructed real-time data, a novel data-driven controller and a parameter estimation algorithm are designed, offering adaptability to varying driving conditions and rapid response in dynamic environments. A numerical simulation showcases the potential of the proposed approach as a reliable and efficient solution for the speed problem in nonlinear automated vehicles with challenging communication environments.

Keywords: Maritime control, Adaptive control, Nonlinear systems
Abstract: This paper presents the maneuvering adaptive line-of-sight (MALOS) algorithm, which guarantees global asymptotic path following and crab angle estimation for a class of underactuated vehicles in the presence of an unknown crab angle. Notably, MALOS is the first line-of-sight (LOS) guidance scheme with integral action for curved paths with truly global stability results, and not just global under the assumption that the path parameter can be selected such that the along-track error is identically zero. A case study of an autonomous underwater vehicle demonstrates the effectiveness of the MALOS algorithm.

Keywords: Traffic control, Predictive control for nonlinear systems, Autonomous vehicles
Abstract: In this letter, we present a modeling and control design framework for modeling and influencing the drivers’ decisions in highway scenarios using one or more vehicles as actuators. Our approach relies on a driver’s decision-making model that is used to design a scenario-tree model predictive controller, which calculates acceleration and lane change commands for a set of controlled vehicles. We illustrate our modeling and control framework in a two-lane highway example, with two vehicles, one autonomous and one human-driven. Results from numerical simulations demonstrate how our approach can efficiently influence the lane changes of one vehicle using the other as a control actuator.

Keywords: Pattern recognition and classification, Adaptive control, Identification
Abstract: A given region in 2-D Euclidean space is divided by a unknown linear classifier in to two sets each carrying a label. An agent with known dynamics traversing the given region is able to measure the true label perfectly at its position. By following a trajectory, the agent collects data points comprising of its true position and the label at that position. The objective of the agent is to plan a trajectory across the given region to identify the true classifier with high accuracy while minimizing the control cost across the trajectory. We present the following: (i) the classifier identification problem formulated as a control problem; (ii) geometric interpretation of the control problem resulting in one step modified control problems; (iii) control algorithm that results in a data set which is used to identify the true classifier with high accuracy; (iv) convergence of estimated classifier to the true classifier when observed label is not corrupted by noise; (iv) numerical example demonstrating the utility of the control algorithm.

Keywords: Process Control, Petri nets, Manufacturing systems and automation
Abstract: This paper proposes a novel approach for modeling and scheduling of flexible multi-batch processes (MBP) by using timed Petri nets (TPN) and Monte-Carlo Tree Search (MCTS). A TPN-based approach to model MBP is developed, which takes into account the key factors in MBP such as material quantities, tank and pipe capacities, conditional cleaning and storage location. To schedule the multi-batch process, we propose an improved MCTS-based approach that is tailored for the MBP and is able to find the optimal firing sequence to to bring the system from its initial marking to a destination marking. The improved MCTS approach is able to find global optimal or near optimal solutions efficiently and doesn't need heuristic functions for node evaluation. The effectiveness of the proposed approach is illustrated with the help of an example of a chemical multi-batch process.

Keywords: Modeling, Robotics, Mechatronics
Abstract: Dielectric Elastomer Actuators (DEAs) have been used in various applications in wearable assistive devices and energy harvesting systems. However, material safety assurance control, which prevents dielectric elastomer failures, is not fully investigated. In this work, a state boundary avoidance control of DEA for material safety assurance is developed. Since various DEA configurations share common failure modes, incorporating these modes into the system is crucial for extending DEA lifetime and improving robustness. To expand the DEA's working range, the algorithm for internal safety control allows operation within a broader feasible region while preventing electrical breakdown (EB), electromechanical instability (EMI), loss of tension (LT), or rupture by stretch (RS). This algorithm prioritizes safety control when the feasible space is violated and allows primary control when operating within the safe space. Two case studies to validate the theory are discussed for reference tracking and energy harvesting. An algorithm for internal safety control in DEAs, considering both closed and open-loop control for reference tracking and energy harvesting, is proposed. The safety control algorithm can maximize energy harvesting output power without violating material safety rules, making it applicable to various energy source conversions like human motion, tidal wave, and wind energy.

Keywords: Formal Verification/Synthesis, Switched systems, Linear systems
Abstract: In this paper, we address the safety verification problem of switched linear dynamical systems under arbitrary switching via barrier functions. Our approach is based on a notion of path-complete barrier functions, which utilizes a collection of barrier functions associated with a directed labeled graph that can encode all the possible switching sequences. We show that path-complete barrier functions effectively generalize notions of common and multiple barrier functions studied in existing literature, and can potentially provide less conservative conditions for safety verification. We demonstrate that, for switched linear systems, the inequalities imposed via path-complete barrier functions can be easily encoded into simple linear matrix inequalities under some assumptions on the regions of interest and appropriately chosen templates for the barrier functions. We also study the relationship between path-complete barrier functions and common barrier functions, and show that for any path-complete graph with an admissible path-complete barrier function, one can derive a suitable (possibly non-smooth) common barrier function by utilizing the path-complete barrier function. Finally, we utilize several examples to illustrate the effectiveness of our approach, and briefly discuss the challenges that lay foundations for future research.

Keywords: Control Systems Privacy, Cooperative control, Agents-based systems
Abstract: Drawing inspiration from the dynamics of biological groups, flocking behavior has captivated interest due to its adaptive, self-organizing, and resilient characteristics. However, the presence of numerous agents in an open network environment raises concerns regarding the potential for information leakage during flocking movements. To address this issue, we present a decentralized output mapping function, executed independently by each individual agent, to ensure the maintenance of flocking behavior, including velocity alignment, cohesion and collision avoidance. Additionally, to enhance resource efficiency and convergence speed, an event-triggered mechanism is employed to mitigate the excessive consumption of bandwidth and computation resources in traditional flocking control algorithms. Moreover, the designed finite-time controller facilitates rapid convergence of flocking behavior. Finally, the efficacy of our proposed approach is corroborated through numerical simulation experiments.

Keywords: Control over communications
Abstract: This letter explores safety-critical control of nonlinear systems in settings where a finite-rate communication channel stands in the path of state feedback. We show that the mere existence of a nominally safe control law (certified by an exponential barrier function) suffices to provide safe control in these limited-information settings. We introduce the notion of ``safety escape time'', the minimum time a system takes to become unsafe in the absence of actuation. The results complement the existing literature on stabilizing control with limited information and represent a step towards a complete understanding of safety-critical control with limited information.

Keywords:
Abstract: As urban areas continue to face environmental and logistical challenges associated with increased traffic and emissions, micromobility solutions like electric scooters (e-scooters) offer a promising alternative for sustainable transportation. However, the rapid adoption of e-scooter sharing systems has introduced new challenges, such as congestion on sidewalks, or the need for frequent recharging and manual redistribution. To address these challenges, we present a prototype of an autonomous e-scooter designed for self-balancing and autonomous navigation within urban environments. Our system employs control algorithms and sensor technologies to enable autonomous navigation, demand-based repositioning, and automated docking at charging stations, all of which enhance both efficiency and sustainability. For instance, we use model predictive control strategies to follow a planned path, where the respective control inputs are commanded to the actuators via additional low-level controllers. By autonomously relocating to high-demand areas, this fleet of e-scooters minimizes the manual assistance needed for operating a sharing system.

