Keywords: Biomolecular systems, Systems biology, Biological systems
Abstract: In this paper we consider the high--affinity nitrate acquisition in plant roots. This process is governed by a mechanism including two loops of opposite signs we call Incoherent FeedBack (IFB) loop. A positive feedback loop acting in the short term, increases the intake when the roots are exposed to nitrate. An additional negative loop drastically reduces the acquisition in the long run by inhibiting the synthesis of transporters. We propose a model that fits nicely the experimental data. We investigate about the robustness of the model proving its structural stability, namely, stability for all possible parameters under some technical assumptions. We compare our model to the well known Incoherent FeedForward (IFF) loop which is a very popular network motif.

Keywords: Systems biology, Stability of nonlinear systems, Biological systems
Abstract: Since its introduction by Briat, Gupta and Khammash, the antithetic feedback controller design has attracted considerable attention in both theoretical and experimental systems biology. The case in which the plant is a two-dimensional linear system (making the closed-loop system a four-dimensional nonlinear system) has been analyzed in much detail. This system has a unique equilibrium e but, depending on parameters, it may exhibit periodic orbits. An interesting question is for what parameter values periodic orbits exist. Another open question is whether other dynamical behaviors, such as chaotic attractors, might be possible for some parameter choices. We show that, for any parameter choices, every compact omega-limit set that does not include e is a periodic solution. We also show that if the Jacobian of the vector field at the equilibrium is unstable then a (non-trivial) periodic orbit exists, and provide an explicit open set of initial conditions that are attracted to a periodic orbit. The analysis is based on the theory of strongly 2-cooperative systems.

Keywords: Genetic regulatory systems, Systems biology, Markov processes
Abstract: Bursty protein production is a key source of gene expression noise. In this study, we analyze a Markovian model of cellular protein dynamics, where proteins are produced in geometrically distributed bursts. Extending this model, we incorporate a feedback mechanism by assuming that higher protein levels reduce both cell growth and protein decay rates. We study both single-cell dynamics and an expanding cell population. Without feedback, the protein level follows a negative binomial distribution with the same parameters in both cases. With feedback, however, single-cell and population-level distributions differ, each expressible as a mixture of two negative binomial distributions with framework-dependent parameters. Using numerical integration of the master and population balance equations, we calculate the time-dependent distributions in both settings. This work extends previous continuous models and provides new insights into how population expansion influences intrinsic cellular heterogeneity.

Keywords: Biomolecular systems, Genetic regulatory systems, Systems biology
Abstract: In this contribution, we systematically investigate how intracellular constraints on resources impact stochastic gene expression. We first consider a model of a single gene with discrete integer-valued mRNA and protein copy numbers that evolved stochastically based on probability occurrences of biochemical reactions. The resource constraints are imposed by considering a finite number of ribosomes binding to mRNAs to form a translation complex, and the complex dissociates to give back a free ribosome and a protein molecule. Analytical analysis reveals that ribosomal constraints reduce the magnitude of stochastic fluctuations in protein copy numbers, and also lead to lower statistical single-cell concordance between mRNA and protein levels of the same gene. We also identify parameter regimes where copy-number fluctuations become sub-Poisson -- less variation than expected from a Poisson distribution. Considering fast ribosomal binding/unbinding to mRNAs, we also develop a reduced stochastic model that faithfully captures the statistical fluctuation of the system. The results help towards exploiting resource as design parameter to minimize noise in synthetic biology.

Keywords: Biological systems, Reinforcement learning, Control applications
Abstract: Achieving real-time control of genetic systems is critical for improving the reliability, efficiency, and reproducibility of biological research and engineering. Yet the intrinsic stochasticity of these systems makes this goal difficult. Prior efforts have faced three recurring challenges: (a) predictive models of gene expression dynamics are often inaccurate or unavailable, (b) nonlinear dynamics and feedback in genetic circuits frequently lead to multi-stability, limiting the effectiveness of deterministic control strategies, and (c) slow biological response times make data collection for learning-based methods prohibitively time-consuming. Recent experimental advances now allow the parallel observation and manipulation of over a million individual cells, opening the door to model-free, data-driven control strategies. Here we investigate the use of Parallelized Q-Networks (PQN), a recently-developed reinforcement learning algorithm, to learn control policies for a simulated bi-stable gene regulatory network. We show that PQN can not only control this self-activating system more accurately than other model-free and model-based control methods previously used in the field, but also converges efficiently enough to be practical for experimental application. Our results suggest that parallelized experiments coupled with advances in reinforcement learning provide a viable path for real-time, model-free control of complex, multi-stable biological systems.

Keywords: Genetic regulatory systems, Biological systems, Biomolecular systems
Abstract: Gene expression in response to stimuli is regulated by transcription factors (TFs) through feedback loop motifs, aimed at maintaining the desired TF concentration despite uncertainties and perturbations. In this work, we consider a stochastic model of the positive gene autoregulating feedback loop and we probabilistically quantify its resilience, i.e., its ability to preserve the equilibrium associated with a prescribed concentration of TFs, and the corresponding basin of attraction, in the presence of noise. We show that the formation of larger oligomers, corresponding to larger Hill coefficients of the regulation function, and thus to sharper non-linearities, improves the system resilience, even close to critical concentrations of TFs. We also explore a complementary definition of resilience that can be assessed within a stochastic formulation relying on the Fokker-Planck equation. Our formal results are accompanied by numerical simulations.

Keywords: Genetic regulatory systems, Cellular dynamics, Biomolecular systems
Abstract: Biomolecular integral feedback controllers offer precise regulation of molecular species copy numbers, making them valuable for synthetic biology applications. Antithetic integral feedback controllers, in particular, can be effective in low-copy-number regimes with stochastic dynamics. In this work, we introduce a modified variant of this controller, called the antithetic dual-rein integral feedback motif, and analyze its performance from a stochastic perspective in the presence of intrinsic dynamic randomness. We demonstrate that our controller enables first-moment control while maintaining a tractable steady-state variance bound under specific parametric regimes. Notably, this variance bound is tunable, as it depends solely on the controller parameters. We derive these results using stochastic model-order reduction and validate them through numerical simulations. Our findings provide new insights into achieving both precise regulation and noise suppression in stochastic genetic circuits.

Keywords: Genetic regulatory systems, Optimal control, Hybrid systems
Abstract: In this work, we tackle the problem of inducing optimal transfers between the two oscillatory regimes of a birhythmic genetic network, represented through a piecewise affine dynamical system. For that, we resort to an adaptation of Pontryagin's Maximum Principle to the hybrid setting, with a cost function that combines the transfer time and an L¹-control cost. We focus on a two-dimensional PWA model of the p53-Mdm2 network, a well-known tumor suppressor module that represents a key example of birhythmicity naturally found in mammalian cells. The resulting optimal control can be expressed in feedback form, and is able to remove an oscillatory mode of the system, allowing selection between low or high frequency oscillations of the bimodal genetic network.

Keywords: Identification for control, Linear parameter-varying systems, Uncertain systems
Abstract: We present an approach to identify a quasi Linear Parameter Varying (qLPV) model of a plant, with the qLPV model guaranteed to admit a robust control invariant (RCI) set. It builds upon the concurrent synthesis framework recently presented by the authors, in which the requirement of existence of an RCI set is modeled as a control-oriented regularization. Here, we reduce the conservativeness of the approach by bounding the qLPV system with an uncertain LTI system, which we derive using bound propagation approaches. The resulting regularization function is the optimal value of a nonlinear robust optimization problem that we solve via a differentiable algorithm. We numerically demonstrate the benefits of the proposed approach over two benchmark approaches.er synthesized from data.

Keywords: Data driven control, Machine learning, Optimization algorithms
Abstract: Many safety-critical real-world problems, such as autonomous driving and collaborative robots, are of a distributed multi-agent nature. To optimize the performance of these systems while ensuring safety, we can cast them as distributed optimization problems, where each agent aims to optimize their parameters to maximize a coupled reward function subject to coupled constraints. Prior work either studies a centralized setting, does not consider safety, or struggles with sample efficiency. Since we require sample efficiency and work with unknown and nonconvex rewards and constraints, we solve this optimization problem using safe Bayesian optimization with Gaussian process regression. Moreover, we consider nearest-neighbor communication between the agents. To capture the behavior of non-neighboring agents, we reformulate the static global optimization problem as a time-varying local optimization problem for each agent, essentially introducing time as a latent variable. To this end, we propose a custom spatio-temporal kernel to integrate prior knowledge. We show the successful deployment of our algorithm in simulations.

Keywords: Reduced order modeling, Identification for control, Lyapunov methods
Abstract: We initiate a formal study on the use of low-dimensional latent representations of dynamical systems for verifiable control synthesis. Our main goal is to enable the application of verification techniques—such as Lyapunov or barrier functions—that might otherwise be computationally prohibitive when applied directly to the full state representation. Towards this goal, we first provide dynamics-aware, approximate conjugacy conditions which formalize the notion of reconstruction error necessary for systems analysis. We then utilize our conjugacy conditions to transfer the stability and invariance guarantees of a latent certificate function (e.g., a Lyapunov or barrier function) for a latent space controller back to the original system. Importantly, our analysis contains several important implications for learning latent spaces and dynamics, by highlighting the necessary geometric properties which need to be preserved by the latent space, in addition to providing concrete loss functions for dynamics reconstruction that are directly related to control design. We conclude by demonstrating the applicability of our theory to two case studies: (1) stabilization of a cartpole system, and (2) collision avoidance for a two-vehicle system.

Keywords: Machine learning, Constrained control, Data driven control
Abstract: Learning control barrier functions (CBFs) offers a promising approach to enforcing safety but doing so with formal guarantees remains challenging. This is compounded by the complexity of the dynamics considered in this paper, given by systems in Brunovsk'y canonical form, which naturally require high-order CBFs (HOCBFs). The signed distance function (SDF) naturally encodes HOCBF properties but is often non-smooth, limiting its applicability in learning-based methods and safety-critical control. To address this, we propose a smoothing technique that ensures continuous differentiability with respect to the relative degree of the system dynamics while preserving key safety properties of the SDF. We then leverage Gaussian Process regression to learn an HOCBF candidate from noisy measurements, providing probabilistic safety guarantees through an inner approximation of the safe set. Additionally, we establish formal feasibility guarantees for the HOCBF-based controller and ensure the safety of the resulting closed-loop dynamics with high probability. Our approach enables online adaptation by efficiently updating the learned HOCBF with new data. We demonstrate our approach in simulation on a planar system and robotic manipulator with 2DOF.

Keywords: Optimal control, Data driven control, Formal Verification/Synthesis
Abstract: In continuous-time optimal control, evaluating the Hamiltonian requires solving a constrained optimization problem using the system's dynamics model. Hamilton-Jacobi reachability analysis for safety verification has demonstrated practical utility only when efficient evaluation of the Hamiltonian over a large state-time grid is possible. In this study, we introduce the concept of a data-driven Hamiltonian (DDH), which circumvents the need for an explicit dynamics model by relying only on mild prior knowledge (e.g., Lipschitz constants), thus enabling the construction of reachable sets directly from trajectory data. Recognizing that the Hamiltonian is the optimal inner product between a given costate and realizable state velocities, the DDH estimates the Hamiltonian using the worst-case realization of the velocity field based on the observed state trajectory data. This formulation ensures a conservative approximation of the true Hamiltonian for uncertain dynamics. The reachable set computed based on the DDH is also ensured to be a conservative approximation of the true reachable set. Next, we propose a data-efficient safe experiment framework for gradual expansion of safe sets using the DDH. This is achieved by iteratively conducting experiments within the computed data-driven safe set and updating the set using newly collected trajectory data. To demonstrate the capabilities of our approach, we showcase its effectiveness in safe flight envelope expansion for a tiltrotor vehicle transitioning from near-hover to forward flight.

Keywords: Constrained control, Data driven control, Control applications
Abstract: Ensuring constraint satisfaction in control systems without relying on accurate models is essential for real-world applications. Learning-based Reference Governors (LRGs) address this challenge by leveraging data-driven adaptation to improve constraint handling. However, existing safety-critical LRG methods often suffer from slow learning speeds and require full state measurements. This paper presents an enhanced safety-critical LRG framework that accelerates learning by redefining the peak deviation function and proposes an output-only measurement version that increases its practical applicability. A case study on a spacecraft with a flexible appendage demonstrates the effectiveness of the approach, showing improved learning speed and closed-loop convergence.

Keywords: Data driven control, Nonlinear systems, Autonomous robots
Abstract: We present a data-driven safety filtering framework for nonlinear discrete-time systems that combines neural network-based control barrier functions (CBFs) with conformal prediction (CP) to provide probabilistic safety guarantees. This method utilizes CBFs learned via neural networks to determine whether the system can remain in a safe state. Furthermore, by incorporating CP, the method evaluates the error between the predicted and true values of the CBF, enabling reliable, probability-based safety certification. We applied the proposed method to the mobile robot path planning task combined with the potential field method, demonstrating its applicability even in hazardous scenarios such as deadlocks, which are difficult to formalize explicitly. Moreover, CP enables quantification of the likelihood that the system remains within the safe set. By combining data-driven control design with probabilistic safety guarantees, the proposed method contributes to improving the safety of control systems.

Keywords: Data driven control, Uncertain systems, Stability of nonlinear systems
Abstract: We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal robustness, which robustifies the Lyapunov and zeroing barrier certificates of data-driven dynamical systems against model prediction uncertainties using conformal prediction. It quantifies these uncertainties by leveraging rank statistics of prediction scores over system trajectories, without assuming any specific underlying structure of the prediction model or distribution of the uncertainties. With the quantified uncertainty information, we further construct the conformally robust control Lyapunov function (CR-CLF) and control barrier function (CR-CBF), data-driven counterparts of the CLF and CBF, for fully data-driven control with statistical guarantees of finite-horizon exponential stability and safety. The performance of the proposed concept is validated in numerical simulations with four benchmark nonlinear control problems.

Keywords: Robust control, Optimal control, Data driven control
Abstract: This paper considers the problem of data-driven robust control design for nonlinear systems, for instance, obtained when discretizing nonlinear partial differential equations (PDEs). A robust learning control approach is developed for nonlinear affine in control systems based on Lyapunov redesign technique. The robust control is developed as a sum of an optimal learning control which stabilizes the system in absence of disturbances, and an additive Lyapunov-based robustification term which handles the effects of disturbances. The dual ensemble Kalman filter (dual EnKF) algorithm is utilized in the optimal control design methodology. A simulation study is done on the heat equation and Burgers partial differential equation.

Keywords: Distributed parameter systems, LMIs
Abstract: In recent years, the control of singularly perturbed reaction-diffusion systems has gained increasing attention. Differently from the existing qualitative methods with stability guaranteed for small enough value of the singular perturbation parameter, in this paper we give a quantitative upper bound on this parameter. We study finite-dimensional state-feedback control of singularly perturbed linear 1D reaction-diffusion systems with scalar slow and fast systems under Neumann actuation in each system. We employ modal decomposition, and the two actuators are efficient for unstable fast system and the non-standard singularly perturbed system. The controller gain is designed based on the slow (descriptor) system. We provide LMIs for finding a quantitative upper bound of the singular perturbation parameter along with the controller gain and decay rate. Numerical examples demonstrate the efficiency of the proposed method.

Keywords: Backstepping, Machine learning, Distributed parameter systems
Abstract: We present an event-triggered boundary control scheme for a class of reaction-diffusion PDEs using operator learning and the backstepping method. Our contribution aims to learn the backstepping kernels, which inherently induce the learning of the gains in the event trigger and the control law. The kernel functions in constructing the control law are approximated with neural operators (NOs) to improve the computational efficiency. Then, a dynamic event-triggering mechanism is designed, based on the plant and the continuous-time control law using kernels given by NOs, 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 the L^2 norm of the reaction-diffusion PDE state and the dynamic variable in the event-triggering mechanism is proved via Lyapunov analysis. The effectiveness of the proposed method is illustrated by numerical simulation.

Keywords: Autonomous systems, Distributed parameter systems, Large-scale systems
Abstract: We address the problem of controlling the density of a large ensemble of follower agents by acting on a group of leader agents that interact with them. Using coupled partial integro-differential equations to describe leader and follower density dynamics, we establish feasibility conditions and develop two control architectures ensuring global stability. The first employs feed-forward control on the followers' and a feedback on the leaders' density. The second implements a dual feedback loop through a reference-governor that adapts the leaders' density based on both populations' measurements. Our methods, initially developed in a one-dimensional setting, are extended to multi-dimensional cases, and validated through numerical simulations for representative control applications, both for groups of infinite and finite size.

Keywords: Backstepping, Distributed parameter systems, Constrained control
Abstract: This paper presents a safe stabilization of the Stefan PDE model with a moving boundary governed by a high-order dynamics. We consider a parabolic PDE with a time-varying domain governed by a second-order response with respect to the Neumann boundary value of the PDE state at the moving boundary. The objective is to design a boundary heat flux control to stabilize the moving boundary at a desired setpoint, with satisfying the required conditions of the model on PDE state and the moving boundary. We apply a PDE backstepping method for the control design with considering a constraint on the control law. The PDE and moving boundary constraints are shown to be satisfied by applying the maximum principle for parabolic PDEs. Then the closed-loop system is shown to be globally exponentially stable by performing Lyapunov analysis. The proposed control is implemented in numerical simulation, which illustrates the desired performance in safety and stability. An outline of the extension to third-order moving boundary dynamics is also presented.

Keywords: Distributed parameter systems, Stability of nonlinear systems, Nonlinear systems
Abstract: This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the convergence objective (finite-time) and the rejection of perturbations are achieved. Second, we consider a class of nonlinear systems and design a feedback control that ensures the closed-loop system is finite-time stable. All proofs presented in this paper regarding convergence are based on Lyapunov theory. The existence of solutions to the closed-loop system and its well-posedness are established using maximal monotone theory. To illustrate the applicability of the theoretical results, a heat equation is considered as an application of the main results.

Keywords: Distributed parameter systems, Stability of nonlinear systems, Sampled-data control
Abstract: We show that if a linear infinite-dimensional system is exponentially stabilizable by compact feedback, it is also stabilizable by means of a sampled-data feedback that is fed through a globally Lipschitz nonlinearity, provided that the sector bound for the nonlinearity and the sampling time is small enough. Next we develop a switching-based event-triggered control scheme stabilizing the system with a reduced number of switching events. We further show how the proposed event-triggering scheme can be adapted to handle uncertain input nonlinearities, where only the sector bound parameter and a bound on the Lipschitz constant of the nonlinearity are assumed to be known.

Keywords: Distributed parameter systems, Stochastic optimal control, Stochastic systems
Abstract: In this paper, we design a controller for an interconnected system where a linear Stochastic Differential Equation (SDE) is actuated through a linear parabolic heat equation. These dynamics arise in various applications, such as coupled heat transfer systems and chemical reaction processes that are subject to disturbances. Our goal is to develop a computational method for approximating the controller that minimizes a quadratic cost associated with the state of the SDE component. To achieve this, we first perform a change of variables to shift the actuation inside the PDE domain and reformulate the system as a linear Stochastic Partial Differential Equation (SPDE). We use a spectral approximation of the Laplacian operator to discretize the coupled dynamics into a finite-dimensional SDE and compute the optimal control for this approximated system. The resulting control serves as an approximation of the optimal control for the original system. We then establish the convergence of the approximated optimal control and the corresponding closed-loop dynamics to their infinite-dimensional counterparts. Numerical simulations are provided to illustrate the effectiveness of our approach.