See our prototype in action in demonstrations at 10 am and 11 am. There will be time to ask questions and discuss challenges after these demonstrations. Just stop by and follow up on our project: http://estarling.io/

Keywords:
Abstract: Intelligent control systems, integrating both classical and contemporary methodologies, are pivotal in managing complex systems that exceed the capabilities of traditional control mechanisms. Utilizing adaptive and learning capabilities —often by employing artificial intelligence algorithms—these systems address intricate challenges effectively. This session will highlight an innovative engineering course designed to embed intelligent control principles within the curriculum, utilizing state-of-the-art MATLAB and Simulink tools.

*The lunch sessions are scheduled to start at 12:10 and conclude at 13:10. This timing is intended to allow for a smooth transition between the morning and afternoon sessions, giving participants sufficient time to navigate between consecutive events.*

Keywords: Finance, Control applications, Stochastic systems
Abstract: The target audience for the line of research to be described in this tutorial paper is control system researchers with an interest in algorithmic stock trading but without substantial background in finance and economics. To this end, we focus our attention on just a few hand-picked problem areas to illustrate how algorithmic trading research might be carried out from a control-theoretic perspective and refer the reader to a number of references where extensive survey-style material can be found. The paper begins with the exposition of some basicsassociated with opening a brokerage account and mathematical modelling of common order types. Subsequently, we consider a number of trading scenarios involving feedback control design, optimization problems arising in portfolio management, the theory of Kelly Betting in a stock trading context and an introduction to the Limit Order Book which is crucial for smooth market operation. Given the control-theoretic point of view taken in this paper, many of our basic tools come into play; e.g., standard results from areas such as convex optimization, discrete probability theory and Markov processes, to name a few. One of the salient features of this tutorial is our use of idealizing assumptions whenever convenient for pedagogical and motivational purposes. In the conclusion section, we revisit some of these assumptions which are not straightforward to relax and suggest challenging new research problems.

Keywords: Finance, Markov processes, Robust control 
Abstract: The first part of this talk will cover many of the "rules of the road'' for a small trader who is typically operating from a desktop at home with an internet connection. The speaker will begin by describing the mechanics of setting up an account and the issues which arise in the process. These include but are not limited to funding and titling the account, decision on account type (margin, cash and retirement are possibilities), subtleties associated with short selling, quality of customer service, choice of trading platform and account insurance provided by companies and governmental agencies. Subsequently, the topic of order entry and associated mathematical modelling of order types will be considered.

Keywords: Finance, Markov processes, Robust control 
Abstract: In the realm of financial markets, the use of feedback control theory has garnered increasing attention due to its potential to define new trading strategies and enhance existing ones. This talk explores the integration of automatic control principles into trading schemes, considering both model-based and data-driven approaches. To this end, in the context of stock trading, we emphasize the role of dynamic models in decision-making processes and highlight the advantages and limitations of the feedback control approach. Finally, we describe some potential avenues for future research involving issues which will be of interest to both theoreticians and practitioners.

Keywords: Finance, Markov processes, Robust control 
Abstract: Optimization methods play a pivotal role in modern quantitative portfolio management. Beginning with this premise, this talk is devoted to explaining how optimization theory and related algorithms can be used to efficiently solve various portfolio optimization problems. To this end, we shall delve into classical mean–variance models as well as its various extensions. These include the Black-Litterman approach which integrates market equilibrium and investors’ views into the analysis and more recent developments such as stochastic and robust portfolio theory. Our goal is to equip both theoreticians and practitioners with valuable insights and toolkits for optimizing portfolios and enhancing decision-making under uncertainty.

Keywords: Finance, Markov processes, Robust control 
Abstract: The Kelly criterion, devised in 1956 by John L. Kelly Jr., a scientist at Bell Laboratories, involves an elegant mathematical formula for determining the optimal bet size in games of chance and sports betting. This formula, which is also widely utilized in investing, determines the optimal proportion of one’s bankroll to be wagered at each round of betting so as to maximize the expected logarithmic growth of wealth over time. This proportion depends solely on the probability distribution of random returns, which is assumed to be known. As explained in the talk, Kelly’s simple strategy is a form of proportional feedback controller and is seen to be "unbeatable” by any other causal betting strategy. Towards the end of the talk, we consider a more realistic scenario where the probability distribution of the return variable can be uncertain, we discuss adaptive Kelly betting, which involves estimating the distribution of returns on the fly, as well as a robust version of the Kelly criterion. Unlike the ideal case of a known distribution, these generalizations deal with nonlinear data-driven control policies.

Keywords: Finance, Markov processes, Robust control 
Abstract: The starting point for this talk is the point of view that many market mechanisms'' are dynamic systems that receive messages from prospective traders and use them to update a data structure called the Limit Order Book (LOB). In practice, an LOB is constructed for each ticker traded on the market, and the information we commonly regard as the "price'' of a stock is derived for its corresponding LOB. This tutorial talk will focus on the NASDAQ as an exemplar market and how it interacts with the traders. In particular, we will describe the types of messages it uses, characterize the LOB as a data structure, and demonstrate how a time-stamped stream of messages generates the LOB. Finally we will describe the development of a state-space model capturing the dynamics of the LOB updating process.

Keywords: Predictive control for nonlinear systems, Machine learning, Constrained control
Abstract: Learning uncertain dynamics models using Gaussian process (GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller’s closed-loop constraint satisfaction properties. To address these challenges, we propose a robust MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GP-MPC approach that iteratively generates consistent dynamics samples from the GP within a Sequential Quadratic Programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as real-time feasible computation times, using two numerical examples.

Keywords: Predictive control for nonlinear systems, Neural networks, Power electronics
Abstract: This paper considers learning online (implicit) nonlinear model predictive control (MPC) laws using neural networks and Laguerre functions. Firstly, we parameterize the control sequence of nonlinear MPC using Laguerre functions, which typically yields a smoother control law compared to the original nonlinear MPC law. Secondly, we employ neural networks to learn the coefficients of the Laguerre nonlinear MPC solution, which comes with several benefits, namely the dimension of the learning space is dictated by the number of Laguerre functions and the complete predicted input sequence can be used to learn the coefficients. To mitigate constraints violation for neural approximations of nonlinear MPC, we develop a constraints-informed loss function that penalizes the violation of polytopic state constraints during learning. Box input constraints are handled by using a clamp function in the output layer of the neural network. We demonstrate the effectiveness of the developed framework on a nonlinear buck-boost converter model with sampling rates in the sub-millisecond range, where online nonlinear MPC would not be able to run in real time. The developed constraints-informed neural-Laguerre approximation yields similar performance with long-horizon online nonlinear MPC, but with execution times of a few microseconds, as validated on a field-programmable gate array (FPGA) platform.

Keywords: Predictive control for nonlinear systems, Robust control, Neural networks
Abstract: This letter proposes a novel robust nonlinear model predictive control (NMPC) algorithm for systems described by a generic class of recurrent neural networks. The algorithm enables tracking of constant setpoints in the presence of input and output constraints. The terminal set and cost are defined based on linear matrix inequalities to ensure convergence and recursive feasibility in presence of process disturbances. Simulation results on a quadruple tank nonlinear process demonstrate the effectiveness of the proposed control approach.

Keywords: Predictive control for nonlinear systems, Optimal control, Robotics
Abstract: We present a nonlinear non-convex model predictive control approach to solving a real-world labyrinth game. We introduce adaptive nonlinear constraints, representing the non-convex obstacles within the labyrinth. Our method splits the computation-heavy optimization problem into two layers; first, a high-level model predictive controller which incorporates the full problem formulation and finds pseudo-global optimal trajectories at a low frequency. Secondly, a low-level model predictive controller that receives a reduced, computationally optimized version of the optimization problem to follow the given high-level path in real-time. Further, a map of the labyrinth surface irregularities is learned. Our controller is able to handle the major disturbances and model inaccuracies encountered on the labyrinth and outperforms other classical control methods.

Keywords: Predictive control for nonlinear systems, Data driven control, Stochastic systems
Abstract: Manual tuning required for Model Predictive Control (MPC) schemes can be labor-intensive and prone to errors due to the requisite domain expertise. In this paper, we propose a new procedure called SelfMPC: an automated, data-driven method for tuning MPC for an unknown system within a specific nonlinear class. We pursue a maximum likelihood approach using Gaussian processes to uncover system dynamics and to optimize a tracking cost function. We show the effectiveness of our approach through extensive simulations on a benchmark case study, illustrating its superior performance over traditional manual tuning techniques. Furthermore, we offer formal assurances regarding the stability and robustness of the resulting controller, ensuring its versatility across diverse operating conditions and uncertainties within the system.

Keywords: Predictive control for linear systems, Indirect adaptive control, Optimal control
Abstract: We present a model predictive control (MPC) formulation to directly optimize economic criteria for linear constrained systems subject to disturbances and uncertain model parameters. The proposed formulation combines a certainty equivalent economic MPC with a simple least-squares parameter adaptation. For the resulting adaptive economic MPC scheme, we derive strong asymptotic and transient performance guarantees. We provide a numerical example involving building temperature control and demonstrate performance benefits of online parameter adaptation.

Keywords: Aerospace, Robust control, Stochastic systems
Abstract: We develop a guidance policy for lunar landing under navigational uncertainty with feasible divert in the event a hazard is detected. Offline, we compute stochastic controllable sets under convexified dynamics and constraints that characterize the set of noisy state estimates from which the lander can be driven to a landing site with a pre-specified, sufficiently high probability. We establish that the sets computed for the convexified problem are inner-approximations of the true stochastic controllable sets. The controllable sets are parameterized by available fuel mass and length of trajectory, and provide a tractable method to quickly assess online whether a landing site is reachable. Numerical simulations demonstrate the efficacy of the approach.

Keywords: Aerospace, Estimation, Optimization
Abstract: An iterative algorithm based on the solution of a Quadratic Programming (QP) problem is presented for on- line inertia estimation of tumbling uncontrolled spacecraft using discrete attitude measurements. This estimation is crucial for various applications, chiefly among them active debris removal, where the rotational state of tumbling debris must be accurately determined to enable safe approach and capture maneuvers. Linear constraints are employed to guarantee that the optimization problem solution is consistent with the physical constraints of the inertia tensor. The inertia estimation, derived from discrete mechanics principles, can be formally posed as a Semidefinite Programming (SDP) optimization problem. To reduce the complexity, a local parametrization compatible with the structure of inertia tensors is proposed to derive a QP algorithm. Numerical simulations are used to validate the effec- tiveness of this methodology and demonstrate its potential for real-time implementation in scenarios involving uncontrolled tumbling spacecraft. The proposed QP-based iterative approach offers a computationally efficient alternative to SDP methods while maintaining estimation accuracy, making it well-suited for on-board implementation with limited computational resources.

Keywords: Predictive control for linear systems, Aerospace, Robust control
Abstract: This paper presents a novel control strategy for the problem of minimum-time rendezvous with a moving target, which is relevant to several aerospace applications. The proposed approach leverages tube-based model predictive control techniques to achieve robustness against disturbances and minimize the maneuver time. By suitably adapting the terminal constraints, recursive feasibility of the optimization problem is ensured, while guaranteeing finite-time completion of the rendezvous mission. Simulation studies show that less conservative trajectories are obtained, compared to existing robust predictive control methodologies. The effectiveness of the approach is demonstrated on a simulated rendezvous maneuver with a tumbling body.

Keywords: Control applications, Autonomous vehicles, Lyapunov methods
Abstract: Many of the existing works on quadrotor control address the trajectory tracking problem by employing a cascade design in which the translational and rotational dynamics are stabilized by two separate controllers. The stability of the cascade is often proved by employing trajectory-based arguments, most notably, integral input-to-state stability. In this paper, we follow a different route and present a control law ensuring that a composite function constructed from the translational and rotational tracking errors is a Lyapunov function for the closed-loop cascade. In particular, starting from a generic control law for the double integrator, we develop a suitable attitude control extension, by leveraging a backstepping-like procedure. Using this construction, we provide an almost global stability certificate. The proposed design employs the unit sphere mathcal{S}^2 to describe the rotational degrees of freedom required for position control. This enables a simpler controller tuning and an improved tracking performance with respect to previous global solutions. The new design is demonstrated via numerical simulations and on real-world experiments.

Keywords: Cooperative control, Agents-based systems, Observers for Linear systems
Abstract: This paper proposes an observer-based forma- tion tracking control approach for multi-vehicle systems with second-order motion dynamics, assuming that vehicles’ relative or global position and velocity measurements are unavailable. It is assumed that all vehicles are equipped with sensors capable of sensing the bearings relative to neighboring vehicles and only one leader vehicle has access to its global position. Each vehicle estimates its absolute position and velocity using relative bearing measurements and the estimates of neighboring vehicles received over a communication network. A distributed observer-based controller is designed, relying only on bearing and acceleration measurements. This work further explores the concept of the Bearing Persistently Exciting (BPE) formation by proposing new algorithms for bearing-based localization and state estimation of second-order systems in centralized and decentralized manners. It also examines conditions on the desired formation to guarantee the exponential stability of distributed observer-based formation tracking controllers. In support of our theoretical results, some simulation results are presented to illustrate the performance of the proposed observers as well as the observer-based tracking controllers.

Keywords: Autonomous robots, Autonomous systems, Optimization
Abstract: In this paper, we investigate the problem of decomposing 2D environments for robot coverage path planning (CPP). CPP involves computing a cost-minimizing path so that the robot's coverage or sensing tool visits all points in the environment. CPP is an NP-Hard problem, so existing approaches simplify the problem by decomposing the environment into the minimum number of sectors, i.e., sub-regions that can each be covered using a lawnmower path (along parallel straight-line paths) oriented at an angle. However, traditional methods either limit the coverage orientations to be axis-parallel (horizontal/vertical) or provide no guarantees on the number of sectors in the decomposition. We introduce an approach to decompose the environment into possibly overlapping rectangular sectors, with an approximation guarantee on the number of sectors computed for an environment. We do this by leveraging the submodular property of the sector coverage function, which enables us to formulate the decomposition problem as a submodular set cover (SSC) problem with well-known approximation guarantees for the greedy algorithm. Our approach improves upon existing coverage planning methods, as verified on example maps of complex real-world environments.