Keywords: Maritime control, Hierarchical control, Control applications
Abstract: We develop a hierarchical control architecture for autonomous docking maneuvers of a dynamic positioning vessel and provide formal safety guarantees. At the upper-level, we treat the vessel’s desired surge, sway, and yaw velocities as control inputs and synthesize a symbolic controller in real-time. The desired velocities are then executed by the vessel's low-level velocity feedback control loop. We next investigate methods to optimize the performance of the proposed control scheme. The results are evaluated on a simulation model of a marine surface vessel in the presence of static obstacles and, for the first time, through physical experiments on a scale model vessel.

Keywords: Control system architecture, Hierarchical control
Abstract: Layered control architectures have been a standard paradigm for efficiently managing complex constrained systems. A typical architecture consists of: i) a higher layer, where a low-frequency planner controls a simple model of the system, and ii) a lower layer, where a high-frequency tracking controller guides a detailed model of the system toward the output of the higher-layer model. A fundamental problem in this layered architecture is the design of planners and tracking controllers that guarantee both higher- and lower-layer system constraints are satisfied. Toward addressing this problem, we introduce a principled approach for layered multirate control of linear systems subject to output and input constraints. Inspired by discrete-time simulation functions, we propose an efficient control design that guarantees the lower-layer system tracks the output of the higher-layer system with computable precision. Using this design, we derive conditions and present a method for propagating the constraints of the lower-layer system to the higher-layer system. The propagated constraints are integrated into the design of an arbitrary planner that can handle higher-layer system constraints. Our framework ensures that the output constraints of the lower-layer system are satisfied at all high-level time steps, while respecting its input constraints at all low-level time steps. We apply our approach in a scenario of motion planning, highlighting its critical role in ensuring collision avoidance.

Keywords: Learning, Feedback linearization, Nonlinear systems
Abstract: We study residual dynamics learning for differentially flat systems, where a nominal model is augmented with a learned correction term from data. A key challenge is that generic residual parameterizations may destroy flatness, limiting the applicability of flatness-based planning and control methods. To address this, we propose a framework for learning flatness-preserving residual dynamics in systems whose nominal model admits a pure-feedback form. We show that residuals with a lower-triangular structure preserve both the flatness of the system and the original flat outputs. Moreover, we provide a constructive procedure to recover the flatness diffeomorphism of the augmented system from that of the nominal model. Building on these insights, we introduce a parameterization of flatness-preserving residuals using smooth function approximators, making them learnable from trajectory data with conventional algorithms. Our approach is validated in simulation on a 2D quadrotor subject to unmodeled aerodynamic effects. We demonstrate that the resulting learned flat model achieves a tracking error 5times lower than the nominal flat model, while being 20times faster over a structure-agnostic alternative.

Keywords: Genetic regulatory systems, Biological systems, Systems biology
Abstract: The development of genetic memory devices in synthetic biology is a challenging process that requires extensive analysis and characterization. In mammalian systems, this complexity is compounded by the need for a small DNA payload for efficient delivery into the cell. Previous genetic memory devices have relied exclusively on protein-based regulation, which are limited by their large size; in this paper, we propose a microRNA-based multistable network, which effectively halves the payload size for more efficient delivery. We demonstrate that the system can be multistable, and use formal methods to characterize constraints on design parameters that guarantee multistability. Our results provide a new genetic network topology that can achieve multistability and demonstrate the use of formal methods in the design of sophisticated genetic network architectures against non-convex top-level specifications.

Keywords: Autonomous systems, Autonomous robots, Formal Verification/Synthesis
Abstract: Optimizing the design of complex systems requires navigating interdependent decisions, heterogeneous components, and multiple objectives. Our monotone theory of co-design offers a compositional framework for addressing this challenge, modeling systems as design problems (DPs), representing trade-offs between functionalities and resources within partially ordered sets. While current approaches model uncertainty using intervals, capturing worst- and best-case bounds, they fail to express probabilistic notions such as risk and confidence. These limitations hinder the applicability of co-design in domains where uncertainty plays a critical role. In this paper, we introduce a unified framework for composable uncertainty in co-design, capturing intervals, distributions, and parametrized models. This extension enables reasoning about risk-performance trade-offs and supports advanced queries such as experiment design, learning, and multi-stage decision making. We demonstrate the expressiveness and utility of the framework via a numerical case study on the uncertainty-aware co-design of task-driven unmanned aerial vehicles (UAVs).

Keywords: Cooperative control, Distributed control, Optimal control
Abstract: Techniques for coordination of multi-agent systems are vast and varied, often utilizing purpose-built solvers or controllers with tight coupling to the types of systems involved or the coordination goal. In this paper, we introduce a general unified framework for heterogeneous multi-agent coordination using the language of cellular sheaves and nonlinear sheaf Laplacians, which are generalizations of graphs and graph Laplacians. Specifically, we introduce the concept of a nonlinear homological program encompassing a choice of cellular sheaf on an undirected graph, nonlinear edge potential functions, and constrained convex node objectives, which constitutes a standard form for a wide class of coordination problems. We use the alternating direction method of multipliers to derive a distributed optimization algorithm for solving these nonlinear homological programs. To demonstrate the applicability of this framework, we show how heterogeneous coordination goals including combinations of consensus, formation, and flocking can be formulated as nonlinear homological programs and provide numerical simulations showing the efficacy of our distributed solution algorithm.

Keywords: Robotics, Stability of hybrid systems, Lyapunov methods
Abstract: Reduced-order models (ROMs) provide a powerful means of synthesizing dynamic walking gaits on legged robots. Yet this approach lacks the formal guarantees enjoyed by methods that utilize the full-order model (FOM) for gait synthesis, e.g., hybrid zero dynamics. This paper aims to unify these approaches through a layered control perspective. In particular, we establish conditions on when a ROM of locomotion yields stable walking on the full-order hybrid dynamics. To achieve this result, given an ROM we synthesize a zero dynamics manifold encoding the behavior of the ROM---controllers can be synthesized that drive the FOM to this surface, yielding hybrid zero dynamics. We prove that a stable periodic orbit in the ROM implies an input-to-state stable periodic orbit of the FOM's hybrid zero dynamics, and hence the FOM dynamics. This result is demonstrated in simulation on a linear inverted pendulum ROM and a 5-link planar walking FOM.

Keywords: Biologically-inspired methods, Control system architecture, Biological systems
Abstract: Motivated by the challenge of reverse-engineering biological control systems, this paper establishes a mathematical foundation for a central property of layered control design: virtualization. Despite its ubiquity in engineered systems, virtualization lacks a rigorous, comprehensive theoretical treatment.

We begin to address this gap by proposing a formal definition of internal virtualization within reference tracking architectures-- a simple but foundational step toward a broader theory of virtualization in layered control architecture. Using minimal, standard tools from control theory, we present examples, counterexamples, and empirical explorations to illustrate key properties of internal virtualization and its relationship to classic control concepts such as feasible trajectory planning and differential flatness, as well as the more general concepts of modularity and predictive coding.

Altogether, the rich insight demonstrated in such a simple, mathematically minimal treatment of virtualization in layered reference tracking reflects the urgent need for a more expansive, formal theory of Internal Virtualization in layered control architectures.

Keywords: Autonomous vehicles, Vision-based control, Uncertain systems
Abstract: Autonomous driving systems heavily depend on deep neural network-based perception to interpret their environment and support decision-making. To enhance robustness in these safety-critical settings, this paper proposes a Deep Ensemble of neural network regressors integrated with Conformal Prediction to estimate both vehicle states and associated perception uncertainties. Within the Adaptive Cruise Control framework, the method uses RGB image inputs to jointly predict states and generate non-uniform, probabilistically calibrated uncertainty bounds. A Conformal Tube Model Predictive Control scheme incorporates these uncertainty estimates to ensure probabilistic safety guarantees under exchangeability assumptions. Evaluations in a high-fidelity driving simulator demonstrate the algorithm’s effectiveness in maintaining safe following distances and accurate speed tracking, including under Out-Of-Distribution conditions.

Keywords: Automotive control, Predictive control for nonlinear systems, Optimal control
Abstract: Optimizing the energy consumption of electric vehicles (EVs) during operation is a key factor in mitigating their overall environmental impact. Autonomous vehicle functions, such as Adaptive Cruise Control (ACC), typically disregard economic criteria such as energy optimization, being, in general, not trivial to conciliate tracking and economic control tasks. Within the domain of optimal control, Economic Nonlinear MPC (E-NMPC) is designed to deliver an economically optimal control action, optimizing the economic profit of the plant. However, E-NMPC does not allow us to include additional adversarial tasks, such as tracking, and its closed-loop stability is not easy to guarantee. In this work, we propose a novel E-NMPC formulation for conflicting control objectives - such as tracking and economic tasks - that attains the optimal trade-off between them. Furthermore, we propose a constructive procedure to design stabilizing terms for E-NMPC, ensuring its closed-loop stability with minimal impact on economic performance. We apply the proposed E-NMPC strategy to the ACC case study, proving its effectiveness in simulation: the E-NMPC-based ACC proficiently attains the conflicting tasks, delivering a higher economic profit than standard NMPC, while ensuring closed-loop stability.

Keywords: Automotive control, Stochastic optimal control, Machine learning
Abstract: This paper presents an online energy management system for an energy hub where electric vehicles are charged combining on-site photovoltaic generation and battery energy storage with the power grid, with the objective to decide on the battery (dis)charging to minimize the costs of operation. To this end, we devise a scenario-based stochastic model predictive control (MPC) scheme that leverages probabilistic 24-hour-ahead forecasts of charging load, solar generation and day-ahead electricity prices to achieve a cost-optimal operation of the energy hub. The probabilistic forecasts leverage conformal prediction providing calibrated distribution-free confidence intervals starting from a machine learning model that generates no uncertainty quantification. We showcase our controller by running it over a 280-day evaluation in a closed-loop simulated environment to compare the observed cost of two scenario-based MPCs with two deterministic alternatives: a version with point forecast and a version with perfect forecast. Our results indicate that, compared to the perfect forecast implementation, our proposed scenario-based MPCs are 13% more expensive, and 1% better than their deterministic point-forecast counterpart.

Keywords: Autonomous vehicles, Robotics, Robust control
Abstract: This paper proposes a safety-critical controller for dynamic and uncertain environments, leveraging a robust environment control barrier function (ECBF) to improve robustness against the uncertainties associated with moving obstacles. The approach reduces conservatism, compared with a worst-case uncertainty approach, by incorporating a state observer for obstacles into the ECBF design. The safety-guaranteed controller is achieved by efficiently solving a quadratic programming problem. The proposed method's effectiveness is demonstrated via a dynamic obstacle-avoidance problem for an autonomous vehicle, including comparisons with established baseline approaches.

Keywords: Autonomous robots, Optimal control, Reinforcement learning
Abstract: Safe navigation in unknown and cluttered environments remains a challenging problem in robotics. Model Predictive Contour Control (MPCC) has shown promise for performant obstacle avoidance by enabling precise and agile trajectory tracking, however, existing methods lack formal safety assurances. To address this issue, we propose a general Control Lyapunov Function (CLF) and Control Barrier Function (CBF) enabled MPCC framework that enforces safety constraints derived from a free-space corridor around the planned trajectory. To enhance feasibility, we dynamically adapt the CBF parameters at runtime using a Soft Actor-Critic (SAC) policy. The approach is validated with extensive simulations and an experiment on mobile robot navigation in unknown cluttered environments.

Keywords: Autonomous robots, Autonomous systems, Control applications
Abstract: Control Barrier Functions (CBFs) have emerged as efficient tools to address the safe navigation problem for robot applications. However, synthesizing informative and obstacle motion-aware CBFs online using real-time sensor data remains challenging, particularly in unknown and dynamic scenarios. Motived by this challenge, this paper aims to propose a novel Gaussian Process-based formulation of CBF, termed the Dynamic Log Gaussian Process Control Barrier Function (DLGP-CBF), to enable real-time construction of CBF which are both spatially informative and responsive to obstacle motion. Firstly, the DLGP-CBF leverages a logarithmic transformation of GP regression to generate smooth and informative barrier values and gradients, even in sparse-data regions. Secondly, by explicitly modeling the DLGP-CBF as a function of obstacle positions, the derived safety constraint integrates predicted obstacle velocities, allowing the controller to proactively respond to dynamic obstacles’ motion. Simulation results demonstrate significant improvements in obstacle avoidance performance, including increased safety margins, smoother trajectories, and enhanced responsiveness compared to baseline methods.

Keywords: Autonomous systems, Reinforcement learning, Distributed control
Abstract: We propose a decentralized reinforcement learning solution for multi-agent shepherding of non-cohesive targets using policy-gradient methods. Our architecture integrates target-selection with target-driving through Proximal Policy Optimization, enabling continuous action spaces and smoother agent trajectories compared to discrete-action approaches. This model-free framework effectively solves the shepherding problem while exhibiting better performance than model-based solutions previously presented in the literature. Experiments demonstrate our method's effectiveness and scalability with increased target numbers and limited sensing capabilities.

Keywords: Autonomous systems, Constrained control, Reinforcement learning
Abstract: In this paper we combine Reinforcement Learning (RL), Behavior Trees (BTs), and Control Barrier Functions (CBFs) to create controllers for complex tasks. Pairwise, these tools have been combined in several earlier works. RL and BTs have been combined to break down tasks into subtasks that are solved by RL. BTs and CBFs have been combined to avoid undoing already achieved subtasks, and CBFs have been used to provide safety guarantees for RL. By combining all three, we are able to break down tasks into subtasks and learn controllers for those tasks that are both safe and avoid undoing previously achieved subtasks. We provide experimental results that show that the proposed approach leads to more efficient training and shorter completion times of missions.

Keywords: Optimal control, Constrained control, Algebraic/geometric methods
Abstract: We consider control and inference problems where control protocols and internal dynamics are informed by two types of constraints. Our data consist of i) statistics on the ensemble and ii) trajectories or final disposition of selected tracer particles embedded in the flow. Our aim is i’) to specify a control protocol to realize a flow that meets such constraints or ii’) to recover the internal dynamics that are consistent with such a data set. We analyze these problems in the setting of linear flows and Gaussian distributions. The control cost is taken to be a suitable action integral constrained by either the trajectories of tracer particles or their terminal placements.

Keywords: Nonlinear systems, Optimal control, Optimization
Abstract: In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We derive a convex dual of the problem using dual optimal control techniques developed before and during the 1990s,transforming the non-convex optimization into a more tractable form. At the core of this formulation is the smooth sub-solutions to an HJB equation. A first-order algorithm based on the dual formulation is proposed to solve the problem numerically.

Keywords: Variational methods, Markov processes, Information theory and control
Abstract: We consider the Schrodinger bridge problem in discrete time, where the pathwise cost is replaced by a sum of quadratic functions, taking the form of a linear quadratic regulator (LQR) cost. This cost comprises potential terms that act as attractors and kinetic terms that control the diffusion of the process. When the two boundary marginals are Gaussian, we show that the LQR-Schrodinger bridge problem can be solved in closed form. We follow the dynamic programming principle, interpreting the Kantorovich potentials as cost-to-go functions. Under the LQR-Gaussian assumption, these potentials can be propagated exactly in a backward and forward passes, leading to a system of dual Riccati equations, well known in estimation and control. This system converges rapidly in practice. We then show that the optimal process is Markovian and compute its transition kernel in closed form as well as the Gaussian marginals. Through numerical experiments, we demonstrate that this approach can be used to construct complex, non-homogeneous Gaussian processes with acceleration and loops, given well-chosen attractive potentials. Moreover, this approach allows extending the Bures transport between Gaussian distributions to more complex geometries with negative curvature.

Keywords: Fluid flow systems, Optimal control, Algebraic/geometric methods
Abstract: The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question “what do efficient flow fields for mixing look like, and how do they behave?” We approach this question by developing a framework which is inspired by the dynamic and geometric approach to optimal mass transport. Specifically, we formulate the fluid mixing problem as an optimal control problem where the dynamics are given by the continuity equation together with an incompressibility constraint. We show that within this framework, the set of reachable fluid configurations can formally be endowed with the structure of an infinite-dimensional Riemannian manifold, with a metric which is induced by the control effort, and that flow fields which are maximally efficient at mixing correspond to geodesics in this Riemannian space.

Keywords: Stochastic systems, Variational methods, Stochastic optimal control
Abstract: We revisit the optimal transport problem over angular velocity dynamics given by the controlled Euler equation. The solution of this problem enables stochastic guidance of spin states of a rigid body (e.g., spacecraft) over a hard deadline constraint by transferring a given initial state statistics to a desired terminal state statistics. This is an instance of generalized optimal transport over a nonlinear dynamical system. While prior work has reported existence-uniqueness and numerical solution of this dynamical optimal transport problem, here we present structural results about the equivalent Kantorovich a.k.a. optimal coupling formulation. Specifically, we focus on deriving the ground cost for the associated Kantorovich optimal coupling formulation. The ground cost is equal to the cost of transporting unit amount of mass from a specific realization of the initial or source joint probability measure to a realization of the terminal or target joint probability measure, and determines the Kantorovich formulation. Finding the ground cost leads to solving a structured deterministic nonlinear optimal control problem, which is shown to be amenable to an analysis technique pioneered by Athans et al. We show that such techniques have broader applicability in determining the ground cost (thus Kantorovich formulation) for a class of generalized optimal mass transport problems involving nonlinear dynamics with translated norm-invariant drift.

Keywords: Autonomous robots, Optimization algorithms, Networked control systems
Abstract: In this paper, we propose a novel methodology for path planning and scheduling for multi-robot navigation that is based on optimal transport theory and model predictive control. We consider a setup where~N robots are tasked to navigate to~M targets in a common space with obstacles. Mapping robots to targets first and then planning paths can result in overlapping paths that lead to deadlocks. We derive a strategy based on optimal transport that not only provides minimum cost paths from robots to targets but also guarantees non-overlapping trajectories. We achieve this by discretizing the space of interest into~K cells and by imposing a~{Ktimes K} cost structure that describes the cost of transitioning from one cell to another. Optimal transport then provides textit{optimal and non-overlapping} cell transitions for the robots to reach the targets that can be readily deployed without any scheduling considerations. The proposed solution requires~mathcal O(K^3log K) computations in the worst-case and~mathcal O(K^2log K) for well-behaved problems. To further accommodate potentially overlapping trajectories (unavoidable in certain situations) as well as robot dynamics, we show that a temporal structure can be integrated into optimal transport with the help of textit{replans} and textit{model predictive control}.