Keywords: Formal Verification/Synthesis, Machine learning, Stochastic systems
Abstract: This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all probabilities over a finite horizon. We achieve this by constructing the level sets of the probability measure for all probability values and, since our approach is only for autonomous systems, we can determine the level sets via forward simulations of the system from a point in the state space at some time step in the finite horizon to estimate the reach probability. We devise a training procedure which exploits this forward simulation and employ it to design a deep neural network (DNN) to predict the reach probability provided the current state and time step. We validate the effectiveness of our approach through three examples.

Keywords: Stability of nonlinear systems, Machine learning, Optimal control
Abstract: We demonstrate that a convex optimization formulation of physics-informed neural networks for solving partial differential equations can address a variety of computationally challenging tasks in nonlinear system analysis and control. This includes computing Lyapunov functions, region-of-attraction estimates, and optimal controllers. Through numerical examples, we illustrate that the formulation is effective in solving both low- and high-dimensional analysis and control problems. We compare it with alternative approaches, including semidefinite programming and nonconvex neural network optimization, to demonstrate its potential advantages.

Keywords: Machine learning, Stochastic systems, Data driven control
Abstract: In stochastic and dynamic environments, the ability to infer an accurate model of the underlying dynamical system is crucial for ensuring objectives such as responsiveness, performance, or reliability. We present a novel approach to update predictive models of discrete-time, stochastic, dynamical systems in an online fashion. Our approach is based in physics-informed conditional distribution embeddings, a non-parametric machine learning technique that approximates an integral operator to assess the most likely distribution. We propose an efficient numerical method to update the predictive model as new data is gathered, employing low-rank updates. We validate our approach on examples of varying complexity, including an F-16 ground collision avoidance scenario.

Keywords: Lyapunov methods, Stability of nonlinear systems, Neural networks
Abstract: Homogeneous vector fields play an important role in approximating general nonlinear systems. We propose a neural network approach for finding global Lyapunov functions for homogeneous vector fields. We first establish a universal approximation result that guarantees the existence of neural Lyapunov functions for homogeneous systems. We then propose a specific neural network structure for computing such Lyapunov functions, with verifiable sufficient conditions for global asymptotic stability. We demonstrate the potential advantage of neural Lyapunov functions over sums-of-squares Lyapunov functions through numerical examples.

Keywords: Data driven control, Linear systems
Abstract: We illustrate a novel version of Willems’ lemma for data-based representation of continuous-time systems. The main novelties compared to previous works are two. First, the proposed framework relies only on measured input-output trajectories from the system and no internal (state) information is required. Second, our system representation makes use of exact system trajectories, without resorting to orthogonal bases representations and consequent approximations. We first establish sufficient and necessary conditions for data-based generation of system trajectories in terms of suitable latent variables. Subsequently, we reformulate these conditions using measured input-output data and show how to span the full behavior of the system. Furthermore, we show how to use the developed framework to solve the data-based continuous-time simulation problem.

Keywords: Stochastic systems, Statistical learning, Markov processes
Abstract: The abstraction of dynamical systems is a powerful tool that enables the design of feedback controllers using a correct-by-design framework. We investigate a novel scheme to obtain data-driven abstractions of discrete-time stochastic processes in terms of richer discrete stochastic models, whose actions lead to nondeterministic transitions over the space of probability measures. The data-driven component of the proposed methodology lies in the fact that we only assume samples from an unknown probability distribution. We also rely on the model of the underlying dynamics to build our abstraction through backward reachability computations. The nondeterminism in the probability space is captured by a collection of Markov Processes, and we identify how this model can improve upon existing abstraction techniques in terms of satisfying temporal properties, such as safety or reach-avoid. The connection between the discrete and the underlying dynamics is made formal through the use of the scenario approach theory. Numerical experiments illustrate the advantages and main limitations of the proposed techniques with respect to existing approaches.

Keywords: Distributed parameter systems, Adaptive systems, Observers for Linear systems
Abstract: The problem of estimating the reaction coefficient of a system governed by a reaction-diffusion partial differential equation is tackled. An estimator relying on boundary measurements only is proposed. The estimator is based upon a setpoint regulation strategy and leads to an asymptotically converging estimate of the unknown reaction coefficient. The proposed estimator is combined with a state observer and shown to provide an asymptotic estimate of the actual system state. A numerical example supports and illustrates the theoretical results.

Keywords: Model/Controller reduction, Neural networks, Data driven control
Abstract: Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper explores a deep autoencoding learning method for reduced-order modeling and control of dynamical systems governed by spatiotemporal PDEs. We first analytically show that an optimization objective for learning a linear autoencoding reduced-order model can be formulated to yield a solution closely resembling the result obtained through the dynamic mode decomposition with control algorithm. We then extend this linear autoencoding architecture to a deep autoencoding framework, enabling the development of a nonlinear reduced-order model. Furthermore, we leverage the learned reduced-order model to design controllers using stability-constrained deep neural networks. Numerical experiments are presented to validate the efficacy of our approach in both modeling and control using the example of a reaction-diffusion system.

Keywords: Distributed parameter systems, Delay systems, Robust control
Abstract: This paper addresses the problem of input-to-state stability (ISS) and stabilization of linear ordinary differential equations (ODEs) coupled with a system of homogeneous linear hyperbolic partial differential equations(PDEs) through the boundaries. First, a Lyapunov result characterizing the ISS property for finite-dimensional systems is extended to deal with coupled ODE and PDE systems. The proposed ISS condition is then applied to derive stability and stabilization conditions in terms of linear matrix inequality constraints assuming magnitude bounded disturbances at the boundaries. Two convex optimization problems are also proposed in order to obtain either an optimized reachable set estimate or a boundary controller that minimizes the disturbance effects on the L2-norm of the system states. Numerical examples illustrate the potential of the proposed approach.

Keywords: Distributed parameter systems, Optimal control
Abstract: We consider the linear quadratic regulator of the heat equation on a finite interval. Previous frequency-domain methods for this problem rely on discrete Fourier transform and require symmetric boundary conditions. We use the Fokas method to derive the optimal control law for general Dirichlet and Neumann boundary conditions. The Fokas method uses the continuous Fourier transform restricted to the bounded spatial domain, with the frequency domain extended from the real line to the complex plane. This extension, together with results from complex analysis, allows us to eliminate the dependence of the optimal control on the unknown boundary values. As a result, we derive an integral representation of the control similar to the inverse Fourier transform. This representation contains integrals along complex contours and only depends on known initial and boundary conditions. We also show that for the homogeneous Dirichlet boundary value problem, the integral representation recovers an existing series representation of the optimal control. Moreover, the integral representation exhibits numerical advantages compared to the traditional series representation.

Keywords: Distributed parameter systems, Stability of linear systems
Abstract: A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics to be a Riesz-spectral operator. In that case, its spectrum is computed explicitly, together with the corresponding eigenfunctions, which constitutes the main result of our letter. In particular, this enables to characterize easily many different concepts, such as stability. We apply our results to characterize exponential stability of a co-current heat exchanger.

Keywords: Distributed parameter systems, Predictive control for nonlinear systems, Agents-based systems
Abstract: We consider a problem of optimal swarm tracking which can be formulated as a tracking problem for distributions in the Wasserstein space. Optimal solutions to this problem are non-causal and require knowing the time-trajectory of the reference distribution in advance. We propose a scheme where these non-causal solutions can be used together with a predictive model for the reference to achieve causal tracking of a priori-unknown references. We develop a model-predictive control scheme built around the simple case where the reference is constant-in-time. A computational algorithm based on particle methods and discrete optimal mass transport is presented, and numerical simulations are provided for various classes of reference signals. The results demonstrate that the proposed control algorithm achieves reasonable performance even when using simple predictive models.

Keywords: Hierarchical control, Networked control systems, Hybrid systems
Abstract: Autonomous systems typically leverage layered control architectures, created by interconnecting components that operate at multiple timescales, i.e., evolve under various clocks. To formalize this typically heuristic procedure, we introduce a new logic, Multiclock Logic (MCL), that can express the requirements of components from the point of view of their local clocks, promoting independent design and component reuse. We then use assume-guarantee contracts expressed in MCL to prove global stability properties of a system using the stability properties of its components. In particular, we consider the classic layered architecture consisting of model predictive control (MPC) layered on top of feedback linearization, and prove overall stability of the systems.

Keywords: Information theory and control, Networked control systems, Estimation
Abstract: We analyze the rate-distortion performance of two quantized event-based encoding paradigms estimating a two-dimensional Wiener process. Each encoder remains silent until the estimation error reaches a threshold and then transmits a packet from a finite codebook over a noiseless, zero-delay channel to a decoder that updates the estimate. Both encoding methods are parameterized by the radius of the event threshold and the size of the codebook. The first encoding scheme simply quantizes the error of the source process on the event threshold. The second scheme employs a dithered quantizer, which simplifies the derivation of an analytical rate-distortion upper bound. Each method is simulated in discrete time to inform the choice of the bitrate-optimal codebook size and event radius for a given distortion constraint. The rate-distortion performance of these encoding schemes are compared to a known lower bound and a conservative upper bound that we derive herein.

Keywords: Resilient Control Systems, Networked control systems, Compartmental and Positive systems
Abstract: This paper addresses the issue of data injection attacks on the actuators of positive networked control systems. We introduce an impact metric that quantifies the worst-case performance loss caused by stealthy attacks. By leveraging the properties of positive systems, we show that the impact metric admits an equivalent linear program representation, offering scalability advantages. Under mild assumptions, we prove the existence of a solution for the linear program, thereby proving that the impact metric admits a finite value. Furthermore, we extend such scalable metrics for uncertain systems and provide brief insights into cone positive systems.

Keywords: Control over communications, Networked control systems, Stability of nonlinear systems
Abstract: In this paper, an event–triggered safety–critical control algorithm is designed for quasi–linear systems evolving on any arbitrary time domains using the concept of measure chain theory. The concept of input–to–state (ISS) safe barrier functions on measure chains is used to prove safety of the closed–loop quasi–linear system. The stability of the closed–loop system on measure chains is also analyzed. The results are valid not only for continuous– time and discrete–time systems with constant sampling but also for systems evolving in any other time domains. Numerical simulations are performed for systems on some measure chains which justify the proposed approach.

Keywords: Cooperative control, Networked control systems, Stability of nonlinear systems
Abstract: This paper proposes a distributed control law for the coverage of time-varying density functions and coverage regions with dynamics that are integrable. Asymptotic stability guarantees are established via a variation of Barbalat's Lemma. In doing so we propose an objective function that accounts for the explicit time dynamics associated with the local minima of a standard objective function used in the coverage control literature. This work advances upon existing literature on time-varying coverage control by providing stability guarantees in the distributed case without requiring unbounded control inputs. These guarantees are then validated through simulation, where the performance of a proposed controller is then compared to an existing feedback control law that is well known in the literature.

Keywords: Human-in-the-loop control, Networked control systems, Stochastic systems
Abstract: In this paper, we propose a switching policy based on the Age of Information (AoI) to enhance safety in haptic teleoperation over a wireless network, which is a key application of interest in upcoming 6G networks. Given the unique challenges of human-in-the-loop scenarios, our focus is on safety-oriented control since imperfect transmissions could introduce safety risks in typical haptic teleoperation scenarios. We introduce an AoI-based Markov Jump Linear System (MJLS) to model the closed-loop system, considering the AoI-based safety switching policy. This policy activates a ``safe" controller on the remote side when the AoI exceeds a predefined threshold. While the safe controller does not know the desired human control, it is able to bring the robot or plant to a safe state. For a given AoI-based threshold, we utilize MJLS properties to ensure closed-loop stability. We also introduce and optimize performance criteria that address safety issues as well as transparency for the human controller, i.e., how closely the system can follow the human's intention. Numerical results demonstrate that our safe control scheme improves performance in 2D reference tracking tasks while ensuring safety and reducing undesirable behavior like overshoots.

Keywords: Distributed control, Nonholonomic systems, Autonomous vehicles
Abstract: This letter presents a distributed nonlinear control approach for the formation of nonholonomic mobile robots aimed at acquiring a desired geometric pattern in the plane without requiring velocity measurements. The control law provides the wheel torques and affects both the linear and angular acceleration of the mobile robot. The proposed control strategy facilitates formation maintenance through a dynamic control design incorporating a consensus structure. Utilizing local interactions, the control law is designed to ensure asymptotic convergence of consensus errors towards zero. The design of a position error enables mobile robots to attain the desired formation, defined in terms of distances from a formation center.

Keywords: Distributed control, Optimization, Autonomous vehicles
Abstract: This letter studies the circular formation control problem from a perspective of distributed optimization. Two types of algorithms are developed, i.e., a synchronous Jacobi iteration method and its asynchronous variant, both of which are proven to achieve the convergence with exponential rates. As distinct from the existing continuous-time approaches, a step-size has to be imposed into our discrete-time methods and its influence on the convergence rate is analyzed explicitly. According to the analysis, the optimal choice of step-size is provided with respect to the convergence rate. Extensive numerical results are finally present to demonstrate the theoretical findings in this work.

Keywords: Distributed control, Optimization, Learning
Abstract: This paper studies the distributed feedback optimization problem for linear multi-agent systems without precise knowledge of local costs and agent dynamics. The proposed solution is based on a hierarchical approach that uses upper-level coordinators to adjust reference signals toward the global optimum and lower-level controllers to regulate agents' outputs toward the reference signals. In the absence of precise information on local gradients and agent dynamics, an extremum-seeking mechanism is used to enforce a gradient descent optimization strategy, and an adaptive dynamic programming approach is taken to synthesize an internal-model-based optimal tracking controller. The whole procedure relies only on measurements of local costs and input-state data along agents' trajectories. Moreover, under appropriate conditions, the closed-loop signals are bounded and the output of the agents exponentially converges to a small neighborhood of the desired extremum. A numerical example is conducted to validate the efficacy of the proposed method.

Keywords: Distributed control, Machine learning, Predictive control for linear systems
Abstract: In this paper, we propose a cooperative Multi-Agent Reinforcement Learning (MARL) approach based on Distributed Model Predictive Control (DMPC). In the proposed framework, the local MPC schemes are formulated based on the dual decomposition method in the context of DMPC and will be used to derive the local state (and action) value functions required in a cooperative Q-learning algorithm. We further show that the DMPC scheme can yield a framework based on the Value Function Decomposition (VFD) principle so that the global state (and action) value functions can be decomposed into several local state (and action) value functions captured from the local MPCs. In the proposed cooperative MARL, the coordination between individual agents is then achieved based on the multiplier-sharing step, a.k.a inter-agent negotiation in the DMPC scheme.