Keywords: Mean field games, Game theory, Stochastic optimal control
Abstract: A natural assumption in games is to consider static payoffs. Yet, this is not true when the environment changes independently or as a result of players' interactions, e.g., geopolitical decisions in the global financial market, or weather conditions in autonomous driving. Indeed, these environmental aspects have a significant impact on the strategic interactions between players and vice versa. With the growing interest in machine learning approaches, disregarding these environmental changes leads to nonstationarity and instability of the corresponding algorithms. Motivated by this issue, we develop a novel framework for continuous-time finite-state feedback-evolving mean-field games (FEMFG) where the population dynamics are paired with an environmental resource which determines the payoffs and in turn evolves according to the population distribution across the underlying Markov chain. We derive the corresponding initial-terminal value problem and show the conditions for the existence of a feedback-evolving mean-field Nash equilibrium as the solution to the FEMFG, namely, when the population dynamics given by the Kolmogorov equation and the value function obtained via the Hamilton-Jacobi-Bellman equation do not change over time.

Keywords: Data driven control
Abstract: This paper introduces a novel parameterization to characterize unknown linear time-invariant systems using noisy data. The presented parameterization describes exactly the set of all systems consistent with the available data. We then derive verifiable conditions when the consistency constraint reduces the set to the true system and when it does not have any impact. Furthermore, we demonstrate how to use this parameterization to perform a direct data-driven estimator synthesis with guarantees on the H∞-norm. Lastly, we conduct numerical experiments to compare our approach to existing methods.

Keywords: Data driven control, Predictive control for linear systems, Quantized systems
Abstract: Cloud-assisted system identification and control have emerged as practical solutions for low-power, resource-constrained control systems such as micro-UAVs. In a typical cloud-assisted setting,state and input data are transmitted from local agents to a central computer over low-bandwidth wireless links, leading to quantization. This letter investigates the impact of state and input data quantization on system identification and subsequent Model Predictive Controller (MPC). We establish a fundamental relationship between the quantization resolution and the resulting model error, and analyze how this error propagates to affect the stability and boundedness of the MPC tracking error. In particular, we show that, given a sufficiently rich dataset, the model error is bounded as a function of the quantization resolution, and the MPC tracking error is likewise ultimately bounded.

Keywords: Data driven control
Abstract: We show that algorithms for solving continuous-time infinite-horizon LQR problems using input and state data on intervals require at least as much data as system identification. Using this result, we show that the map from interval data to the optimal gain defined by these algorithms is continuous. We then obtain a convergence criterion that allows us to approximate the optimal gain by using sampled data in place of interval data. In doing so, we uncover a connection with the theory of numerical integration. We corroborate our theoretical results with some numerical experiments, which show how judicious selection of sample points can significantly improve the accuracy of the approximation.

Keywords: Data driven control, Algebraic/geometric methods, Linear systems
Abstract: In this study, we investigate the generalization of controllability in the Data Informativity approach to ensure that it is independent of data space. Our proposed approach is independent of the data space and captures linear space theory from the perspective of abstract algebra, as seen in algebraic systems theory and geometric approaches in model-based control. Subsequently, we use an explicit data representation for deriving the informativity of controllability. Our results naturally derive a series of results on controllability using the Hautus test in model-based control in the context of data-driven control, which includes results of the conventional informativity of controllability.

Keywords: Data driven control, Predictive control for linear systems, Linear systems
Abstract: This paper proposes rank-based criteria for testing R-controllability and C-controllability, as well as R-observability and C-observability of the discrete-time descriptor (singular) systems using purely input-output data matrices. To address the non-causality-induced challenges in C-controllability analysis, forward and backward data matrices are constructed. Furthermore, Willems' fundamental lemma is extended to incompletely controllable descriptor systems, demonstrating that finite-length trajectories with initial states in specific subspaces can be linearly represented by measured trajectories. Numerical examples validate the effectiveness of the proposed criteria and show that Data-enabled Predictive Control (DeePC) achieves output tracking even under incomplete system controllability for descriptor systems.

Keywords: Subspace methods, Linear systems, Data driven control
Abstract: The paper introduces a class of distances for linear behaviors over finite time horizons. These distances allow for comparisons between finite-horizon linear behaviors represented by matrices of possibly different dimensions. They remain invariant under coordinate changes, rotations, and permutations, ensuring independence from input-output partitions. Moreover, they naturally encode complexity-misfit trade-offs for Linear Time-Invariant (LTI) behaviors, providing a principled solution to a longstanding puzzle in behavioral systems theory. The resulting framework characterizes modeling as a minimum distance problem, identifying the Most Powerful Unfalsified Model (MPUM) as optimal among all systems unfalsified by a given dataset.

Keywords: Estimation, Data driven control, Control of networks
Abstract: Controllability evaluation is one of fundamental topics in the analysis and design of network systems. However, the necessary and sufficient condition for the possibility of estimating controllability Gramians by using output measurement data have never been addressed. Therefore, this paper addresses data informativity for this task. First, we characterize the data informativity for computing the output controllability Gramian, where the one-step controllability subspace plays an crucial role. Second, we present data-driven computation methods for computing the output controllability Gramians. Finally, we characterize data informativity for the observability Gramian and provide computation methods for it, based on the duality to the data informativity for computing the controllability Gramian.

Keywords: Algebraic/geometric methods, Modeling, Data driven control
Abstract: Chen-Fliess functional series provide a representation for a large class of nonlinear input-output systems. Like any infinite series, however, their applicability is limited by their radii of convergence. The goal of this paper is to present a computationally feasible method to re-center a Chen-Fliess series in order to expand its time horizon. It extends existing results in two ways. First, it takes a simpler combinatorial approach to the re-centering formula that draws directly on the analogous re-centering problem for Taylor series. Second, a convergence analysis is presented for the re-centered series. This information can be used to compute a lower bound on the radius of convergence for the output function and an estimate of the series truncation error. The method is demonstrated by simulation on a steering problem for a car-trailer steering system.

Keywords: Identification, Optimization algorithms
Abstract: Factor Analysis is an effective way of dimensionality reduction achieved by revealing the low-rank plus sparse structure of the data covariance matrix. The corresponding model identification task is often formulated as an optimization problem with suitable regularizations. In particular, we use the nonconvex discontinuous L0 norm in order to induce the sparsity of the covariance matrix of the idiosyncratic noise. This paper shows that such a challenging optimization problem can be approached via an interior-point method with inner-loop Newton iterations. To this end, we first characterize the solutions to the unconstrained L0 regularized optimization problem through the L0 proximal operator, and demonstrate that local optimality is equivalent to the solution of a stationary-point equation. The latter equation can then be solved using standard Newton's method, and the procedure is integrated into an interior-point algorithm so that inequality constraints of positive semidefiniteness can be handled. Finally, numerical examples validate the effectiveness of our algorithm.

Keywords: Nonlinear systems identification, Grey-box modeling, Machine learning
Abstract: While accurate, black-box system identification models lack interpretability of the underlying system dynamics. This letter proposes State-Space Kolmogorov- Arnold Networks (SS-KAN) to address this challenge by integrating Kolmogorov-Arnold Networks within a state-space framework. The proposed model is validated on two benchmark systems: the Silverbox and the Wiener-Hammerstein benchmarks. Results show that SS-KAN provides enhanced interpretability due to sparsitypromoting regularization and the direct visualization of its learned univariate functions, which reveal system nonlinearities at the cost of accuracy when compared to state-of-the-art black-box models, highlighting SS-KAN as a promising approach for interpretable nonlinear system identification, balancing accuracy and interpretability of nonlinear system dynamics.

Keywords: Nonlinear systems identification, Modeling, Robotics
Abstract: This research provides a theoretical foundation for modeling and real-time estimation of both the pose and inertial parameters of a free-floating multi-link system with link thrusters, which are essential for safe and effective controller design and performance. First, we adapt a planar nonlinear multi-link snake robot model to represent a planar chain of bioinspired salp robots by removing joint actuators, introducing link thrusters, and allowing for non-uniform link lengths, masses, and moments of inertia. Second, we conduct a nonlinear observability analysis of the multi-link system with link thrusters, proving that the link angles, angular velocities, masses, and moments of inertia are locally observable when equipped with inertial measurement units and operating under specific thruster conditions. The analytical results are demonstrated in simulation with a three-link system.

Keywords: Nonlinear systems identification, Neural networks, Optimization
Abstract: Meta learning aims at learning how to solve tasks, and thus it allows to estimate models that can be quickly adapted to new scenarios. This work explores distributionally robust minimization in meta learning for system identification. Standard meta learning approaches optimize the expected loss, overlooking task variability. We use an alternative approach, adopting a distributionally robust optimization paradigm that prioritizes high-loss tasks, enhancing performance in worst-case scenarios. Evaluated on a meta model trained on a class of synthetic dynamical systems and tested in both in-distribution and out-of-distribution settings, the proposed approach allows to reduce failures in safety-critical applications.

Keywords: Energy systems, Modeling, Identification
Abstract: Electrochemical impedance contains a wealth of information about the physical parameters and state of lithium battery cells. As such, efficient ways to predict impedance from partial differential algebraic equation (PDAE) models are valuable for white-box system identification and health estimation. This paper reviews several approaches to calculate impedance from PDAE cell models found dispersed in the literature: direct time-domain simulation, frequency-domain linear perturbation analysis, and transfer function analysis. We construct a PDAE model of a lithium-ion battery cell and compute the model’s impedance using each approach. We cross-validate the approaches by matching impedance results and evaluate their differences in terms of computational workload, model flexibility, and functionality. We provide MATLAB and Python code to compute PDAE model impedance with each approach—including time-domain and linear perturbation analyses with COMSOL and PyBaMM solvers—useful for practical application.

Keywords: Emerging control applications, Learning, Identification
Abstract: The increasing complexity of machine learning models highlights the need for interpretability, especially in critical domains requiring trust and transparency. Local Interpretable Model-agnostic Explanations (LIME) is a popular eXplainable AI (XAI) method that provides localized, instance-specific explanations using an interpretable surrogate model. However, its effectiveness is limited by the lack of systematic guidelines for tuning its hyperparameters. This paper addresses this limitation by proposing Automatic LIME (AutoLIME), a bi-level optimization framework to tune LIME’s kernel width. Additionally, we introduce PieceWise Affine LIME (PWALIME), a clustering-based extension of LIME for multi-instance explanations, particularly useful for interpreting black-box models of dynamical systems. Preliminary numerical results validate the potential of these methods in explaining opaque dynamical models.

Keywords: Identification, Statistical learning, Energy systems
Abstract: This paper addresses the adaptation and performance monitoring of ensemble data-based models over time. Once a model of a system is identified using a specific training dataset, it may fail to accurately represent system dynamics under varying operating conditions not included in the original training dataset. To continuously adapt a data-based model to evolving operating conditions, we propose an ensemble learning framework characterized by (i) a combination rule that weights different models based on the statistical proximity of their training dataset to the current operating condition, and (ii) a monitoring algorithm leveraging statistical control charts to supervise the ensemble model's reliability and trigger the identification and integration of a new model when a new operating condition is encountered. The proposed methodology is tested on an energy system referenced in the literature, which exhibits multiple operating conditions, showing promising results from both adaptation and monitoring perspectives.

Keywords: Biological systems, Learning, Modeling
Abstract: Biomolecular Neural Networks (BNNs), artificial neural networks with biologically synthesizable architectures, achieve universal function approximations beyond simple biological circuits. However, training BNNs remains challenging due to the lack of target data. To address this, we propose leveraging Signal Temporal Logic (STL) specifications to define training objectives for BNNs. We build on the quantitative semantics of STL, enabling gradient-based optimization of the BNN weights, and introduce a learning algorithm that enables BNNs to perform regression and control tasks in biological systems. Specifically, we investigate two regression problems in which we train BNNs to act as reporters of dysregulated states, and a feedback control problem in which we train the BNN in closed loop with a chronic disease model, learning to reduce inflammation while avoiding adverse responses to external infections. Our numerical experiments demonstrate that STL-based learning can solve the investigated regression and control tasks efficiently.

Keywords: Distributed control, Decentralized control, Quantized systems
Abstract: In this paper, the average consensus problem has been considered for undirected networks under finite bit-rate communication. While other algorithms reach approximate average consensus or require global information about the network for reaching the exact average consensus, we propose a fully distributed consensus algorithm that incorporates an adaptive quantization scheme and achieves convergence to the exact average while only requiring knowledge of an upper bound of the network diameter. Using Lyapunov stability analysis, we characterize the convergence properties of the resulting nonlinear quantized system. Moreover, we provide a fully distributed strategy to escape plateaux, i.e., situations where the Lyapunov function stops descending. Simulation results justify the performance of our proposed algorithm.

Keywords: Distributed control, Predictive control for nonlinear systems, Constrained control
Abstract: For nonlinear multi-agent systems with high relative degrees, achieving formation control and obstacle avoidance in a distributed manner remains a significant challenge. To address this issue, we propose a novel distributed safety-critical model predictive control (DSMPC) algorithm that incorporates discrete-time high-order control barrier functions (DHCBFs) to enforce safety constraints, alongside discrete-time control Lyapunov functions (DCLFs) to establish terminal constraints. To facilitate distributed implementation, we develop estimated neighbor states for formulating DHCBFs and DCLFs, while also devising a compatibility constraint to limit estimation errors and ensure convergence. Additionally, we provide theoretical guarantees regarding the feasibility and stability of the proposed DSMPC algorithm based on a mild assumption. The effectiveness of the proposed method is evidenced by the simulation results, demonstrating improved performance and reduced computation time compared to existing approaches.

Keywords: Distributed control, Adaptive control, Cooperative control
Abstract: This paper focuses on the leaderless consensus problem of third order multi-agent systems with parametric uncertainties over a directed graph, where the agents reach consensus on their positions and high order derivatives. We design a novel extended state reference model using only relative position information as the input. Then an adaptive tracking algorithm is proposed to track the reference model in the presence of parametric uncertainties. We focus on the dynamical consensus, and prove the prerequisite of consensus is that the directed graph has a directed spanning tree and the eigenvalues of the transformed system matrix needs to have negative real parts except for three zero eigenvalues. Numerical simulation results are given to verify the effectiveness of proposed control algorithms.

Keywords: Distributed control, Large-scale systems, Cooperative control
Abstract: This paper addresses the formation control problem for multi-agent systems operating in three-dimensional space by introducing the novel concept of z-similar formation. Unlike traditional rigid formations, z-similar formations ensure geometric invariance specifically under translation, scaling, and rotations around the vertical (z) axis. Our method features significantly relaxed graphical conditions, requiring only a 2-rooted sensing graph and ensuring each follower node has at least three neighbors for both realizability and stability. Moreover, by leveraging local coordinate systems and relative position measurements with alignment solely in the z-axis direction, we uniquely define formations, substantially reducing reliance on global references. We provide rigorous theoretical analyses to establish conditions for formation realizability and stability, which are validated through comprehensive simulations.

Keywords: Human-in-the-loop control, Distributed control, Learning
Abstract: This paper introduces a distributed deep neural networks (DNNs) adaptive observer-based optimal control framework for cooperative manipulation. At the high level, a multilayer NN-based observer estimates human intent-based desired trajectories using limited local information, ensuring real-time tracking consistency. Novel NN weight update laws, derived via singular value decomposition, enhance adaptive estimation performance. At the low level, a cooperative game-theoretic DNNs controller ensures optimal robotic agent coordination through neighborhood optimization, considering the effects of neighboring agents, and adaptive dynamic programming (ADP), enabling efficient decision-making and coordination. Safety constraints are enforced using neighbor-dependent barrier Lyapunov functions (BLFs) that encode individual robot tracking constraints and inter-agent safety requirements. Unlike prior methods, the constrained optimization problem is transformed using enhanced Karush-Kuhn-Tucker (KKT) conditions, where Lagrange multipliers, defined as functions of neighboring states, dynamically enforce safety constraints without incorporating them directly into the cost function. Simulation results validate the framework, showing zero safety violations during cooperative manipulation tasks and a 45% reduction in cost compared to recent methods.

Keywords: Distributed control, Quantized systems, Control of networks
Abstract: This paper considers formation control of nonholonomic agents capable of straight, lateral, and rotational movements, subject to discrete constraints on the control inputs. In particular,　we aim to extend existing formation controllers so that each agent can perform the multi-step movement, i.e., achieving the desired movement in multiple steps. The multi-step movements allow us to reduce the performance degradation due to the input constraints while eliminating complicated components from the existing controllers. We present controllers to achieve the desired formation through the multi-step movements. We then present theoretical results on the performance of our controllers and the behavior of the resulting feedback system.

Keywords: Adaptive control, Biologically-inspired methods, Distributed control
Abstract: This paper presents an adaptive distributed coordination framework designed for synchronizing networks of oscillators by introducing two novel virtual dynamic states. These states facilitate cooperative behavior and enable memory-based adaptation within the network. Specifically, the Adaptive Virtual Cooperative Influence (AVCI) dynamically adjusts the cooperative interactions based on local frequency deviations, while the Virtual Influence Memory (VIM) accumulates historical interaction data to regulate the influence distribution and mitigate persistent dependency effects. A rigorous Lyapunov-based analysis is provided, proving the mathcal{D}-global asymptotic stability of the resulting closed-loop system. Numerical simulations demonstrate that the interplay between AVCI and VIM enhances coordination, counteracting the individualities of the oscillators, even in the event of improperly parameterized local controllers.

Keywords: Distributed control, Large-scale systems, Information technology systems
Abstract: Maintaining consistent time in distributed systems is a fundamental challenge. The bittide system addresses this by providing logical synchronization through a decentralized control mechanism that observes local buffer occupancies and controls the frequency of an oscillator at each node. A critical aspect of bittide's stability and performance is ensuring that these elastic buffers operate around a desired equilibrium point, preventing data loss due to overflow or underflow. This paper introduces a novel method for centering buffer occupancies in a bittide network using a technique we term frame rotation. We propose a control strategy utilizing a directed spanning tree of the network graph. By adjusting the frequencies of nodes in a specific order dictated by this tree, and employing a pulsed feedback controller that targets the buffer occupancy of edges within the spanning tree, we prove that all elastic buffers in the network can be driven to their desired equilibrium. This ordered adjustment approach ensures that prior centering efforts are not disrupted, providing a robust mechanism for managing buffer occupancy in bittide synchronized systems.

Keywords: Networked control systems, Control over communications, Stochastic systems
Abstract: This paper develops a framework for synthesizing safety controllers for discrete-time stochastic linear control systems (dt-SLS) operating under communication imperfections. The control unit is remote and communicates with the sensor and actuator through an imperfect wireless network. We consider a constant delay in the sensor-to-controller channel (uplink), and data loss in both sensor-to-controller and controller-to-actuator (downlink) channels. In our proposed scheme, data loss in each channel is modeled as an independent Bernoulli-distributed random process. To systematically handle the uplink delay, we first introduce an augmented discrete-time stochastic linear system (dt-ASLS) by concatenating all states and control inputs that sufficiently represent the state-input evolution of the original dt-SLS under the delay and packet loss constraints. We then leverage control barrier certificates for dt-ASLS to synthesize a controller that ensures the stochastic safety of dt-SLS, guaranteeing that all trajectories remain outside unsafe regions with a quantified probabilistic bound. Our approach translates safety constraints into matrix inequalities, leading to an optimization problem that eventually quantifies the probability of satisfying the safety specification in the presence of communication imperfections. We validate our results on an RLC circuit subject to both constant delay and probabilistic data loss.