Keywords: Distributed control, Predictive control for linear systems, Robust control
Abstract: This work explores a coalitional control approach for input-coupled multi-agent systems to robustly track changing setpoints. In this partially cooperative framework, agents can share a public portion of their input with neighboring agents while keeping the remainder private. Negotiations over the bounds defining the public and private input sets can be triggered on demand. Additionally, coupling disturbances are addressed using a tube-based approach, guiding the system towards desired target points. The effectiveness of the proposed approach is demonstrated through its application to a simulated eight-input coupled tank benchmark.

Keywords: Distributed control, Reinforcement learning, Markov processes
Abstract: In this paper we propose a novel distributed gradient-based two-time-scale algorithm for decentralized multi-agent multi-task learning (MTL) using a linear approximation of the optimal action value function (Q-function) in POMDPs. The algorithm is based on the idea of using in a concurrent way recursive Bayesian state belief filters for estimation of the system model parameters, prediction of the hidden state and definition of the optimal approximation parameters of the local Q-functions. The main MTL algorithm is composed of: 1) local parameter updates based on an off-policy gradient-based learning algorithm with target policy belonging to the greedy or Gibbs classes, and 2) a linear stochastic time-varying consensus scheme for parameters shared between the agents in order to achieve the MTL goal. It is proved, under general assumptions, that the parameter estimates generated by the proposed algorithm weakly converge to a bounded invariant set of the corresponding ordinary differential equations (ODE). Simulation results illustrate the effectiveness of the algorithm.

Keywords: Queueing systems, Control of networks, Optimization
Abstract: In this paper, we aim to improve the percentage of packets meeting their deadline in discrete-time M/M/1 queues with infrequent monitoring. More specifically, we look into policies that only monitor the system (and subsequently take actions) after a packet arrival. We model the system as an MDP and provide the optimal policy for some special cases. Furthermore, we introduce a heuristic algorithm called "AB-n" for general deadlines. Finally, we provide numerical results demonstrating the desirable performance of "AB-n" policies.

Keywords: Randomized algorithms, Autonomous systems, Robotics
Abstract: We consider a perimeter defense problem in which a vehicle seeks to defend a compact region from mobile intruders in a one-dimensional environment parameterized by the perimeter size relative to the environment and the intruder-to-vehicle speed ratio. The intruders move with fixed speed and direction to reach the perimeter. We present a competitive analysis approach to this problem by measuring the performance of randomized online algorithms for the vehicle against arbitrary inputs, relative to an optimal offline algorithm that has information about entire input sequence in advance. In particular, we characterize regimes in the parameter space in which, for any online randomized algorithm, (i) the competitive ratio has to be at least 2 and (ii) the competitive ratio has to be at least 1.33. We then design three randomized algorithms and characterize their competitive ratios. Finally, we present parameter regime plots that provide insights into parameter ranges in which the algorithms’ performances are near optimal.

Keywords: Statistical learning, Machine learning
Abstract: Unsupervised feature selection is a critical task in data analysis, particularly when faced with high-dimensional datasets and complex and nonlinear dependencies among features. In this paper, we propose a family of Gram-Schmidt feature selection approaches to unsupervised feature selection that addresses the challenge of identifying non-redundant features in the presence of nonlinear dependencies. Our method leverages probabilistic Gram-Schmidt (GS) orthogonalization to detect and map out redundant features within the data. By applying the GS process to capture nonlinear dependencies through a pre-defined, fixed family of functions, we construct variance vectors that facilitate the identification of high-variance features, or the removal of these dependencies from the feature space. In the first case, we provide information-theoretic guarantees in terms of entropy reduction. In the second case, we demonstrate the efficacy of our approach by proving theoretical guarantees under certain assumptions, showcasing its ability to detect and remove nonlinear dependencies. To support our theoretical findings, we experiment over various synthetic and real-world datasets, showing superior performance in terms of classification accuracy over state-of-the-art methods. Further, our information-theoretic feature selection algorithm strictly generalizes a recently proposed Fourier-based feature selection mechanism at significantly reduced complexity.

Keywords: Mean field games, Stochastic optimal control, Large-scale systems
Abstract: Mean Field Game equilibria are based on the assumption of instantaneous interactions within a population of interchangeable agents, where each agent's impact diminishes as the population size increases. However, in practical scenarios, agents may not continuously observe the overall population state. Instead, in some situations, agents observe the empirical mean state only at discrete time intervals. This observation structure likely influences the nature of Nash equilibria that agents can attain. This paper characterizes the best responses of agents under such discrete observation conditions. Sufficient conditions for the existence of a so-called Markov Nash equilibrium within a finite population of agents are presented. Additionally, the difference in cost due to discrete versus continuous mean observations is evaluated.

Keywords: Fluid flow systems, Optimal control, Modeling
Abstract: In this work, structured input-output analysis is employed to investigate how asymptotic suction control affects the growth of different types of disturbances to boundary layer flow. Application of the method in both the Blasius and asymptotic suction boundary layer settings demonstrates that, as in the case of channel flow, structured analysis produces results consistent with non-linear optimal perturbation analysis and direct numerical simulations. A comparison of the structured response at Re_{delta^*}=610 for the two configurations highlights changes in the structural features of the disturbances that require the least energy to induce transition (optimal perturbations), as well as an overall reduction in the structured response of the actuated boundary layer. Further efforts to understand how this well-known flow control technique achieves this broadband reduction in flow sensitivity can provide insights that can be exploited to develop new actuation strategies to delay transition in boundary layers.

Keywords: Air traffic management, Optimization algorithms
Abstract: The rise of advanced air mobility (AAM) is expected to become a multibillion-dollar industry in the near future. Market-based mechanisms are touted to be an integral part of AAM operations, which comprise heterogeneous operators with private valuations. In this work, we study the problem of designing a mechanism to coordinate the movement of electric vertical take-off and landing (eVTOL) aircraft, operated by multiple operators each having heterogeneous valuations associated with their fleet, between vertiports, while enforcing the arrival, departure, and parking constraints at vertiports. Particularly, we propose an incentive-compatible and individually rational vertiport reservation mechanism that maximizes a social welfare metric, which encapsulates the objective of maximizing the overall valuations of all operators while minimizing the congestion at vertiports. Additionally, we improve the computational tractability of designing the reservation mechanism by proposing a mixed binary linear programming approach that leverages the network flow structure.

Keywords: Observers for nonlinear systems, Estimation, Nonlinear systems
Abstract: Estimation algorithms and nonlinear observers are widespread tools used in a variety of real-world applications, from satellite control to epidemiological studies. Their primary purpose is to provide an estimate of the state computed from available measurements and a model of the dynamics. When state estimates are used to enforce safety properties, it is essential to understand and characterize how accurate these estimates are so that safety is still guaranteed. While several observer design techniques provide bounds for the estimation error, they are either computationally expensive or too conservative and thus difficult to use in practice. Our work tackles these issues by providing error bounds for observers based on Savitzky-Golay filtering which are applicable to nonlinear systems satisfying a suitable observability assumption. Moreover, the error bounds are computed online based on measured data are thus tighter than offline bounds based on worst case assumptions. We generalize prior theoretical results by some of the authors from polynomial approximations to other functions and use this added flexibility to obtain tighter bounds. Finally, we illustrate the results using multiple examples, including an application to in-host models used in epidemiology.