Keywords: Networked control systems, Cooperative control, Identification for control
Abstract: This paper investigates the one-bit consensus control of multi-agent systems (MASs) with independent and identically distributed (i.i.d.) and Markovian packet loss. To explore the impact of packet loss on one-bit communication, this paper first quantitatively characterizes the information loss of one-bit communications caused by packet loss, which provides the proportional relationship between one-bit data with and without packet loss in the sense of expectation.Based on quantitative characterizations, a one-bit packet loss onsensus algorithm with a packet loss proportional coefficient is proposed to compensate for the information loss, where the coefficient is designed as the reciprocal of the information loss proportion.Furthermore, this paper demonstrates that the proposed algorithm enables the MAS to achieve one-bit consensus in the mean square sense at a rate of O(1/t) with packet loss. Two simulation examples are given to validate the algorithm.

Keywords: Networked control systems, Observers for Linear systems, Large-scale systems
Abstract: This paper proposes a distributed observer that utilizes intermittent communication and accommodates a broad range of scenarios, including asynchronous operation, unidirectional communication, packet loss, and communication delays. An analysis over jointly connected switching topology supports this and provides a condition for exponential convergence of the estimation error. This condition can be used to determine a communication rate. The analysis is valid when the unobservable subspace of each agent admits an invariant orthogonal complement. This is a property that is always achievable via a coordinate transformation when the system matrix is diagonalizable over the complex field.

Keywords: Control over communications, Markov processes
Abstract: This letter presents a framework for designing optimal state-feedback control that uses a wireless actuation link with imperfect channel state information to transfer the current and future control inputs that actuators can apply if future control messages are lost. The dropout compensation strategy supports scaling inputs to actuators when necessary. We analytically solve finite- and infinite-horizon control problems and present a necessary and sufficient stability condition for any given infinite-horizon state-feedback control law. We validate the results using an illustrative example.

Keywords: Control over communications, Networked control systems, Autonomous vehicles
Abstract: Wireless networks are vital for implementing flexible Networked Controlled Systems (NCS) in distributed applications, yet they introduce sampling errors, delays, and packet losses that can compromise control performance. While emerging communication services such as Ultra-Reliable Low Latency Communications (URLLC) can mitigate these issues, they consume more shared network resources and may not be efficient if the NCS does not manage its transmissions. Event Triggered Control (ETC) addresses this challenge by determining when an update is needed, thereby specifying a Minimum Inter-Event Time (MIET) and Maximum Allowable Delay (MAD) to ensure a prescribed L2 norm condition or robust stability criterion. This letter proposes an Encoder-Decoder (E/D) architecture for NCS that requires that a control signal is transmitted over a wireless link. Instead of sending the original control signal whenever a trigger occurs, this method transmits an error signal produced by the comparison between the original control signal and a locally estimated signal. This estimated signal is assumed to be locally available at the transmitter and receiver to be used as the encoder and decoder, respectively. Assuming that the estimated signal is correlated to the original control signal, the transmitted error has a lower magnitude than the original transmitted signal. As a result, the NCS can guarantee its robust stability criterion while increasing the achievable MIET, thus reducing network resource usage. This approach is validated in a Cooperative Adaptive Cruise Control (CACC) setup, demonstrating an at least 20% improvement in MIET compared to conventional ETC, while maintaining L2 (string) stability and robust performance with fewer transmissions.

Keywords: Sampled-data control, Networked control systems
Abstract: This paper is concerned with the L_{infty}/L_{2}-gain analysis of periodic event-triggered control (PETC) systems, in which the feedback connection between a continuous-time plant and a discrete-time controller is intermittently activated. An operator-based description of PETC systems is first presented by applying the lifting technique to take into account their hybrid continuous/discrete-time behavior. On top of the fast-lifted treatment of PETC systems, in which the sampling interval [0,h) is divided into N subintervals of equal width, the piecewise constant approximation (PCA) is developed for the output operator. This PCA allows us to convert the PETC system into an equivalent discrete-time event-triggered control (ETC) system. It is also shown that the l_infty/l_2-gain of the discretized ETC system converges to the gain-gain of the original PETC system at a rate of 1/N. Based on this fact, we further introduce a method for estimating the L_{infty}/L_{2}-gain of PETC systems through the linear matrix inequality (LMI)-based approach. Finally, a numerical example is given to verify the effectiveness of the arguments developed in this paper.

Keywords: Autonomous vehicles, Networked control systems, Cooperative control
Abstract: This article studies vehicle platoons whose communication is affected by additive noise. A predecessor-leader topology is considered, with additive noises affecting both communication channels. A control law is implemented that weights the importance of leader-following and predecessor-following tasks through a weighting parameter. Given this setup, a characterization of the second order statistics of the platoon is obtained, and also conditions are derived for Lp-mean Lq-variance string stability and also for mean-square string stability. Numerical examples are also provided to illustrate our findings.

Keywords: Cooperative control, Optimal control, Autonomous vehicles
Abstract: The contribution of this work is a control system architecture enabling a safe trains Virtual Coupling in realistic railway communication. Specifically, the proposed architecture addresses unreliability and variability in data communication, ensuring safety through incorporating a safety control barrier function to guarantee operational safety and through a real-time collision prediction block. Further, a real-time cruise distance from the leader train is continuously computed and updated to allow for a smooth follower motion and avoid unnecessary braking. Further, the proposed architecture supports diverse possible control laws and leaves the control designer free to design it (in the paper we propose a switched MPC strategy but other choices are possible). A railway simulation tool for VC scenarios, developed in collaboration with the Italian railway company, validates the effectiveness and potential of the proposed system in advancing safe virtual coupling in railway systems.

Keywords: Optimization, Uncertain systems, Constrained control
Abstract: This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with respect to all possible realizations of the disturbances within prescribed uncertainty sets. To address this problem, we introduce a bi-level optimization algorithm. The outer level employs a trust-region successive convexification approach which relies on linearizing the nonlinear dynamics and robust constraints. The inner level involves solving the resulting linearized robust optimization problems, for which we derive tractable convex reformulations and present an Augmented Lagrangian method for efficiently solving them. To further enhance the robustness of our methodology on nonlinear systems, we also illustrate that potential linearization errors can be effectively modeled as unknown disturbances as well. Simulation results verify the applicability of our approach in controlling nonlinear systems in a robust manner under unknown disturbances. The promise of effectively handling approximation errors in such successive linearization schemes from a robust optimization perspective is also highlighted.

Keywords: Optimization, Identification for control, Data driven control
Abstract: In this letter we study optimization problems where the cost function contains time-varying parameters that are unmeasurable and evolve according to linear, yet unknown, dynamics. We propose a solution that leverages control theoretic tools to identify the dynamics of the parameters, predict their evolution, and ultimately compute a solution to the optimization problem. The identification of the dynamics of the time-varying parameters is done online using measurements of the gradient of the cost function. This system identification problem is not standard, since the output matrix is known and the dynamics of the parameters must be estimated in the original coordinates without similarity transformations. Interestingly, our analysis shows that, under mild conditions that we characterize, the identification of the parameter dynamics and, consequently, the computation of a time-varying solution to the optimization problem, requires only a finite number of measurements of the gradient of the cost function. We illustrate the effectiveness of our algorithm on a series of numerical examples.

Keywords: Optimization, Decentralized control, Autonomous vehicles
Abstract: We present ATOMICA, Anytime Trajectory Optimization for MultI-drone systems with guaranteed Collision Avoidance, a novel algorithm designed to generate guaranteed collision-free trajectories for multi-UAV systems. Each UAV communicates with the others and treats them as dynamic obstacles within a receding-horizon guidance framework. Recursive feasibility is ensured by maintaining a safe backup trajectory at all times. The time-dependent collision avoidance constraints are efficiently handled using positivity certificates, eliminating the need for potentially unsafe time discretizations while enabling fast collision checking. The non convex optimization problem is solved using the convex concave procedure, which provides ATOMICA with anytime capability, allowing users to predefine the duration of each replanning step. We evaluate the algorithm through simulations, demonstrating a 22% reduction in mission duration compared to state-of-the-art methods. Additionally, we validate its real-time capabilities through real-world experiments.

Keywords: Autonomous systems, Optimization, Uncertain systems
Abstract: Effective risk monitoring in dynamic environments such as disaster zones requires an adaptive exploration strategy to detect hidden threats. We propose a bi-level unmanned aerial vehicle (UAV) monitoring strategy that efficiently integrates high-level route optimization with low-level path planning for known and unknown hazards. At the high level, we formulate the route optimization as a vehicle routing problem (VRP) to determine the optimal sequence for visiting known hazard locations. To strategically incorporate exploration efficiency, we introduce an edge-based centroidal Voronoi tessellation (CVT), which refines baseline routes using pseudo-nodes and allocates path budgets based on the UAV's battery capacity using a line segment Voronoi diagram. At the low level, path planning maximizes information gain within the allocated path budget by generating kinematically feasible B-spline trajectories. Bayesian inference is applied to dynamically update hazard probabilities, enabling the UAVs to prioritize unexplored regions. Simulation results demonstrate that edge-based CVT improves spatial coverage and route uniformity compared to the node-based method. Additionally, our optimized path planning consistently outperforms baselines in hazard discovery rates across a diverse set of scenarios.

Keywords: Hybrid systems, Optimization
Abstract: Mixed integer set representations, and specifically hybrid zonotopes, have enabled new techniques for reachability and verification of nonlinear and hybrid systems. Mixed-integer sets which have the property that their convex relaxation is equal to their convex hull are said to be sharp. This property allows the convex hull to be computed with minimal overhead, and is known to be important for improving the convergence rates of mixed-integer optimization algorithms that rely on convex relaxations. This paper examines methods for formulating sharp hybrid zonotopes and provides sharpness-preserving methods for performing several key set operations. The paper then shows how the reformulation-linearization technique can be applied to create a sharp realization of a hybrid zonotope that is initially not sharp. A numerical example applies this technique to find the convex hull of a level set of a feedforward ReLU neural network.

Keywords: Optimization algorithms, Stability of nonlinear systems, Optimization
Abstract: Online Feedback Optimization steers a dynamical plant to a cost-efficient steady-state, only relying on input-output sensitivity information, rather than on a full plant model. Unlike traditional feedforward approaches, OFO leverages real-time measurements from the plant, thereby inheriting the robustness and adaptability of feedback control. Unfortunately, existing theoretical guarantees for OFO assume that the controller operates on a slower timescale than the plant, which can affect responsiveness and transient performance. In this paper, we focus on relaxing this ``timescale separation'' assumption. Specifically, we consider the class of monotone systems, and we prove that OFO can achieve an optimal operating point, regardless of the time constants of controller and plant. By leveraging a small gain theorem for monotone systems, we derive several sufficient conditions for global convergence. Notably, these conditions depend only on the steady-state behavior of the plant, and are entirely independent of its transient dynamics.

Keywords: Uncertain systems, Hybrid systems, Optimization
Abstract: This paper presents a unified framework for robust trajectory planning and optimization of multirotor systems in uncertain environments, addressing challenges posed by stochastic disturbances, model inaccuracies, and safety-critical constraints. Traditional deterministic methods often yield overly conservative solutions, while existing probabilistic approaches struggle with computational complexity and scalability. To bridge these gaps, we integrate probabilistic reachability analysis with scenario-based convex program. The framework is validated through numerical examples demonstrating collision-free navigation in cluttered environments with stochastic obstacles, outperforming baseline methods in both safety and computational efficiency. This work advances robust trajectory planning by harmonizing probabilistic safety guarantees with tractable optimization under uncertainty.

Keywords: Kalman filtering, Optimization, Nonlinear systems
Abstract: We review optimization-based approaches to smoothing nonlinear dynamical systems. These approaches leverage the fact that the Extended Kalman Filter and corresponding smoother can be framed as the Gauss-Newton method for a nonlinear least squares maximum a posteriori loss, and stabilized with standard globalization techniques. We compare the performance of the Optimized Kalman Smoother (OKS) to Unscented Kalman smoothing techniques, and show that they achieve significant improvement for highly nonlinear systems, particularly in noisy settings. The comparison is performed across standard parameter choices (such as the trade-off between process and measurement terms). To our knowledge, this is the first comparison of these methods in the literature.

Keywords: Game theory, Optimization algorithms, Linear systems
Abstract: In the context of infinite-horizon general-sum linear quadratic (LQ) games, the convergence of gradient descent remains a significant yet not completely understood issue. While the convergence in the finite-horizon setting has already been proved in [1], the extension to infinite setting is challenging. We focus on a specific instance, the two-agent scalar game, and prove the algorithm's convergence in this simplified scenario. Using this example as a foundation, we demonstrate that even in the presence of equilibria that are saddle point of the gradient descent dynamics, gradient descent can still converge, and that the inclusion of noise is unnecessary.

Keywords: Game theory, Modeling
Abstract: We present a Stackelberg game model to investigate how individuals make their decisions on timing and route selection. Group formation can naturally result from these decisions, but only when individuals arrive at the same time and choose the same route. Although motivated by bird migration, our model applies to scenarios such as traffic planning, disaster evacuation, and other animal movements. Early arrivals secure better territories, while traveling together enhances navigation accuracy, foraging efficiency, and energy efficiency. Longer or more difficult migration routes reduce predation risks but increase travel costs, such as higher elevations and scarce food resources. Our analysis reveals a richer set of subgame perfect equilibria (SPEs) and heightened competition, compared to earlier models focused only on timing. By incorporating individual differences in travel costs, our model introduces a ``neutrality" state in addition to ``cooperation" and ``competition."

Keywords: Game theory, Uncertain systems, Decentralized control
Abstract: Stochastic games provide a powerful framework for controller synthesis in multi-agent systems where cooperation between agents cannot be assumed. They also serve as a core model for modular and decentralized control, where interactions between components can be captured using assume-guarantee contracts. In this setting, synthesis for an individual module reduces to computing a policy robust to the behavior of the environment, modeled as a stochastic two-player game. Many control objectives reduce to reachability objectives, leading to the study of simple stochastic games, a well-known class whose exact computational complexity remains unresolved.

A classic result of Condon reformulates the value and policy computation in such games as a quadratic program—a linear program with a quadratic objective. Motivated by their “almost linear” structure, we ask whether efficient linear programming solvers can be leveraged by iterating over a sequence of linear objectives. We introduce the Objective Improvement Algorithm, which iteratively solves linear programs to compute the optimal value and policy. Unlike strategy improvement, our method treats both players symmetrically, and unlike value iteration, it terminates with the optimal value in finitely many steps. We prove convergence and correctness and present experimental results demonstrating practical effectiveness.

Keywords: Game theory, Optimization
Abstract: Noncooperative dynamic game theory provides a principled approach to modeling sequential decision-making among multiple noncommunicative agents. A key focus is on finding Nash equilibria in two-agent zero-sum dynamic games under various information structures. A well-known result states that in linear-quadratic games, unique Nash equilibria under feedback and open-loop information structures yield identical trajectories. Motivated by two key perspectives---(i) real-world problems extend beyond linear-quadratic settings and lack unique equilibria, making only local Nash equilibria computable, and (ii) local open-loop Nash equilibria (OLNE) are easier to compute than local feedback Nash equilibria (FBNE)---it is natural to ask whether a similar result holds for local equilibria in zero-sum games. To this end, we establish that for a broad class of zero-sum games with potentially nonconvex-nonconcave objectives and nonlinear dynamics: (i) the state/control trajectory of a local FBNE satisfies local OLNE first-order optimality conditions, and vice versa, (ii) a local FBNE trajectory satisfies local OLNE second-order necessary conditions, (iii) a local FBNE trajectory satisfying feedback sufficiency conditions also constitutes a local OLNE, and (iv) with additional hard constraints on agents' actuations, a local FBNE where strict complementarity holds satisfies local OLNE first-order optimality conditions, and vice versa.

Keywords: Switched systems, Game theory, Optimal control
Abstract: The competitive spectral radius extends the notion of joint spectral radius to the two-player case: two players alternatively select matrices in prescribed compact sets, resulting in an infinite matrix product; one player wishes to maximize the growth rate of this product, whereas the other player wishes to minimize it. We show that when the matrices represent linear operators preserving a cone and satisfying a “strict positivity” assumption, the competitive spectral radius depends continuously — and even in a Lipschitz-continuous way — on the matrix sets. Moreover, we show that the competive spectral radius can be approximated up to any accuracy. This relies on the solution of a discretized infinite dimensional non-linear eigenproblem. We illustrate the approach with an example of age-structured population dynamics.

Keywords: Switched systems, Network analysis and control, Game theory
Abstract: We propose a model of opinion formation on resource allocation among multiple topics by multiple agents, who are subject to hard budget constraints. We define a utility function for each agent and then derive a projected dynamical system model of opinion evolution assuming that each agent myopically seeks to maximize its utility subject to its constraints. Inter-agent coupling arises from an undirected social network, while inter-topic coupling arises from resource constraints. We show that opinions always converge to the equilibrium set. For special networks with very weak antagonistic relations, the opinions converge to a unique equilibrium point. We further show that the underlying opinion formation game is a potential game. We relate the equilibria of the dynamics and the Nash equilibria of the game and characterize the unique Nash equilibrium for networks with no antagonistic relations. Finally, simulations illustrate our findings.

Keywords: Game theory, Optimal control, Autonomous systems
Abstract: The classic Homicidal Chauffeur game is a pursuit-evasion game played in an unbounded planar environment between a pursuer constrained to move with fixed speed on curves with bounded curvature, and a slower evader with fixed speed but with simple kinematics. We introduce a new variant of this game with asymmetric information in which the evader has the ability to choose its speed among a finite set of choices that is unknown to the pursuer a priori. Therefore the pursuer is required to estimate the evader's maximum speed based on the observations so far. This formulation leads to the question of whether the evader can exploit this asymmetry by moving deceptively by first picking a slower speed to move with and then switching to a faster speed when a specified relative configuration is attained to increase the capture time as compared to moving with the maximum speed at all times. Our contributions are as follows. First, we derive optimal feedback Nash equilibrium strategies for the complete information case of this game in which the evader is allowed to vary its speed in a given interval. Second, for the version with asymmetric information, we characterize regions of initial player locations in the game space from which the evader does not have any advantage in using deceptive strategies. Finally, we provide numerical evidence of regions in the game space from which the evader can increase the capture time by moving deceptively.

Keywords: Biological systems, Game theory
Abstract: We study a bi-virus epidemiological model where individuals can either be susceptible or infected by one of two virus strains. We account for mutations that lead to transitions between these two strains. In this work, we primarily focus on uni-directional mutation, and analyze the existence and stability of equilibrium points when mutation is permissible from the strain with a larger reproduction number and infection rate to the other strain. The novelty of our work lies in framing the mutation model within a game-theoretic context and examining the impact of strategic protection adoption on the survival of different virus strains. In this setting, each susceptible individual acts as a player, choosing an action (either adopting protection or remaining unprotected) to maximize its instantaneous payoff. We completely characterize the stationary Nash equilibrium (SNE) of the setting in which both strains coexist, and investigate how mutation rate affects the protection adoption and infection prevalence at the SNE. Finally, we present numerical results to illustrate the effects of mutation rate and cost of protection adoption on the infection prevalence of different strains.