Keywords: Observers for nonlinear systems, LMIs, Lyapunov methods
Abstract: This work investigates the problem of H-infinity fixed-order filtering design in continuous-time Lur'e systems with sector-bounded nonlinearities. The conditions, formulated in terms of linear matrix inequalities, rely on a quadratic Lyapunov function and are solved through an iterative algorithm. The novelty comes from the fact that the matrices of the filter realization appear in isolation, being treated as decision variables of the optimization problem. Numerical examples demonstrate the advantages of the proposed approach, which can be less conservative compared to other existing methods.

Keywords: Observers for nonlinear systems, Modeling
Abstract: Relative pose (position and orientation) estimation is an essential component of many robotics applications. Fiducial markers, such as the AprilTag visual fiducial system, yield a relative pose measurement from a single marker detection and provide a powerful tool for pose estimation. In this paper, we perform a Lie algebraic nonlinear observability analysis on a nonlinear dual quaternion system that is composed of a relative pose measurement model and a relative motion model. We prove that many common dual quaternion expressions yield Jacobian matrices with advantageous block structures and rank properties that are beneficial for analysis. We show that using a dual quaternion representation yields an observability matrix with a simple block triangular structure and satisfies the necessary full rank condition.

Keywords: Observers for nonlinear systems, Optimization algorithms
Abstract: This letter considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurements. The recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This letter presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. The assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of IPG observer with Newton observer, which was only hypothesized earlier.

Keywords: Uncertain systems, Observers for nonlinear systems, Filtering
Abstract: This work proposes an interval observer design for nonlinear discrete-time systems based on the Kazantzis-Kravaris/Luenberger (KKL) paradigm. Our design extends to generic nonlinear systems without any assumption on the structure of its dynamics and output maps. Relying on a transformation putting the system into a target form where an interval observer can be directly designed, we then propose a method to reconstruct the bounds in the original coordinates using the bounds in the target coordinates, thanks to the Lipschitz injectivity of this transformation achieved under Lipschitz distinguishability when the target dynamics have a high enough dimension and are pushed sufficiently fast. An academic example serves to illustrate our methods.

Keywords: Observers for nonlinear systems, Biological systems, Variable-structure/sliding-mode control
Abstract: We propose an observer design for a 3-dimensional model of cortical activity dynamics in the visual cortex, under the measurement of the averaged activity. It is based on the construction of an embedding of the system into a triangular 4-dimensional system where the dynamics are not Lipschitz-continuous but bear Hölder-continuity properties allowing us to implement a sliding mode observer. We discuss stability of the convergence of the observer with respect to relevant perturbations and provide simulations illustrating the method.

Keywords: Systems biology, Stochastic systems, Genetic regulatory systems
Abstract: Epigenetic cell memory is the property enabling multicellular organisms to keep distinct cell types despite sharing the same genotype. DNA methylation and histone modifications play a crucial role in maintaining the long-term memory of gene expression patterns specific to each cell type. Experimental results in semi-synthetic genetic systems show that these modifications silence and reactivate genes in an “all or none” manner, suggesting binary epigenetic memory (only extremal gene expression levels have long-term memory). However, in recent years, continuous and graded variations of gene expression levels have been identified across multiple cell types. Here, by introducing and analyzing a chromatin modification circuit model, we demonstrate that the experimentally observed bimodal probability distributions of gene expression level, used to support the binary memory hypothesis, are also compatible with the analog memory hypothesis, where cells can maintain any initially set gene expression level. Our study shows that intrinsic noise combined with an ultrasensitive response between the level of DNA methylation writer DNMT3A and DNA methylation grade at a gene can explain how analog epigenetic cell memory leads to a bimodal gene expression level distribution. The model can help design experiments to help distinguish between binary and analog memory, thereby offering a tool for interrogating the very essence of epigenetic cell memory.

Keywords: Biomolecular systems, Discrete event systems, Systems biology
Abstract: Numerous biological timing mechanisms are associated with the duration required for key regulatory molecules to reach critical threshold levels. Recent studies have mainly explored how random fluctuations affect the timing of events as molecules accumulate to reach a high threshold. This study examines the complementary scenario: decrease in protein levels until they reach a low critical threshold. We aim to study the timing precision resulting from different degradation pathways and their inherent stochastic nature, especially under low-copy number conditions. More specifically, we explore how integer-valued protein molecular counts decrease stochastically following Michaelis-Menten kinetics. This approach encompasses both zero-order (where the net degradation rate is independent of protein levels) and first-order (where the rate is proportional to protein levels) decay processes. Our results show that, while zero-order decay can be sluggish in terms of mean timing, it provides the highest precision in timing with the lowest noise in threshold-crossing time. Conversely, upon considering randomness in the initial protein levels, first-order decay demonstrates better precision compared to zero-order. Interestingly, in the presence of multiple noise sources, timing stochasticity can be minimized when Michaelis-Menten decay kinetics operate under sub-saturation conditions. This characterization of timing driven by decreasing copy numbers has implications for improving the precision of biological clocks and understanding the timing of cell-cycle events.

Keywords: Genetic regulatory systems, Markov processes, Estimation
Abstract: Control of gene regulation requires quantitatively accurate predictions of heterogeneous cellular responses. When inferred from single-cell experiments, discrete stochastic models can enable such predictions, but such experiments are highly adjustable, allowing for almost infinitely many potential designs (e.g., at different induction levels, for different measurement times, or considering different observed biological species). Not all experiments are equally informative, experiments are time-consuming or expensive to perform, and research begins with limited prior information with which to construct models. To address these concerns, we developed a sequential experiment design strategy that starts with simple preliminary experiments and then integrates chemical master equations to compute the likelihood of single-cell data, a Bayesian inference procedure to sample posterior parameter distributions, and a finite state projection based Fisher information matrix to estimate the expected information for different designs for subsequent experiments. Using simulated then real single-cell data, we determined practical working principles to reduce the overall number of experiments needed to achieve predictive, quantitative understanding of single-cell responses.

Keywords: Filtering, Nonlinear systems identification, Biological systems
Abstract: For joint parameter-state estimation problems, classical particle filters often suffer from sample degeneracy or problems related to artificial noise, stemming from the particles representing unknown parameters. To address this challenge, this paper provides a novel filtering approach that avoids generating such particles by utilizing Rao-Blackwellization, which therefore provides more accurate estimates. Moreover, our method employs a modularization approach when integrating out the parameters, significantly reducing the computational complexity. All these designs ensure the superior performance of our method. Finally, a couple of numerical examples are presented to illustrate the superior performance of our method compared with several existing approaches.