Keywords: Robust control, Optimal control, Uncertain systems
Abstract: Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a trajectory that meets the desired properties over a fixed prediction horizon, apply a portion of the resulting input, and then re-solve the MPC problem using newly obtained measurements at the next time step. However, this approach fails to account for the fact that the control trajectory will be updated in the future, potentially leading to conservative designs. In this paper, we present a novel update-aware robust optimal MPC algorithm for decreasing horizon problems on nonlinear systems that explicitly accounts for future control trajectory updates. This additional insight allows our method to provably expand the feasible solution set and guarantee improved worst-case performance bounds compared to existing techniques. Our approach formulates the trajectory generation problem as a sequence of nested existence-constrained semi-infinite programs (SIPs), which can be efficiently solved using local reduction techniques. To demonstrate its effectiveness, we evaluate our approach on a planar quadrotor problem, where it clearly outperforms an equivalent method that does not account for future updates at the cost of increased computation time.

Keywords: Model Validation, Uncertain systems, Optimization
Abstract: We present a novel, input-output data-driven approach to uncertainty model identification. As the true bounds and distributions of system uncertainties ultimately remain unknown, we depart from the goal of identifying the uncertainty model and instead look for minimal concrete statements that can be made based on an uncertain system model and available input-output data. We refer to this as unfalsifying an uncertainty model. Two different unfalsification approaches are taken. The optimistic approach determines the smallest uncertainties that could explain the given data, while the pessimistic approach finds the largest possible uncertainties suggested by the data. The pessimistic problem is revealed to be a semi-infinite program, which is solved using the local reduction algorithm. It is also shown that the optimistic and pessimistic approaches to uncertainty model unfalsification are mathematical duals. Finally, both approaches are tested using an uncertain linear model with data from a simulated nonlinear system.

Keywords: Uncertain systems, Lyapunov methods, Stability of nonlinear systems
Abstract: We present a novel robust control framework for continuous-time, perturbed nonlinear dynamical systems with uncertainty that depends nonlinearly on both the state and control inputs. Unlike conventional approaches that impose structural assumptions on the uncertainty, our framework enhances contraction-based robust control with data-driven uncertainty prediction, remaining agnostic to the models of the uncertainty and predictor. We statistically quantify how reliably the contraction conditions are satisfied under dynamics with uncertainty via conformal prediction, thereby obtaining a distribution-free and finite-time probabilistic guarantee for exponential boundedness of the trajectory tracking error. We further propose the probabilistically robust control invariant (PRCI) tube for distributionally robust motion planning, within which the perturbed system trajectories are guaranteed to stay with a finite probability, without explicit knowledge of the uncertainty model. Numerical simulations validate the effectiveness of the proposed robust control framework and the performance of the PRCI tube.

Keywords: Switched systems, Uncertain systems, LMIs
Abstract: This paper presents a new strategy that incorporates past state measurements to enhance the design of stabilizing switching laws for discrete-time switched uncertain linear systems. Inspired by techniques used in uncertain and time-varying linear systems, conditions that extend the Lyapunov-Metzler inequalities by embedding past states into the switching rule are proposed. The objective is to achieve improved performance in terms of less conservative bounds on the decay rate of the trajectories of the system. The proposed approach eliminates the need for grid-based strategies commonly required in conventional methods, resulting in more efficient numerical procedures. A numerical example illustrates the effectiveness of the approach, highlighting its advantages over existing methods.

Keywords: Predictive control for linear systems, Robust control
Abstract: In this work, we propose an output-feedback tube-based model predictive control (MPC) scheme for linear systems under dynamic uncertainties that are described via integral quadratic constraints (IQC). By leveraging IQCs, a large class of nonlinear and dynamic uncertainties can be addressed. We leverage recent IQC synthesis tools to design a dynamic controller and an observer that are robust to these uncertainties and minimize the size of the resulting constraint tightening in the MPC. Thereby, we show that the robust estimation problem using IQCs with peak-to-peak performance can be convexified. We guarantee recursive feasibility, robust constraint satisfaction, and input-to-state stability of the resulting MPC scheme.

Keywords: Resilient Control Systems, LMIs, Uncertain systems
Abstract: This paper proposes conditions for the design of safe, robust state-feedback controllers and barrier certificates for uncertain polytopic continuous-time linear systems subject to input saturation. The generalized sector condition is employed to assess the presence of saturation and the level set of the Lyapunov function is utilized to define the barrier function. Numerical experiments are used to illustrate the features of the proposed method.

Keywords: Nonlinear output feedback, Constrained control, Uncertain systems
Abstract: Control barrier functions (CBFs) are a popular approach to design feedback laws that achieve safety guarantees for nonlinear systems. The CBF-based controller design relies on the availability of a model to select feasible inputs from the set of CBF-based controls. In this paper, we develop a model-free approach to design CBF-based control laws, eliminating the need for knowledge of system dynamics or parameters. Specifically, we address safety requirements characterized by a time-varying distance to a reference trajectory in the output space and construct a CBF that depends only on the measured output. Utilizing this particular CBF, we determine a subset of CBF-based controls without relying on a model of the dynamics by using techniques from funnel control. The latter is a model-free high-gain adaptive control methodology, which achieves tracking guarantees via reactive feedback. In this paper, we discover and establish a connection between the modular controller synthesis via zeroing CBFs and model-free reactive feedback. The theoretical results are illustrated by a numerical simulation.

Keywords: Computational methods, Uncertain systems, Modeling
Abstract: Decision-making in complex scenarios often involves multiple, conflicting criteria, making it difficult for decision-makers to precisely determine the relative importance of each one. Traditional Multi-Criteria Decision Analysis (MCDA) methods, which rely on crisp data, typically assume complete knowledge of criteria weights, an assumption that is rarely met in practice. This study addresses this limitation by incorporating partial knowledge of decision-makers into the weighting process without relying on fuzzy logic. Unlike standard approaches that rely on a single predefined weight vector, the proposed method generates diverse weight distributions spanning the entire space of feasible criteria weights.

The Partial Knowledge Weighting (PKW) is integrated with the Stable Preference Ordering Towards Ideal Solution (SPOTIS) method and tested in the context of city selection for quality of life, where decision-makers often cannot rank all criteria precisely. The methodology progressively incorporates known ranking relationships while generating consistent distributions for the remaining weights. Results show that increasing the number of known ranking relationships reduces uncertainty in weight assignments and leads to more refined decision outcomes. The study demonstrates that accommodating partial knowledge significantly enhances the robustness and applicability of MCDA, supporting more reliable decision support systems in real-world contexts characterized by incomplete information.

Keywords: Stochastic optimal control, Optimal control
Abstract: Traditional solvable optimal control theory mainly addresses quadratic costs due to its analytical tractability. Nevertheless, quadratic costs are not appropriate to model critical non-linearities found in many real systems such as water, energy, agriculture, financial networks, among many others. In this paper, we present a unified framework for solving discrete-time optimal control problems with higher-order state and control costs. To this end, we rely on convex-completion techniques, and derive semi-explicit solutions. Key contributions include variance-aware solutions under additive and multiplicative noise. We show that higher-order costs induce less aggressive control policies compared to quadratic formulations, a finding that is validated through numerical analyses.

Keywords: Stochastic optimal control, Predictive control for linear systems, Markov processes
Abstract: Modern real-time control systems can sporadically exceed the computation deadlines, which may lead to a deterioration in performance or even instability if not actively accounted for. This letter proposes a stochastic model predictive control approach that incorporates deadline miss probabilities of subsequent control task executions in a scenario tree. To account for the effect of missed deadlines, we utilize Markov jump linear systems that allow us to prove mean-square stability and recursive feasibility under hard input and mixed hard/soft state constraints. The proposed stochastic controller is benchmarked using a Furuta pendulum, demonstrating improved performance and an increased feasible region compared to a nominal and a hard-constrained stochastic controller, respectively.

Keywords: Stochastic optimal control, Optimization algorithms, Constrained control
Abstract: This paper presents a novel algorithm for solving distribution steering problems featuring nonlinear dynamics and chance constraints. Covariance steering (CS) is an emerging methodology in stochastic optimal control that poses constraints on the first two moments of the state distribution — thereby being more tractable than full distributional control. Nevertheless, a significant limitation of current approaches for solving nonlinear CS problems, such as sequential convex programming (SCP), is that they often generate infeasible or poor results due to the large number of constraints. In this paper, we address these challenges, by proposing an operator splitting CS approach that temporarily decouples the full problem into subproblems that can be solved in parallel. This relaxation does not require intermediate iterates to satisfy all constraints simultaneously prior to convergence, which enhances exploration and improves feasibility in such non-convex settings. Simulation results across a variety of robotics applications verify the ability of the proposed method to find better solutions even under stricter safety constraints than standard SCP. Finally, the applicability of our framework on real systems is also confirmed through hardware demonstrations.

Keywords: Stochastic optimal control, Stochastic systems, Optimal control
Abstract: We consider the problem of optimally steering the state covariance matrix of a discrete-time linear stochastic system to a desired terminal covariance matrix, while inducing the control input to be zero over many time intervals. We propose to induce sparsity in the feedback gain matrices by using a sum-of-norms version of the iteratively reweighted ell_1-norm minimization. We show that the lossless convexification property holds even with the regularization term. Numerical simulations show that the proposed method produces a Pareto front of transient cost and sparsity that is not achievable by a simple ell_1-norm minimization and closely approximates the ell_0-norm minimization obtained from brute-force search.

Keywords: Queueing systems, Stochastic optimal control, Optimal control
Abstract: We consider an arbitrary network of M/M/∞ queues with controlled transitions between queues. We consider optimal control problems where the costs are linear functions of the state and inputs over a finite horizon or infinite. We provide in both cases an explicit characterization of the optimal control policies. We also show that these do not involve state feedback, but they depend on the network topology and system parameters. The results are also illustrated with various examples.

Keywords: Formal Verification/Synthesis, Stochastic systems, Lyapunov methods
Abstract: This paper presents a method for the simultaneous synthesis of a barrier certificate and a safe controller for discrete-time nonlinear stochastic systems. Our approach, based on piecewise stochastic control barrier functions, reduces the synthesis problem to a minimax optimization, which we solve exactly using a dual linear program with zero gap. This enables the joint optimization of the barrier certificate and safe controller within a single formulation. The method accommodates stochastic dynamics with additive noise and a bounded continuous control set. The synthesized controllers and barrier certificates provide a formally guaranteed lower bound on probabilistic safety. Case studies on linear and nonlinear stochastic systems validate the effectiveness and scalability of our approach.

Keywords: Uncertain systems, Randomized algorithms, Stochastic optimal control
Abstract: In this paper, we discuss the utilization of perturbed risk levels (PRLs) for the solution of chance-constrained problems via sampling-based approaches. PRLs allow the consideration of distributional ambiguity by rescaling the risk level of the nominal chance constraint. Explicit expressions of the PRL exist for some discrepancy-based ambiguity sets.

We propose a discrepancy functional not included in previous comparisons of different PRLs based on the likelihood ratio, which we term ,,relative variation distance" (RVD). If the ambiguity set can be described by the RVD, the rescaling of the risk level with the PRL is in contrast to other discrepancy functionals possible even for very low risk levels. We derive distributionally robust one- and two-level guarantees for the solution of chance-constrained problems with randomized methods. We demonstrate the viability of the derived guarantees for a randomized MPC under distributional ambiguity.

Keywords: Biomolecular systems, Stochastic systems, Genetic regulatory systems
Abstract: Living organisms maintain stable functioning amid environmental fluctuations through homeostasis, a property that preserves a system's behavior despite changes in environmental conditions. To elucidate homeostasis in stochastic biochemical reactions, theoretical tools for assessing population level invariance under parameter perturbations are crucial. In this paper, we propose a systematic method for identifying the stationary moments that remain invariant under parameter perturbations by leveraging the structural properties of the stationary moment equations. A key step in this development is addressing the underdetermined nature of moment equations, which has traditionally made it difficult to characterize how stationary moments depend on system parameters. To overcome this, we utilize the Dulmage-Mendelsohn (DM) decomposition of the coefficient matrix to extract welldetermined subequations and reveal their hierarchical structure. Leveraging this struc ture, we identify stationary moments whose partial derivatives with respect to parameters are structurally zero, facilitating the exploration of fundamental constraints that govern homeostatic behavior in stochastic biochemical systems.

Keywords: Maritime control, Robotics, Nonlinear systems
Abstract: This paper presents a novel terrain-following guidance scheme for underwater vehicles utilizing full orientation actuation. Unlike existing approaches that primarily rely on pitch control, the proposed method exploits both roll and pitch to enable more accurate adaptation to complex terrain. The proposed control law simultaneously accomplishes three objectives: (i) it aligns the vehicle's body-fixed downward axis with the seafloor's normal vector, (ii) ensures convergence to a horizontal trajectory, and (iii) maintains a specified altitude. We prove that the proposed control law ensures global asymptotic stability of a desired altitude and horizontal path, and that the body-fixed downward axis is aligned with the seafloor's normal vector at this equilibrium. The effectiveness of the proposed guidance approach is demonstrated through numerical simulations of a six-degree-of-freedom dynamic model of the REMUS 100 AUV.

Keywords: Stability of nonlinear systems, Nonlinear systems
Abstract: The scaled graph has been introduced recently as a nonlinear extension of the classical Nyquist plot for linear time-invariant systems. In this paper, we introduce a modified definition for the scaled graph, termed the signed scaled graph (SSG), in which the phase component is characterized by making use of the Hilbert transform. Whereas the original definition of the scaled graph uses unsigned phase angles, the new definition has signed phase angles which ensures the possibility to differentiate between phase-lead and phase-lag properties in a system. Making such distinction is important from both an analysis and a synthesis perspective, and helps in providing tighter stability estimates of feedback interconnections. We show how the proposed SSG leads to intuitive characterizations of positive real and negative imaginary nonlinear systems, and present various interconnection results. We showcase the effectiveness of our results through a motivating example.

Keywords: Algebraic/geometric methods, Time-varying systems, Computational methods
Abstract: Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of a broad class of boundary value problems for these systems is formulated in the sense of Carathéodory solutions. It is shown that, under the dominant linearization assumption, the considered class of boundary value problems admits a unique solution for any admissible control. These solutions can be obtained as the limit of the proposed simple iterative scheme and, in the case of periodic boundary conditions, via the developed Newton-type schemes. Under additional technical assumptions, sufficient contraction conditions of the corresponding generating operators are derived analytically. The proposed iterative approach is applied to compute periodic solutions of a realistic chemical reaction model with discontinuous control inputs.

Keywords: Aerospace, Stability of nonlinear systems, Flight control
Abstract: This article presents a disturbance torque estimation scheme for a multi-rotor vehicle modeled as a rotating rigid body in the presence of unknown disturbance torque and measurement uncertainties. The proposed estimation scheme depends on the knowledge of rotational inertia, control inputs, and measurements from a combination of inertial measurement units, consisting of a three-axis gyroscope placed at the center of the vehicle and a set of three-axis accelerometers placed around the gyroscope. The angular velocity and angular acceleration vectors are estimated using a simple linear Kalman filter. Thereafter, these estimated motion states are sent to the disturbance observer to provide disturbance torque estimation. A Lyapunov stability analysis proves that the proposed estimation scheme is discrete-time finite-time stable. The estimation scheme is discretized as a geometric integrator for numerical simulations and practical implementations. Numerical simulations involve the modeling of industrial-grade inertial measurement units to demonstrate the feasibility, stability, and robustness properties of the proposed scheme.

Keywords: Resilient Control Systems, Nonlinear systems, Power systems
Abstract: In this study, a control theoretic description of resilience is provided to quantify the characteristics of a resilient system. The aim is to establish a paradigm for resilient control design based on tangible control objectives that yield desirable attributes for safety-critical systems. In that regard, durability and recoverability properties are identified as key components of the proposed resilience framework and, to offer a methodology to enforce these attributes, the notion of finite-time robust control barrier function (FR-CBF) is introduced. Furthermore, to offer a comprehensive treatment of the problem, resilient control design is investigated for both continuous and sampled-data systems. To that end, FR-CBF-based design conditions for both continuous and piece-wise constant zero-order hold (ZOH) control inputs are included. Moreover, to provide a concrete example of how the proposed framework could be adopted for safety-critical control applications, in this study we also investigate the voltage regulation problem for inverter-interfaced radial power distribution networks subject to adversarial injections. In that regard, sufficient conditions for both the continuous and sampled-data ZOH control are derived to guarantee finite-time recovery and safe operation of the distribution grid in accordance with the proposed resilience framework. Finally, the efficacy of the proposed results is advocated using a simulation study showing resilient grid performance in the presence of the ‘worst-case’ power injection attack, as reported in (Lindström et al. 2021).

Keywords: Compartmental and Positive systems, Nonlinear systems
Abstract: This paper investigates a behavioral-feedback SIR model in which the infection rate adapts dynamically based on the fractions of susceptible and infected individuals. We introduce an invariant of motion and we characterize the peak of infection. We further examine the system under a threshold constraint on the infection level. Based on this analysis, we formulate an optimal control problem to keep the infection curve below a healthcare capacity threshold while minimizing the economic cost. For this problem, we study a feasible strategy that involves applying the minimal necessary restrictions to meet the capacity constraint and characterize the corresponding cost.

Keywords: Nonlinear output feedback, Lyapunov methods, Power electronics
Abstract: We propose a robustly stabilizing Lyapunov-based control scheme for a Multi-Input Converter using a Nonlinear Disturbance Observer for the load current estimation. The closed-loop system ensures an output voltage regulation and eliminates the requirement of knowing the current load, thus mitigating the impact of current fluctuations, without relying on typically inaccessible or impractical measurements. Robust asymptotic stability is guaranteed by Lyapunov theory. The main result is validated by simulations and experiments.

Keywords: Stability of nonlinear systems, Robust control, Linear parameter-varying systems
Abstract: This paper introduces the concept of parameter-dependent (PD) control Lyapunov functions (CLFs) for gain-scheduled stabilization of nonlinear parameter-varying (NPV) systems. It shows that given a PD-CLF, a min-norm control law can be constructed by solving a robust quadratic program. For polynomial control-affine NPV systems, it provides convex conditions, based on the sum of squares programming, to jointly synthesize a PD-CLF and a PD controller, while maximizing the PD region of stabilization. Simulation results validate the efficacy of the proposed method.

Keywords: Robust adaptive control, LMIs
Abstract: This paper extends the recently introduced symbiotic control framework, which combines fixed-gain and adaptive control methods to suppress the uncertainties in a more predictable way and without the necessities for explicit uncertainty bounds. While the original framework was limited to linear systems, in this paper we generalize it to nonlinear behavior models across different operating conditions with the use of a gain-scheduling approach. The proposed method uses a family of controllers, each designed for a specific equilibrium point, to handle nonparametric uncertainties without requiring prior knowledge of uncertainty bounds. A numerical example is also provided to demonstrate the effectiveness of the proposed gain-scheduled symbiotic control approach.

Keywords: Robust control, Optimal control, Linear systems
Abstract: This paper is concerned with designing a multiobjective tracking controller for linear time-invariant systems subject to both unknown external disturbances and stochastic noise simultaneously. The proposed approach involves two controllers designed separately: a nominal tracking controller that achieves optimal tracking performance and a mixed H_2/H_infty controller that addresses the impacts of external disturbances and stochastic noise. The two controllers are then integrated together to ensure that the nominal optimal tracking performance and the mixed H_2/H_infty performance are complementary to each other, thereby overcoming the conservativeness exhibited in existing robust tracking control designs. Numerical comparisons demonstrate the advantages of the proposed controller over existing ones.