Keywords: Biomolecular systems, Metabolic systems, Biological systems
Abstract: Across diverse cell types, genes are often expressed at low levels resulting in significant stochastic fluctuations (noise) in intracellular copy number of mRNAs and proteins over time. Motivated by single-cell experiments, we capture this stochasticity by considering a given gene that toggles between transcriptionally active and inactive states with the time spent in each state being an arbitrary random variable. mRNAs are synthesized from the active state as per a Poisson process and each molecule degrades after a random lifespan (i.e., random time from birth to death). Modeling this process using the Stochastic Hybrid System (SHS) formalism we derive exact analytical results for the statistical moments of molecular counts. Our results show that for fixed mean mRNA numbers, fluctuations in mRNA levels are amplified with decreasing noise in mRNA lifespan. Relaxing the Poisson process assumption, we next consider a scenario where transcription events occur such that the time between successive events is an arbitrarily distributed random variable. In this case, we show that decreasing noise in mRNA lifespan can both increase/decrease mRNA count fluctuations depending on the underlying transcriptional process. Finally, we extend these results to the protein level, where increasing noise in mRNA counts is sometimes associated with decreasing noise in protein copy numbers.

Keywords: Biomolecular systems, Genetic regulatory systems, Biotechnology
Abstract: The performance of biomanufacturing systems can be improved by incorporating inducible synthetic gene circuits which `switch' the microbial cell factories from growth to production upon the manual addition of a small molecule activator. Here, we consider feedback strategies which enable autonomous activation of a genetic circuit based on cell state. Using a multi-scale modelling framework which takes into account the dynamics of microbial growth and pathway production, we show that population-based feedback offers a promising strategy for autonomous activation of genetic switches.

Keywords: Hybrid systems, Differential-algebraic systems, Switched systems
Abstract: In this paper, we introduce a definition of solutions for linear piecewise affine differential-algebraic equations (PWA-DAEs). Firstly, to address the conflict between projector-based jump rule and active regions, we propose a concept called state-dependent jump path. Unlike the conventional perspective that treats jumps as discrete-time dynamics, we interpret them as continuous dynamics, parameterized by a virtual time-variable. Secondly, by adapting the hybrid time-domain solution theory for continuous-discrete hybrid systems, we define the concept of jump-flow solutions for PWA-DAEs with the help of Filippov solutions for differential inclusions. Subsequently, we study various boundary behaviors of jump-flow solutions. Finally, we apply the proposed solution concepts in simulating a state-dependent switching circuit.

Keywords: Hybrid systems, Nonlinear output feedback, Adaptive control
Abstract: Impulsive switched systems encompass various modes, each exhibiting distinct behaviours. Typically, a switching sequence orchestrates transitions between these modes, where state jumps may occur, potentially undermining output tracking performance or system stability. This work introduces a funnel controller tailored for relative degree one nonlinear impulsive switched systems. Notably, this controller operates solely based on system output without necessitating knowledge of system dynamics. Unlike classical funnel controllers with fixed boundaries, the proposed method dynamically adjusts the funnel boundary for each approaching jump, aiming to preserve adherence to the original boundary. No precise knowledge of jump instances or maps is required; approximate jump intervals and an upper bound for maximum jump height suffice. Theoretical analysis establishes that the error remains within the funnel, facilitating successful reference signal tracking. Performance validation is demonstrated via numerical simulation.

Keywords: Hybrid systems, Nonlinear systems, Robust control
Abstract: This paper introduces an innovative control solution to tackle the problem of robust attitude tracking for fully actuated rigid bodies. The approach resorts to the modified Rodrigues parameters (MRP), whose configuration manifold is a double cover of the three-dimensional rotation group, to design a dynamic hybrid controller that yields uniform global asymptotic and semi-global exponential tracking results in the covering space. The controller includes an integral term to deal with constant disturbances and a smoothing mechanism to generate a jump-free control signal. By relying on a hybrid dynamic path-lifting algorithm and novel equivalence of stability concepts, the authors demonstrate that the MRP-based dynamic controller globally asymptotically and semi-globally exponentially stabilizes the tracking dynamics in the base space SO(3) with robustness to small measurement noise and unknown fixed disturbances. The simulation results showcase the performance of the proposed hybrid controller.

Keywords: Hybrid systems, Stochastic systems, Optimization algorithms
Abstract: A stochastic simulator that approximates the behavior of a hybrid system given in terms of a hybrid inclusion is considered. A hybrid inclusion combines constrained differential and difference inclusions to model the continuous (flows) and discrete (jumps) dynamics, respectively. The simulator is a stochastic discrete-time system that employs a set-valued right-hand side when approximating flows. Under mild conditions on the data defining the simulator and the hybrid system, together with a non-uniform averaging condition, it is shown that almost every sample path of each solution generated by the stochastic simulator is close to a solution of the original hybrid system on compact time domains when the step size sequence is sufficiently small and converges to zero but is not summable. A probabilistic characterization is also provided. An example is provided to illustrate the interest of the proposed framework.

Keywords: Hybrid systems, Observers for nonlinear systems, Energy systems
Abstract: The state of charge (SOC) of lithium-ion batteries needs to be accurately estimated for safety and reliability purposes. For battery packs made of a large number of cells, it is not always feasible to design one SOC estimator per cell due to limited computational resources. Instead, only the minimum and the maximum SOC need to be estimated. The challenge is that the cells having the minimum and maximum SOC typically change over time. In this context, we present a low-dimensional hybrid estimator of the minimum (maximum) SOC, whose convergence is analytically guaranteed. We consider for this purpose a battery consisting of cells interconnected in series, which we model by electrical equivalent circuit models. We then present the hybrid estimator, which runs an observer designed for a single cell at any time instant, selected by a switching-like logic mechanism. We establish a practical exponential stability property for the estimation error on the minimum (maximum) SOC thereby guaranteeing the ability of the hybrid scheme to generate accurate estimates of the minimum (maximum) SOC. The analysis relies on non-smooth hybrid Lyapunov techniques. A numerical illustration is provided to showcase the relevance of the proposed approach.

Keywords: Hybrid systems, Nonlinear systems identification, Learning
Abstract: Most hybrid system identification methods rely on passive learning techniques, limiting the accuracy of the learned model to the data at hand. We present an active learning approach to identify state-dependent switched nonlinear dynamical systems with polynomial ODEs. Counterexample trajectories indicating a divergence between the system under learning and a learned hypothesis model are provided by an approximate equivalence query. Segmentation is applied on the true trajectories of the counterexamples before treating each segment. We provide a way to incrementally update the learned continuous dynamics to accommodate each segment if needed, without any assumption on the number of modes, before updating the mode regions. Our method uses multivariate polynomial regression for finding the continuous dynamics and multinomial logistic regression for the mode regions. We illustrate our approach and its effectiveness on multiple examples, including a parametric one with 20 modes.

Keywords: Neural networks, Adaptive control, Statistical learning
Abstract: Neural networks are regularly employed in adaptive control of nonlinear systems and related methods of reinforcement learning. A common architecture uses a neural network with a single hidden layer (i.e. a shallow network), in which the weights and biases are fixed in advance and only the output layer is trained. While classical results show that there exist neural networks of this type that can approximate arbitrary continuous functions, they are non-constructive, and the networks used in practice have no approximation guarantees. Thus, the approximation properties required for control with neural networks are assumed, rather than proved. In this paper, we aim to fill this gap by showing that for sufficiently smooth functions, ReLU networks with randomly generated weights and biases achieve L-infinity error of O(m^-1/2) with high probability, where m is the number of neurons. We show how the result can be used to construct approximators of required accuracy in a model reference adaptive control application.