Keywords: Robust control, Lyapunov methods, Constrained control
Abstract: This paper discusses the L2 gain of nonlinear systems which, in the absence of exogenous inputs, are uniformly ultimately bounded. Unlike for many systems which are asymptotically stable in the absence of exogenous inputs, it is not possible to infer standard L2 gain conditions for systems which are only known to be ultimately bounded. This paper gives another interpretation of L2 gain and shows that, under some assumptions, consideration of a typical L2 performance objective leads to satisfaction of this new interpretation of L2 gain - called the dist-L2 gain. This is harnessed for performance analysis of systems with quantized inputs and an approach to computing the dist L2 gain is presented.

Keywords: Robust control, Markov processes, LMIs
Abstract: This paper deals with the problem of robust mean-square stabilization of Semi-Markov jump linear systems with a guaranteed decay rate. It is considered that the jump times are modeled through phase-type (PH) distributions and that the system parameters are subject to polytopic uncertainties. The goal is to design state feedback controllers that robustly stabilize the closed-loop system while satisfying an exponential decay rate, thus having better control over the transient behavior of the system. The design problem is written in linear matrix inequalities (LMI) so that it can be readily implemented numerically. The paper concludes with a numerical example.

Keywords: Stability of linear systems, Robust control, Uncertain systems
Abstract: In this work, we proposed and studied a matrix sectored-disk problem in which we wish to determine the invertibility of a matrix with mixed gain and phase uncertainty. The matrix sectored-disk problem can then be carried on to the robust feedback stability problem for multiple-input-multiple-output (MIMO) linear time-invariant (LTI) systems involving sectored-disk uncertainty, namely, dynamic uncertainty subject to simultaneous gain and phase constraints. This problem is thereby called an LTI system sectored-disk problem.

Keywords: Algebraic/geometric methods, Linear parameter-varying systems, Robust control
Abstract: In this paper, we propose a transformation algorithm for a class of Linear Parameter-Varying (LPV) systems with functional affine dependence on parameters, where the system matrices depend affinely on nonlinear functions of the scheduling variable, into Linear Fractional Transformation (LFT) systems. The transformation preserves input-output behavior and minimality. For input-output equivalent LPV systems, the resulting LFT representations are also input-output equivalent for all uncertainty blocks. This ensures consistency in system identification and control, as minimal and input-output equivalent LPV systems yield minimal and isomorphic LFT systems, maintaining consistent performance in controller synthesis.

Keywords: Sampled-data control, Linear parameter-varying systems, Constrained control
Abstract: This paper presents the parameter-dependent aperiodic sampled-data state feedback controller design for linear parameter varying (LPV) systems with actuators subject to magnitude and rate saturation, using Linear Matrix Inequalities (LMIs). The proposed method integrates the looped-functional approach and a parameter-dependent generalized sector condition. The local stabilization is verified through a new definite negativeness lemma for second-order matrix polynomials. The proposed conditions can be simplified to recover a robust controller design whenever the time-varying parameter is unavailable. Two numerical examples demonstrate the effectiveness of the proposed method, highlighting less conservative stability conditions compared to existing approaches.

Keywords: Fault tolerant systems, LMIs, Linear parameter-varying systems
Abstract: This paper addresses the problem of fault-tolerant control of nonlinear parameter-varying (N-LPV) systems. Specifically, it focuses on N-LPV models that effectively represent nonlinear systems by partially embedding nonlinearities while preserving sector-bounded terms. This representation simplifies control design by reducing the number of polytope vertices compared to traditional linear parameter-varying (LPV) approaches. The main contribution of this paper is to present novel fault-hiding approaches for fault-tolerant control of N-LPV models. The proposed approach can recover the stability of N-LPV systems under additive and multiplicative sensor and actuator faults by using a generic static reconfiguration block structure.

Keywords: Linear systems, LMIs
Abstract: In this paper, we study the state-space characterization of multi-input multi-output linear time-invariant systems. A sectored real lemma is developed for phase-bounded systems, serving as a counterpart of bounded real lemma and an extension of positive real lemma. Moreover, we propose a mixed bounded/sectored real lemma that integrates the gain and phase information, thereby enhancing its applicability to practical systems. All results are formulated in a novel phase-related terminology, which is equivalent to the LMI statement but provides a distinct conceptual perspective on phase.

Keywords: Linear systems, Estimation, Kalman filtering
Abstract: This paper addresses the problem of optimal channel selection for remote state estimation in cyber-physical systems, where a sensor transmits measurements over multiple time-varying wireless channels. We model the packet arrival probability of each channel as a non-stationary Bernoulli process and propose two discounted Multi-Armed Bandit (MAB) algorithms-Discounted Upper Confidence Bound (D-UCB) and Discounted Thompson Sampling (D-TS) to select channels with the highest expected packet arrival rates adaptively. The estimation error covariance is analyzed using Kalman filtering, and the cumulative estimation regret is defined as the excess trace of the estimation error covariance compared to an optimal policy. Theoretical analysis shows the algorithms achieve a regret that grows gradually over time, and numerical simulations validate its effectiveness under non-stationary conditions.

Keywords: Linear systems, Observers for Linear systems, Estimation
Abstract: Sample-based observability characterizes the ability to reconstruct the internal state of a dynamical system by using limited output information, i.e., when measurements are only infrequently and/or irregularly available. In this work, we investigate the concept of functional observability, which refers to the ability to infer a function of the system state from the outputs, within a sample-based framework. Here, we give necessary and sufficient conditions for a system to be sample-based functionally observable, and formulate conditions on the sampling schemes such that these are satisfied. Furthermore, we provide a numerical example, where we demonstrate the applicability of the obtained results.

Keywords: Observers for Linear systems, Sensor networks, LMIs
Abstract: This paper presents a Distributed Unknown Input Observer (D-UIO) design methodology based on node-wise observability decomposition to estimate the state of discrete-time linear time-invariant (LTI) systems affected by measurement noise and unknown inputs. The framework models sensors as integral components of logical units, which together constitute the nodes of a distributed observer network. Each node of the network has only partial access to system information—restricted to local measurements—and can exchange data solely with its direct neighbors. The observer design challenge is therefore split into two complementary tasks: (i) determining local output injection gains to intelligently use locally available data, and (ii) defining diffusive coupling gains that, through a consensus mechanism, compensate for incomplete information. The proposed synthesis is cast as a set of linear matrix inequalities (LMI) conditions, which can be efficiently solved via semidefinite programming, yielding a tractable design procedure. The effectiveness of the distributed observer is finally demonstrated through a numerical simulation example.

Keywords: Observers for Linear systems, Sensor networks, Distributed control
Abstract: Distributed estimation is the collaborative asymptotic estimation of the state of (usually large-scale) linear time-invariant (LTI) systems by multiple observers (or sensors). Existing distributed observer designs are scalable and provide a guaranteed rate of convergence, but often these designs require global network information, restricting flexibility. This paper proposes a fully decentralized, reduced-order distributed observer that leverages a local observability decomposition. As usual, a Luenberger observer is designed for observable states, but instead of adopting consensus dynamics, we determine the unobservable states using an algebraic equation. This approach is plug-and-play, reduces computational complexity, allows tunable convergence rates, and is implementable without knowing the global network topology. Numerical simulations validate its efficiency. We also discuss an extension of our approach for distributed estimation in a finite, prescribed time.

Keywords: Predictive control for linear systems, Linear systems
Abstract: In this paper, we investigate the integration of a Mixture of Experts (MoE) architecture into Model Predictive Control (MPC) frameworks. The proposed approach enhances the real-time applicability and computational efficiency of MPC while guaranteeing closed-loop stability and constraint satisfaction. The MoE architecture provides a flexible, modular strategy for representing complex control policies by partitioning the input space into regions, each managed by a specialized expert model coordinated via a gating network. We evaluate the architecture's effectiveness in alleviating the computational burden of traditional MPC and leveraging its universal function approximation capabilities. This involves developing a learning-based control policy through approximations that characterize MPC behavior with stability guarantees. The practicality of the approach is demonstrated via simulations, highlighting its potential for robust, real-time control in diverse dynamic systems. By presenting both theoretical foundations and practical implementations, this paper advances control strategies that adaptively handle computational constraints while maintaining high performance in safety-critical applications.

Keywords: Sensor networks, Kalman filtering, Linear systems
Abstract: In this work, we propose a Symmetric Kullback Leibler Divergence (SKLD) based approach for Optimal Sensor Placement Design (OSPD) for linear dynamical systems subjected to the presence of bounded modelling uncertainty. Use of SKLD as an optimality criterion over conventional alphabetical optimality criteria facilitates incorporation of the end-user specified target performance of the estimates in the problem formulation. The proposed SKLD based SPD formulation is a Robust Sensor Placement Design (R-SPD) that guarantees robustness by accounting for uncertainties in process dynamics. This is achieved by choosing sensors which minimize the worst case SKLD value. Thus, the resulting SKLD value provides an upper bound on SKLD for all admissible uncertainties. The proposed sensor placement design formulation is a Mixed Integer Non-Linear Programming (MINLP) problem and is computationally intractable. In this work, we also provide a computationally tractable reformulation of MINLP problem to a Mixed Integer Semidefinite Programming (MISDP) formulation. Utility of the approach is demonstrated on Tennessee Eastman challenge problem.

Keywords: Model/Controller reduction, Reduced order modeling, LMIs
Abstract: In this paper, we investigate the optimal mathcal{H}_2 model reduction problem for single-input single-output (SISO) continuous-time linear time-invariant (LTI) systems. A semi-definite relaxation (SDR) approach is proposed to determine globally optimal interpolation points, providing an effective way to compute the reduced-order models via Krylov projection-based methods. In contrast to iterative approaches, we use the controllability Gramian and the moment-matching conditions to recast the model reduction problem as a convex optimization by introducing an upper bound gamma to minimize the mathcal{H}_2 norm of the model reduction error system. We also prove that the relaxation is exact for first order reduced models and demonstrate, through examples, that it is exact for second order reduced models. We compare the performance of our proposed method with other iterative approaches and shift-selection methods on examples. Importantly, our approach also provides a means to verify the global optimality of known locally convergent methods.

Keywords: Optimal control, Linear systems, Variational methods
Abstract: Time-optimal control for high-order chain-of-integrator systems with full state constraints and arbitrarily given terminal states remains a challenging problem in the optimal control theory domain, yet to be resolved. To enhance further comprehension of the problem, a novel notation system and theoretical framework is established, providing the switching manifold for high-order problems in the form of augmented switching laws (ASL). Guided by the ASL theory, a trajectory planning method named the manifold-intercept method (MIM) is developed. MIM can plan near-optimal non-chattering higher-order trajectories with full state constraints, achieving strict time-optimality for problems of order n≤3. Experiments indicate that MIM outperforms baselines regarding computational time, computational accuracy, and trajectory quality by a large gap.

Keywords: Optimal control, Markov processes, Optimization
Abstract: Existing methods for deceptive path planning (DPP) address the problem of designing paths that conceal their true goal from a passive, external observer. Such methods do not apply to problems where the observer has the ability to perform adversarial interventions to impede the path planning agent. In this paper, we propose a novel Markov decision process (MDP)-based model for the DPP problem under adversarial interventions and develop new value of information (VoI) objectives to guide the design of DPP policies. Using the VoI objectives we propose, path planning agents deceive the adversarial observer into choosing suboptimal interventions by selecting trajectories that are of low informational value to the observer. Leveraging connections to the linear programming theory for MDPs, we derive computationally efficient solution methods for synthesizing policies for performing DPP under adversarial interventions. In our experiments, we illustrate the effectiveness of the proposed solution method in achieving deceptiveness under adversarial interventions and demonstrate the superior performance of our approach to both existing DPP methods and conservative path planning approaches on illustrative gridworld problems.

Keywords: Optimal control, Nonholonomic systems
Abstract: In this paper, we search for control of minimal L¹-norm steering the solution of a non-linear driftless affine control system from an initial state to a prescribed target state in a prescribed time T>0. This study indicates that minimal L¹-norm controls are not unique and in particular, among others, there always exist purely impulsive controls and controls in L¹. As an outcome of this result, we can also say that there are controls of minimal L¹-norm which are sparse in the sense that their support is of null Lebesgue measure. To tackle this problem, we use the graph-completion method introduced by Bressan and Rampazzo in 1988.

Keywords: Optimal control, Markov processes, Linear systems
Abstract: This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the class of Linearly Solvable MDP is reformulated as a continuous-state optimal control problem. It is shown that this class naturally satisfies the conditions for explicit solution of the Bellman equation, motivating the extension of previous results to semilinear dynamics to account for input nonlinearities. The applicability of the given conditions is illustrated in scenarios with linear and quadratic cost, corresponding to the Stochastic Shortest Path and Linear-Quadratic Regulator problems.

Keywords: Optimal control, Variational methods, Stochastic systems
Abstract: In this paper, we address optimal control problems in which the system parameters follow a probability distribution, and the optimization is based on average performance. These problems, known as Riemann-Stieltjes optimal control or optimal ensemble control problems, involve uncertainties that influence system dynamics. Focusing on control-affine systems, we apply the Pontryagin Maximum Principle to characterize singular arcs in a feedback form. To demonstrate the practical relevance of our approach, we show an example of a model for the sterile insect technique, which is a biological pest control method. Numerical simulations confirm the effectiveness of our framework in addressing control problems under uncertainty.

Keywords: Optimal control, Linear systems, Optimization
Abstract: A systematic procedure for solving general linear quadratic optimal control problems with linear equality con- straints is presented. We exploit the theory of exact penalization, in the spirit of [1], to transform a general linear quadratic problem with a set of linear equality constraints on the state into an equivalent penalized unconstrained problem. Both the finite and the infinite horizon cases are discussed, and the results are given under minimal feasibility assumptions on the constrained problem, which are expressed in a coordinate free form. Two simple examples illustrate the theory.

Keywords: Optimal control, Reinforcement learning, Linear systems
Abstract: In this paper, we present a novel method for computing the optimal feedback gain of the infinite-horizon Linear Quadratic Regulator (LQR) problem via an ordinary differential equation. We introduce a novel continuous-time Bellman error, derived from the Hamilton-Jacobi-Bellman (HJB) equation, which quantifies the suboptimality of stabilizing policies and is parametrized in terms of the feedback gain. We analyze its properties, including its effective domain, smoothness, and coerciveness, and show the existence of a unique stationary point within the stability region. Furthermore, we derive a closed-form gradient expression of the Bellman error that induces a gradient flow. This converges to the optimal feedback and generates a unique trajectory that exclusively comprises stabilizing feedback policies. Additionally, this work advances interesting connections between LQR theory and Reinforcement Learning (RL) by redefining suboptimality of the Algebraic Riccati Equation (ARE) as a Bellman error, adapting a state-independent formulation, and leveraging Lyapunov equations to overcome the infinite-horizon challenge. We validate our method in a simulation and compare it to the state of the art.

Keywords: Optimal control, Quantum information and control, Nonlinear systems
Abstract: Motivated by problems in quantum control, we introduce a novel method for studying time-optimal control problems of affine systems with unbounded controls. Intuitively, we construct a relaxation of our problem as follows: for each control of finite amplitude, we appropriately rescale the time variable so that, in the limit, an instantaneous jump in the state of the system becomes a trajectory containing both the state before and after the jump. The main advantage of this method is the direct applicability of the classical Pontryagin maximum principle. Several examples, including the generation of noiseless and noisy qubit gates, as well as population transfer in open two-level systems, are discussed.

Keywords: Optimization, Optimal control, Robotics
Abstract: This tutorial will address the challenges of optimal control for complex robotic systems, particularly those with rich contact dynamics, where traditional methods struggle. While Sampling-Based Optimal Control (SBOC) techniques like Model Predictive Path Integral Control (MPPI) offer empirical success due to their handling of nonlinearities and parallelizability, they lack theoretical guarantees regarding convergence and stability. This tutorial will summarize recent results that advance the theoretical understanding and algorithmic capabilities of SBOC by analyzing convergence, leading to new algorithms named CoVo-MPC [50] with optimal covariance design. Furthermore, by establishing and exploiting a novel connection to generative diffusion models, this work introduces approaches like MBD for trajectory optimization and DIAL-MPC, an online framework with diffusion-inspired annealing. The efficacy of these theoretical insights and algorithms is validated through simulations and experiments, ultimately providing a stronger theoretical foundation for SBOC, yielding more reliable and efficient algorithms for complex robotics, and bridging optimal control with generative modeling.

Keywords: Adaptive control, Nonlinear systems, Game theory
Abstract: We study the problem of controlling evolutionary game-theoretic dynamics when agents follow sophisticated learning rules, in particular the logit protocol. Much previous work focused on settings where agents are less sophisticated learners following imitative protocols that leads to the well-known replicator dynamic. Here, we consider adaptive control schemes for the logit dynamics with the objective of steering the population to a desired equilibrium by modifying the agents' payoff functions in a 2-action coordination game. Through the analysis of the controlled dynamics, we establish sufficient conditions for global convergence to the desired equilibrium. We find that the conditions to control the logit system have fewer requirements than those to control the replicator equation: Adaptive-gain controllers that are successful in performing their task in the logit system may fail in the replicator system. We then provide numerical simulations to illustrate and compare the amount of control effort needed to achieve the objective in the logit system versus the replicator system.

Keywords: Network analysis and control, Agents-based systems, Networked control systems
Abstract: This paper investigates the wisdom of crowds of linear opinion dynamics models in presence of antagonistic interactions. Conditions are given under which models such as the DeGroot, Friedkin-Johnsen (FJ) and concatenated FJ models may or may not improve wisdom.

Keywords: Adaptive systems, Biological systems, Nonlinear systems
Abstract: We propose and analyze a model for the dynamics of the flow into and out of a nest for the arboreal turtle ant Cephalotes goniodontus during foraging to investigate a possible mechanism for the emergence of oscillations. In our model, there is mixed dynamic feedback between the flow of ants between different behavioral compartments and the amount of pheromone along trails. On one hand, the ants deposit pheromone along the trail, which provides a positive feedback by concentrating the flow of ants along specific trail segments and further increasing the rate of deposition. On the other hand, pheromone evaporation is a source of negative feedback, as it depletes the pheromone and inhibits the return rate to the nest. We prove that the model is globally asymptotically stable in the absence of pheromone feedback. Then we show that pheromone feedback can lead to a loss of stability of the equilibrium and onset of sustained oscillations in the flow in and out of the nest via a Hopf bifurcation. This analysis sheds light on a potential key mechanism that enables arboreal turtle ants to effectively change their trail networks to minimize traveled path lengths and eliminate cycles.

Keywords: Network analysis and control, Agents-based systems, Game theory
Abstract: Opinion dynamics studies how interpersonal influence and social network structures shape the evolution of public opinions. Recently, various models of opinion dynamics have been proposed within a game-theoretic framework, where interpersonal influence mechanisms are captured by players’ cost functions, reflecting their motivations. Conventionally, when players have multiple motivations, an aggregated cost function is constructed by summing individual cost functions corresponding to different motivations. However, whether these “costs” in people’s minds are interchangeable remains a subject of debate. In this paper, we propose an opinion dynamics model based on a multi-objective game framework. In our model, individuals experience two distinct costs: social pressure from disagreeing with others and cognitive dissonance from deviating from the truth. Opinion updates are modeled as Pareto improvements between these two cost functions. This approach provides a parsimonious explanation for the emergence of pluralistic ignorance—where individuals may “agree” on something untrue, even though they all know the underlying truth. We conduct a theoretical analysis of the proposed model, establishing conditions for the almost-sure convergence and for the prevalence of truth.

Keywords: Control of networks, Optimization, Control applications
Abstract: We deal with controlling the spread of an epidemic disease on a network by isolating one or multiple locations by banning people from leaving them. To this aim, we build on the susceptible-infected-susceptible and the susceptible-infected-removed discrete-time network models, encapsulating a control action that captures mobility bans via removing links from the network. Then, we formulate the problem of optimally devising a control policy based on mobility bans that trades-off the burden on the healthcare system and the social and economic costs associated with interventions. The binary nature of mobility bans hampers the possibility to solve the control problem with standard optimization methods, yielding a NP-hard problem. Here, this is tackled by deriving a Quadratic Unconstrained Binary Optimization (QUBO) formulation of the control problem, and leveraging the growing potentialities of quantum computing to efficiently solve it.

Keywords: Network analysis and control, Decentralized control
Abstract: This work explores network coalition-based models using dynamic average consensus protocols, where agents in coalitions interact to reach global agreement. We employ hypergraphs to model communication structures and compare their convergence rates with clique expansion graphs. Our results show that hypergraph-based models achieve faster convergence for the case of continuous consensus dynamical systems and also in discrete time for coalitions with an equal number of agents. Our findings suggest that hypergraphs offer a scalable, decentralized approach to improving consensus algorithms in generalized tree like information structures, with significant potential for enhancing performance in applications like finance and economics.

Keywords: Autonomous systems, Control applications, Network analysis and control
Abstract: We consider an opinion dynamics model coupled with an environmental dynamics. Based on a forward invariance argument, we can simplify the analysis of the asymptotic behavior to the case when all the opinions in the social network are synchronized. Our goal is to emphasize the role of the trust given to the environmental signal in the asymptotic behavior of the opinion dynamics and implicitly of the coupled system. To do that, we conduct a bifurcation analysis of the system around the origin when the trust parameter is varying. Specific conditions are presented for both pitchfork and Hopf bifurcation. Numerical illustration completes the theoretical findings.

Keywords: Control of networks, Control over communications, Networked control systems
Abstract: The paper studies the problem of steering multidimensional opinion in a social network. Assuming the society of desire consists of stubborn and regular agents, stubborn agents are considered as leaders who specify the desired opinion distribution as a distributed reward or utility function. In this context, each regular agent is seen as a follower, updating its bias on the initial opinion and influence weights by averaging their observations of the rewards their influencers have received. Assuming random graphs with reducible and irreducible topology specify the influences on regular agents, opinion evolution is represented as a containment control problem in which stability and convergence to the final opinion are proven.

Keywords: Optimal control, Adaptive control, Robotics
Abstract: In this paper we develop a reservoir-based adaptive critic framework for optimal real-time control of nonlinear robotic systems. Unlike traditional neural network (NN) based critics, deterministic reservoir computing significantly reduces computational complexity by requiring only the training of output weights. Using deterministic reservoir computing, the method efficiently approximates the value function and computes optimal control laws, achieving rapid error convergence and computational efficiency. In addition, a momentum-enhanced adaptation law is proposed to accelerate convergence rates. The framework also contributes to robot learning by enabling adaptive behavior through iterative policy improvement, allowing robots to autonomously refine their control strategies by self-learning. It is theoretically validated under the persistency of excitation condition and demonstrated through simulations of trajectory tracking compared against traditional NN parameterization.

Keywords: Identification for control, Reinforcement learning, Nonlinear systems identification
Abstract: This paper investigates nonlinear identification for control learning with provable guarantees. A novel approach is proposed for Model-Based Reinforcement Learning (MBRL) where Neural Ordinary Differential Equation (NODE) based nonlinear system identification in continuous time is integrated within Policy Iteration (PI) based Reinforcement Learning. To that end, first, a continuous-time NODE model is identified from measured data, which is then leveraged to learn an optimal controller using off-policy PI. Rigorous proofs are developed to guarantee boundedness of parameter as well as prediction errors. The identified NODE model enables admissible initialization of the PI algorithm through a Quadratic Program (QP) under NODE-based Control Lyapunov Function (CLF) constraints, leading to guaranteed admissibility and stability at the initialization phase of control learning. During the exploration phase, closed-loop stability is maintained by enforcing NODE-based Input-to-State Stable CLF (ISS-CLF) constraints. The resulting controller achieves closed-loop stability and optimality with respect to the identified model, providing guarantees throughout the MBRL process. Simulation results assess the effectiveness of the proposed approach.

Keywords: Cyber-Physical Security, Large-scale systems, Fault detection
Abstract: Critical infrastructures, such as power and transportation, are frequently modeled as interconnected Cyber-Physical Systems (CPS). This interconnectivity makes CPS vulnerable to cyber-attacks, threatening system stability and operational continuity. Notably, many of these textcolor{black}{malicious attacks involve manipulating} sensor measurements. In this context, accurately reconstructing the attack signal is crucial for recovering true measurements, distinguishing cyber-attacks from natural faults, and enabling appropriate countermeasures. This work presents a distributed scheme that leverages sliding mode observers to reconstruct attack signals targeting sensors. We provide suitable bounds on the reconstruction error that depend on the disturbance characteristics of the system. Additionally, we present an isolation mechanism and analytically show that it accurately determines the attacked nodes. The applicability of the proposed approach is demonstrated through numerical simulations conducted on a six-subsystem interconnected system, which validate our analytic results.

Keywords: Stochastic optimal control, Nonlinear output feedback, Optimal control
Abstract: We consider the problem minimizing a quadratic cost of controlling linear dynamical systems from bilinear observations. Despite the similarity of this problem to the standard Linear-Quadratic-Gaussian (LQG) control, we show that when the observation model is bilinear, neither does the Separation Principle hold, nor is the optimal controller affine in the estimated state. Moreover, the problem of finding the optimal controller is non-convex. Hence, finding an analytical expression for the optimal feedback controller is difficult in general. Under certain settings, we show that the standard LQG controller locally maximizes the cost instead of minimizing, whereas, the optimal controllers (derived analytically) are nonlinear in the estimated state. We also introduce a notion of input dependent observability and derive conditions under which the Kalman filtering covariance remains bounded. We verify our theoretical results through extensive numerical experiments with synthetic data as well as data generated from a double integrator system.

Keywords: Resilient Control Systems, Networked control systems, Control of networks
Abstract: Ensuring resilient consensus in multi-robot systems with misbehaving agents remains a challenge, as many existing network resilience properties are inherently combinatorial and globally defined. While previous works have proposed control laws to enhance or preserve resilience in multi-robot networks, they often assume a fixed topology with known resilience properties, or require global state knowledge. These assumptions may be impractical in physically-constrained environments, where safety and resilience requirements are conflicting, or when misbehaving agents share inaccurate state information. In this work, we propose a distributed control law that enables each robot to guarantee resilient consensus and safety during its navigation without fixed topologies using only locally available information. To this end, we establish a sufficient condition for resilient consensus in time-varying networks based on the degree of non-misbehaving or normal agents. Using this condition, we design a Control Barrier Function (CBF)-based controller that guarantees resilient consensus and collision avoidance without requiring estimates of global state and/or control actions of all other robots. Finally, we validate our method through simulations.

Keywords: Robust control, Reinforcement learning, Uncertain systems
Abstract: The probabilistic ensembles with trajectory sampling (PETS) algorithm is a recognized baseline among model-based reinforcement learning (MBRL) methods. PETS incorporates planning and handles uncertainty using ensemble-based probabilistic models. However, no formal robustness guarantees against epistemic uncertainty exist for PETS. Providing such guarantees is a key enabler for reliable real-world deployment. To address this gap, we propose a distributionally robust extension of PETS, called DR-PETS. We formalize model uncertainty using a distributional ambiguity set and optimize the worst-case expected return. We derive a tractable convex approximation of the resulting min-max planning problem, which integrates seamlessly into PETS’s planning loop as a regularized objective. Experiments on pendulum and cart-pole environments show that DR-PETS certifies robustness against adversarial parameter perturbations, achieving consistent performance in worst-case scenarios where PETS deteriorates.

Keywords: Data driven control, Switched systems
Abstract: This work studies a data-driven security control problem for unknown discrete-time cyber-physical systems (CPSs) under aperiodic denial-of-service (DoS) attacks based on the switched system approach. Particularly, the concerned DoS attacks are characterized by the aperiodicity with the constraints of minimum silent interval and maximum active interval. Compared with the existing data-driven methods, a novel data-driven security control approach via descriptor method and auxiliary matrices is developed for the considered CPSs with the advantage of lower computational complexity and less input-state data information. First, by utilizing the collected data and switching strategy, the considered CPSs under attacks are transformed into a direct data-driven parametrization of the corresponding switched systems. Next, a data-driven control approach via Willems' fundamental lemma is provided. Meanwhile, through introducing auxiliary matrices to construct the connection between data information and stability conditions, a different data-driven control approach via descriptor method is also presented for the considered unknown CPSs. Finally, the efficiency and advantage of the proposed method are validated by the comparative experiment of the two-wheeled robot.

Keywords: Data driven control, Uncertain systems, Optimization
Abstract: A data-driven approach is proposed, formulated as a quadratically constrained quadratic program, to guarantee the safety and stability of safety-critical control systems relying solely on input-output data. Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are utilized to design control inputs that ensure both stability and safety without requiring explicit knowledge of the system model. To achieve this, an augmented system based on historical input-output measurements is constructed, enabling the data-driven formulation of CLFs and CBFs. The efficiency of the proposed method is evaluated in terms of computational complexity, and its performance is validated through a numerical case study with a mobile robot, underscoring its practical utility and potential for real-world implementation.

Keywords: Linear systems, Uncertain systems, Stochastic optimal control
Abstract: Distributional linear quadratic regulator (LQR) is a new framework that integrates the distributional reinforcement learning and classical LQR, which offers a new way to study the random return instead of the expected cost. Unlike iterative approximation using dynamic programming in the DRL, a closed-form expression for the random return can be exactly characterized in the distributional LQR, which is defined over infinitely many random variables. In recent work, it has been shown that this random return can be well approximated by a finite number of random variables, which we call truncated random return. In this paper, we study the truncated random return in the distributional LQR. We show that the truncated random return can be naturally expressed in the quadratic form. We develop a sufficient condition for the positive definiteness of the block symmetric matrix in the quadratic form and provide the lower and upper bounds on the eigenvalues of this matrix. We further show that in this case, the truncated random return follows a positively weighted non-central chi-square distribution if the random disturbances is Gaussian, and its cumulative density distribution is log-concave if the probability density distribution of the random disturbances is log-concave.

Keywords: Nonlinear systems, Stability of nonlinear systems, Lyapunov methods
Abstract: Understanding the effect of inputs on system safety is one of the most important issues in the study of safety-critical systems. Integral input-to-state safety (iISSf) is a concept that can describe the dependence of safety on the integral of external inputs. This paper studies the characterization of iISSf properties from a barrier function perspective. We introduce iISSf barrier functions (iISSf-BFs) as a tool to verify iISSf, and establish that the existence of an iISSf-BF is a sufficient condition for iISSf. With iISSf control barrier functions (iISSf-CBFs) and quadratic programs (QPs), we construct a safety-critical controller to enforce iISSf with respect to a prescribed iISSf gain. Finally, under an additional assumption of integral input-to-state stability, we show that iISSfs-BFs are also necessary for iISSf.

Keywords: Neural networks, Optimal control, Formal Verification/Synthesis
Abstract: Recent approaches to leveraging deep learning for computing reachable sets of continuous-time dynamical systems have gained popularity over traditional level-set methods, as they overcome the curse of dimensionality. However, as with level-set methods, considerable care needs to be taken in limiting approximation errors, particularly since no guarantees are provided during training on the accuracy of the learned reachable set. To address this limitation, we introduce an epsilon-approximate Hamilton-Jacobi partial differential equation (HJ-PDE), which establishes a relationship between training loss and accuracy of the true reachable set. To formally certify this approximation, we leverage Satisfiability Modulo Theories (SMT) solvers to bound the residual error of the HJ-based loss function across the domain of interest. Leveraging Counter Example Guided Inductive Synthesis (CEGIS), we close the loop around learning and verification, by fine-tuning the neural network on counterexamples found by the SMT solver, thus improving the accuracy of the learned reachable set. To the best of our knowledge, Certified Approximate Reachability (CARe) is the first approach to provide soundness guarantees on learned reachable sets of continuous dynamical systems.

Keywords: Formal Verification/Synthesis, Uncertain systems, Linear systems
Abstract: Ensuring safety in cyber-physical systems (CPSs) is a critical challenge, especially when system models are difficult to obtain or cannot be fully trusted due to uncertainty, modeling errors, or environmental disturbances. Traditional model-based approaches rely on precise system dynamics, which may not be available in real-world scenarios. To address this, we propose a data-driven safety verification framework that leverages matrix zonotopes and barrier certificates to verify system safety directly from noisy data. Instead of trusting a single unreliable model, we construct a set of models that capture all possible system dynamics that align with the observed data, ensuring that the true system model is always contained within this set. This model set is compactly represented using matrix zonotopes, enabling efficient computation and propagation of uncertainty. By integrating this representation into a barrier certificate framework, we establish rigorous safety guarantees without requiring an explicit system model. Numerical experiments demonstrate the effectiveness of our approach in verifying safety for dynamical systems with unknown models, showcasing its potential for real-world CPS applications.

Keywords: Stochastic systems, Markov processes, Uncertain systems
Abstract: A classical approach to formal policy synthesis in stochastic dynamical systems is to construct a finite-state abstraction, often represented as a Markov decision process (MDP). The correctness of these approaches hinges on a behavioural relation between the dynamical system and its abstraction, such as a probabilistic simulation relation. However, probabilistic simulation relations do not suffice when the system dynamics are, next to being stochastic, also subject to nondeterministic (i.e., set-valued) disturbances. In this work, we extend probabilistic simulation relations to systems with both stochastic and nondeterministic disturbances. Our relation, which is inspired by a notion of alternating simulation, generalises existing relations used for verification and policy synthesis used in several works. Intuitively, our relation allows reasoning probabilistically over stochastic uncertainty, while reasoning robustly (i.e., adversarially) over nondeterministic disturbances. We experimentally demonstrate the applicability of our relations for policy synthesis in a 4D-state Dubins vehicle.

Keywords: Statistical learning, Formal Verification/Synthesis, Uncertain systems
Abstract: Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional systems, recent work has focused on the use of probabilistic methods for computing approximate reachable sets. In this work, we advocate for the use of a general purpose, practical, and sharp method for data-driven reachability: the holdout method. Despite the simplicity of the holdout method, we show---on several numerical examples including scenario-based reach tubes---that the resulting probabilistic bounds are substantially sharper and require fewer samples than existing methods for data-driven reachability. Furthermore, we complement our work with a discussion on the necessity of probabilistic reachability bounds. We argue that any method that attempts to de-randomize the bounds, by converting the guarantees to hold deterministically, requires (a) an exponential in state-dimension amount of samples to achieve non-vacuous guarantees, and (b) extra assumptions on the dynamics.

Keywords: Formal Verification/Synthesis, Markov processes, Stochastic systems
Abstract: Formal safety guarantees on the synthesis of controllers for stochastic systems can be obtained using correct-by-design approaches. These approaches often use abstractions to finite-state Markov Decision Processes. As the state space of these MDPs grows, the curse of dimensionality makes the computational and memory cost of the probabilistic guarantees, quantified with dynamic programming, scale exponentially. In this work, we leverage decoupled dynamics and unravel, via dynamic programming operations, a tree structure in the Canonical Polyadic Decomposition (CPD) of the value functions.

For discrete-time stochastic systems with syntactically co-safe linear temporal logic (scLTL) specifications, we provide provable probabilistic safety guarantees and significantly alleviate the computational burden. We provide an initial validation of the theoretical results on several typical case studies and showcase that the uncovered tree structure enables efficient reductions in the computational burden.

Keywords: Formal Verification/Synthesis, Stochastic systems, Autonomous systems
Abstract: Uncertainties are inevitable for control of dynamical systems of practical relevance. The conventional robust control methods assume persistent worst-case realisations of uncertainties, which leads to conservative solutions. To relax this assumption, we exploit the fairness notion in formal verification to qualitatively capture realistic epistemic disturbance behaviours. We study the fair control problem, that is, to maximise the probability of satisfying an Linear Temporal Logic subject to an action-based fairness constraint for uncertain dynamical systems. The action-based fairness of epistemic disturbances can be defined flexibly: by their observed behaviour and/or by their interaction with control input, enabling both input-dependent and independent disturbance modelling. We develop a sound and complete methodology to perform correct-by-design synthesis. We show that this optimal control problem is equivalent to a reachability problem in the fairness-realisable sub-product Markov decision process. We validate our results over a case study of room temperature regulation.

Keywords: Optimization algorithms, Optimization, Robust control
Abstract: We consider iterative gradient-based optimization algorithms applied to functions that are smooth and strongly convex. The fastest globally convergent algorithm for this class of functions is the Triple Momentum (TM) method. We show that if the objective function is also twice continuously differentiable, a new, faster algorithm emerges, which we call C2-Momentum (C2M). We prove that C2M is globally convergent and that its worst-case convergence rate is strictly faster than that of TM, with no additional computational cost. We validate our theoretical findings with numerical examples, demonstrating that C2M outperforms TM when the objective function is twice continuously differentiable.

Keywords: Optimization algorithms, Stochastic systems, Network analysis and control
Abstract: In this paper, we design a novel distributed learning algorithm using stochastic compressed communications. In detail, we pursue a modular approach, merging ADMM and a gradient-based approach, benefiting from the robustness of the former and the computational efficiency of the latter. Additionally, we integrate a stochastic integral action (error feedback) enabling almost sure rejection of the compression error. We analyze the resulting method in nonconvex scenarios and guarantee almost sure asymptotic convergence to the set of stationary points of the problem. This result is obtained using system-theoretic tools based on stochastic timescale separation. We corroborate our findings with numerical simulations in nonconvex classification.

Keywords: Optimization algorithms, Output regulation
Abstract: Time-varying optimization problems arise in a variety of engineering applications. The available information about how the problem changes in time dictates the types of algorithms that are applicable to a particular problem as well as the types of convergence guarantees that may be proven. In this paper, we explore the fundamental properties shared by the entire class of gradient-based optimization algorithms for time-varying optimization. By casting the design of such algorithms as an output regulation problem for dynamical systems, we provide necessary and sufficient conditions for the existence of an algorithm that asymptotically tracks an optimizer of the problem of interest. When these conditions hold, we provide a design procedure to construct such an algorithm. As a fundamental limitation, we show that any algorithm that achieves exact tracking needs to incorporate an internal model of the temporal variation, which we refer to as the internal model principle of time-varying optimization.

Keywords: LMIs, Optimal control, Game theory
Abstract: Semidefinite programs (SDPs) play a crucial role in control theory, traditionally as a computational tool. Beyond computation, the duality theory in convex optimization also provides valuable analytical insights and new proofs of classical results in control. In this work, we extend this analytical use of SDPs to study the infinite-horizon linear-quadratic (LQ) differential game in continuous time. Under standard assumptions, we introduce a new SDP-based primal-dual approach to establish the saddle point characterized by linear static policies in LQ games. For this, we leverage the Gramian representation technique, which elegantly transforms linear quadratic control problems into tractable convex programs. We also extend this duality-based proof to the H∞ suboptimal control problem. To our knowledge, this work provides the first primal-dual analysis using Gramian representations for the LQ game and H∞ control beyond LQ optimal control and Hinf analysis.

Keywords: Optimization algorithms, Optimization, Power systems
Abstract: Feedback optimization optimizes the steady state of a dynamical system by implementing optimization iterations in closed loop with the plant. It relies on online measurements and limited model information, namely, the input-output sensitivity. In practice, various issues, including inaccurate modeling, lack of observation, or changing conditions, can lead to sensitivity mismatches, causing closed-loop sub-optimality or even instability. To handle such uncertainties, we pursue robust feedback optimization, where we optimize the closed-loop performance against all possible sensitivities lying in specific uncertainty sets. We provide tractable reformulations for the corresponding min-max problems via regularizations and characterize the online closed-loop performance through the tracking error in case of time-varying optimal solutions. Simulations on a distribution grid illustrate the effectiveness of our robust feedback optimization controller in addressing sensitivity mismatches in a non-stationary environment.

Keywords: Optimization algorithms, Optimization, Robust control
Abstract: Synthesis of optimization algorithms typically follows a design-then-analyze approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a framework grounded in robust control theory has emerged as a powerful tool for automating algorithm synthesis. By integrating design and analysis stages, fundamental performance bounds are revealed and synthesis of algorithms that achieve them is enabled. In this paper, we apply this framework to design algorithms for solving strongly convex optimization problems with linear equality constraints. Our approach yields a single-loop, gradient-based algorithm whose convergence rate is independent of the condition number of the constraint matrix. This improves upon the best known rate within the same algorithm class, which depends on the product of the condition numbers of the objective function and the constraint matrix.

Keywords: Optimization algorithms, Distributed control, Optimization
Abstract: We propose a system-theoretic perspective on Tracking-ADMM, a recently introduced distributed optimization algorithm for constraint-coupled optimization problems that combines ADMM and tracking over networks. Through a judicious coordinate transformation, we formulate the algorithm as a dynamical linear component in closed-loop with a static nonlinearity resulting from an optimization step. We show, by direct calculation, that the linear component is discrete-positive real, while the static nonlinearity is monotone. As both components are passive systems, their feedback interconnection is passive as well, thus ensuring the stability of Tracking-ADMM.

Keywords: Optimization algorithms, Stochastic systems, Optimization
Abstract: This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic barrier function that is appropriately adapted in each optimization iteration. For a strongly convex objective function and affine inequality constraints, step-size rules and barrier adaptation rules are established that guarantee asymptotic convergence with probability one. The theoretical results in the paper are complemented by numerical studies which highlight potential advantages of the proposed algorithm for optimization problems with a large number of constraints.

Keywords: Energy systems, Transportation networks, Agents-based systems
Abstract: We analyze the economic (mechanism design) aspect of incorporating flexibility in electric vehicle (EV) charging demand management. We propose a general two-period model, where EVs can reserve charging sessions in the day-ahead market and swap them in the real-time market. Under the model, we explore several candidate mechanisms for running the two markets, compared using several normative properties such as incentive compatibility, efficiency, reservation awareness, and budget balance. Specifically, reservation awareness is the only property coupling the two markets and dictates that an EV will not get a lower utility by joining the real-time market. Focusing on the real-time market, we show that the classical Vickrey-Clarke-Groves (VCG) mechanism that treats the day-ahead allocations as endowments is not budget-balanced. Moreover, we show that no mechanism satisfies some combinations of the properties. Then, we propose using a posted-price mechanism to resolve the issue, which turns out to be the dynamic pricing mechanism adopted in many real-world systems. The proposed mechanism has no efficiency guarantee but satisfies all the other properties. To improve efficiency, we propose using a VCG auction in the day-ahead market that guides the reserve prices in the real-time market. When EVs' valuations in the two markets are close, the proposed approach is approximately efficient.

Keywords: Traffic control, Nonlinear systems, Optimization
Abstract: We propose an optimal pricing method for multiple charging stations within a congestion game framework. We compute the equilibrium flows for each pricing strategy and select the prices that maximize the operator’s revenue. The demand at each station is influenced by travel times and incentives to charge. Vehicle types and behaviors (thermal vs. electric, must/may/not charge) are considered. This results in a bi-level optimization problem, which is solved using a Branch-and-Bound approach enhanced with pruning techniques for improved efficiency. Our experiment integrates three levels of optimization: maximizing revenue by optimizing the placement of stations when maximizing their pricing strategies, while minimizing the demand derived from the congestion game model. We examine the total travel time and maximizing revenue does not increase congestion.

Keywords: Game theory, Learning, Transportation networks
Abstract: We consider the problem of efficiently learning to play single-leader multi-follower Stackelberg games when the leader lacks knowledge of the lower-level game. Such games arise in hierarchical decision-making problems involving self-interested agents. For example, in electric ride-hailing markets, a central authority aims to learn optimal charging prices to shape fleet distributions and charging patterns of ride-hailing companies. Existing works typically apply gradient-based methods to find the leader's optimal strategy. Such methods are impractical as they require that the followers share private utility information with the leader. Instead, we treat the lower-level game as a black box, assuming only that the followers' interactions approximate a Nash equilibrium while the leader observes the realized cost of the resulting approximation. Under kernel-based regularity assumptions on the leader's cost function, we develop a no-regret algorithm that converges to an epsilon-Stackelberg equilibrium in O(sqrt{T}) rounds. Finally, we validate our approach through a numerical case study on optimal pricing in electric ride-hailing markets.

Keywords: Computational methods, Optimization algorithms, Smart grid
Abstract: The tensor completion problem is to fill-in unobserved entries of a partially observed tensor. However, past approaches to tensor completion either achieved the information-theoretic rate but lacked practical algorithms, or proposed polynomial-time algorithms that require an exponentially-larger number of samples for low estimation error. In this paper, we develop a novel tensor completion algorithm to tackle this challenge by achieving both provable convergence (in numerical tolerance) in a linear number of oracle steps and the information-theoretic rate. We formulate tensor completion as a convex optimization problem constrained using a gauge-based tensor norm and provide proofs of properties of this norm including its computational complexity and tensor rank surrogacy. We formulate this norm such that linear separation problems over the gauge unit-ball can be solved using integer optimization. This enables the use of Frank-Wolfe variant to build our algorithm. We demonstrate effectiveness of our method using experiments with simulated data and with an application towards providing low-computation predictions of battery storage flows that may be beneficial in billion-device-scale integration of electromobility systems with the grid.

Keywords: Control applications, Optimal control, Robust control
Abstract: Battery swapping offers a compelling alternative to fast charging for large EV fleets. By decoupling charging from vehicle dwell time, battery swapping stations (BSS) can charge batteries slower, reducing grid strain and extending battery life, while enabling quick vehicle turnaround. In this work, we present a hierarchical control architecture for large-scale BSS that addresses the computational limits of conventional integer programming approaches. By adopting a macroscopic model that represents battery states as a continuous distribution, our method captures nonlinear battery dynamics without sacrificing tractability. In this framework, the upper level optimizes station power procurement in response to market prices, while the lower level enforces realistic charging constraints across hundreds of batteries. This design enables robust operation under stochastic customer arrivals, ensures high service quality, and ultimately maximizes BSS profit, offering a practically scalable solution for heavy-duty EV fleets.

Keywords: Smart grid, Game theory, Power systems
Abstract: We propose a real-time nodal pricing mechanism for cost minimization and voltage control in distribution networks with autonomous distributed energy resources. Unlike existing methods, the proposed pricing scheme does not require device-aware centralized coordination or communication between prosumers. The resulting market is naturally represented as a stochastic game where prosumers learn feedback control policies to optimize their individual rewards. By developing new sufficient conditions under which a stochastic game is a Markov potential game, we show that the problem of computing an equilibrium for the proposed model is equivalent to solving a single-agent Markov decision process. These new conditions are general and may apply to other applications. An equilibrium is computed for an IEEE test system to empirically demonstrate the near-optimal efficiency of the pricing policy.

Keywords: Energy systems, Predictive control for linear systems, Constrained control
Abstract: Self-powered control technologies derive all the energy needed to implement control by harvesting energy from disturbances. These systems are applicable in cases of vibration suppression, or robotic systems, where the controller cannot rely on external energy sources. Constraints on energy storage impose limitations on control actions, ensuring that stored energy is neither depleted nor exceeded. In this paper the energy constraints are enforced while an integral-quadratic objective is minimized through the use of Model Predictive Control. The presence of multiple storage elements and upper limits on the capacity of the stored energy introduce non-convexities into the optimization problem. To enable real-time implementation, convex-concave techniques are utilized to conservatively bound the energy constraints and determine the optimal control solution. This method is applied to a simple mechanical system composed of three interconnected linkages.

Keywords: Power systems, Stability of nonlinear systems
Abstract: Incentive-based coordination mechanisms for distributed energy consumption have shown promise in aligning individual user objectives with social welfare, especially under privacy constraints. Our prior work proposed a two-timescale adaptive pricing framework, where users respond to prices by minimizing their local costs, and the system operator iteratively updates the prices based on aggregate user responses. A key assumption was that the system cost need to smoothly depend on the aggregate of the user demands. In this paper, we relax this assumption by considering the more realistic model in which the system cost is determined by solving a Direct Current Optimal Power Flow (DCOPF) problem with constraints. We present a generalization of the pricing update rule that leverages the generalized gradients of the system cost function, which may be nonsmooth due to the structure of DCOPF. We prove that the resulting dynamic system converges to a unique equilibrium, which solves the social welfare optimization problem. Our theoretical results provide guarantees on convergence and stability using tools from nonsmooth analysis and Lyapunov theory. Numerical simulations on networked energy systems illustrate the effectiveness of the proposed scheme.

Keywords: Discrete event systems, Petri nets, Estimation
Abstract: In this paper, we address current-state estimation in Timed Labeled Synchronized Petri Nets (TLSPNs), a subclass of Timed Output Synchronized Petri Nets. We introduce the Synchronized State Class Graph to model the state space and propose its transformation into a State Class Interval Automaton (SCIA), a finite state automaton where continuous time is discretized into time tick events. In this framework, a state observer for SCIA is proposed, allowing for current state estimation. The proposed state estimation method is illustrated on an example with secret states, where it is used to infer the net’s current state and compromise confidentiality.

Keywords: Cyber-Physical Security, Autonomous systems, Air traffic management
Abstract: The Cyber-Physical System of Urban Air Mobility (UAM) is among the important pivots of the future smart cities that aim at efficient, safe, and sustainable air transportation of people and goods. UAM technology is characterized by integration and the process of private and state-owned information through wireless tele-communication that exchange important messages, including traffic control commands and geo-fencing rules, public safety announcements, and flight path, etc. Therefore, authentication of transmitted messages is among crucial tasks that require integration to the existing navigation systems, in order to protect the airspace against catastrophic consequences of spoofing cyberattacks. This article aims at introducing an intelligent authentication solution for aerial vehicles, to distinguish legitimate Ground Control Centres (GCCs) from adversaries and intruders by means of behavioural analytics, through consistency examination of the transmitted flight plan with prior waypoint trajectories and flight dynamics of the vehicle. In particular, the proposed authentication technology monitors remotely transmitted flight plans to ensure that firstly, there exists a coherent and consistent path with respect to prior waypoints, and secondly, a deliberate dynamic policy that is consistent with optimal energy conservation practices, both of which require access to information that are rarely available to intruders and adversaries. Consequently, flight plans are only obliged if the likelihood of threats or violations to predetermined constraints and traffic rules are acceptable. Numeric simulations of the results have been provided to validate the developed concepts.

Keywords: Control Systems Privacy, Networked control systems, Linear systems
Abstract: This paper addresses the challenge of privacy preservation for statistical inputs in dynamical systems. Motivated by an autonomous building application, we formulate a privacy preservation problem for statistical inputs in linear time-invariant systems. What makes this problem widely applicable is that the inputs, rather than being assumed to be deterministic, follow a probability distribution, inherently embedding privacy-sensitive information that requires protection. This formulation also presents a technical challenge as conventional differential privacy mechanisms are not directly applicable. Through rigorous analysis, we develop strategy to achieve (0, delta) differential privacy through adding noise. Finally, the effectiveness of our methods is demonstrated by revisiting the autonomous building application.

Keywords: Game theory, Control Systems Privacy, Quantized systems
Abstract: We develop a communication-theoretic framework for privacy-aware and resilient decision making in cyber-physical systems under emph{misaligned} objectives between the encoder and the decoder. The encoder observes two correlated signals (X,theta) and transmits a finite-rate message Z to aid a legitimate controller (the decoder) in estimating X+theta, while an eavesdropper intercepts Z to infer the private parameter theta. Unlike conventional setups where encoder and decoder share a common MSE objective, here the encoder minimizes a Lagrangian that balances legitimate control fidelity emph{and} the privacy leakage about theta. In contrast, the decoder’s goal is purely to minimize its own estimation error without regard for privacy. We analyze fully, partially, and non-revealing strategies that arise from this conflict, and characterize optimal linear encoders when the rate constraints are lifted. For finite-rate channels, we employ gradient-based methods to compute the optimal controllers. Numerical experiments illustrate how tuning the privacy parameter shapes the trade-off between control performance and resilience against unauthorized inferences.

Keywords: Network analysis and control, Networked control systems, Cyber-Physical Security
Abstract: Water distribution networks (WDNs) are aging infrastructure that susceptible to various failures including human errors, malicious cyber-attacks, pipe bursts and leaks. This necessitates vulnerability analysis of WDN topologies and hydraulic models that capture the network physics. Graph-theoretic centrality measures—as a primary class of centrality measures in network science—aim to rank the network components solely based on their influence on the WDN topology in the case of changes, while overlooking the WDN dynamics. To overcome such a limitation, this paper uses a control-theoretic centrality measure to identify the network’s most and least influential pipes in WDNs, by simultaneously incorporating the dynamics and topology of the WDN. We introduce a node centrality-based measure, namely vulnerability vector (VV), to rank the network pipes based on their influence on the dynamics and topology of the WDN in the case of changes. This approach enables water system operators to better understand the network’s vulnerabilities and effectively prioritize the maintenance and operational efforts on the most influential pipes.

Keywords: Attack Detection, Cyber-Physical Security, Discrete event systems
Abstract: This work aims to analyze different aspects of security for a network of two agents in a decentralized framework. Mainly, it deals with two concerns: attack detection and localization. Agents and Attacker are modeled by finite state machines. Agents are interconnected via output feedback composition and share their output information through vulnerable communication channels. Attacker can act in the communication channels between the agents. Using the composed model, necessary and sufficient conditions are developed to ensure the detectability and localizability of the attacked channel. A numerical example is also included at the end of the paper.

Keywords: Attack Detection, Cyber-Physical Security, Resilient Control Systems
Abstract: Interconnected systems consist of multiple subsystems coupled through physical and cyber connections. Within a subsystem, a covert cyberattack manipulates actuator commands to achieve a malicious objective while simultaneously manipulating sensor measurements to mimic nominal behavior, thereby remain undetected. Traditionally in the literature, approaches are proposed to detect and isolate such cyberattacks by using banks of observers, irrespective of any control scheme. In addition, the detection of a covert cyberattack within a subsystem as well as its isolation is feasible only by its neighbouring subsystems. In this paper, we propose an alternative approach, by incorporating a decentralized controller and a decentralized state-disturbance observer within each subsystem, which makes detection of covert cyberattacks feasible locally within each subsystem (i.e., local detection), thereby eliminating the reliance on neighbouring subsystems as well as the need for additional design complexity for isolation. The proposed approach is validated through numerical simulations.

Keywords: Power systems, Optimization, Smart grid
Abstract: Differential privacy (DP) provides a principled approach to synthesizing data (e.g., loads) from real-world power systems while limiting the exposure of sensitive information. However, adversaries may exploit synthetic data to calibrate cyberattacks on the source grids. To control these risks, we propose new DP algorithms for synthesizing data that provide the source grids with both cyber resilience and privacy guarantees. The algorithms incorporate both normal operation and attack optimization models to balance the fidelity of synthesized data and cyber resilience. The resulting post-processing optimization is reformulated as a robust optimization problem, which is compatible with the exponential mechanism of DP to moderate its computational burden.

Keywords: Switched systems, Compartmental and Positive systems
Abstract: This paper studies cone-preserving linear discrete-time switched systems whose switching is governed by an automaton. For this general system class, we present performance analysis conditions for a broadly usable performance measure. In doing so, we generalize several known results for performance and stability analysis for switched and positive switched systems, providing a unifying perspective. We also arrive at novel ℓ1-performance analysis conditions for positive switched systems with constrained switching, for which we present an application-motivated numerical example. Further, the cone-preserving perspective provides insights into appropriate Lyapunov function selection.

Keywords: Cooperative control, Optimal control, Modeling
Abstract: The paper shows that the altruistic behaviour can be interpreted as the solution of an optimal control problem. To this purpose, two discrete-time dynamic models for the interaction between individuals’ fitnesses are described. For the first model, which is linear with constant coefficients, it is possible to prove that the optimal control input is a classic bang-bang function with one switching (at maximum) that can be explicitly located in time. To show that a solution exists also for the second model, which is a non-linear extension of the first one, we adapt to the discrete-time case a result available in the literature and concerning the implicit expression of the solution of optimal control problems for continuous-time positive systems. Numerical examples are also added to highlight the results. Finally, we show that the models can also fit other real problems, among which we consider, in particular, the optimal investment of a capital.

Keywords: Distributed parameter systems, Linear systems
Abstract: This paper generalizes the physical property of relaxation from linear time-invariant (LTI) to linear time-and-space-invariant (LTSI) systems. It is shown that the defining features of relaxation---complete monotonicity, passivity, and memory-based storage---carry over seamlessly to the spatio-temporal domain. An LTSI system is shown to be of relaxation type if and only if its associated spatio-temporal Hankel operator is cyclically monotone. This implies the existence of an intrinsic quadratic storage functional defined uniquely by past inputs, independently of any state-space realization. As in the LTI case, LTSI relaxation systems are shown to be those systems for which the state-space concept of storage coincides with the input-output concept of fading memory functional.

Keywords: Linear systems, Nonlinear systems, PID control
Abstract: Systems that preserve the property of periodic monotonicity, i.e., period-wise unimodality are studied. Leveraging total positivity theory and its geometric interpretations, we derive tractable characterizations of such systems by linking them to our tractable description of sequentially convex contours. Since common static nonlinearities (e.g., ideal relay, saturation, etc.) preserve periodic monotonicity, our findings also apply to discrete-time Lur’e feedback systems. This lays the way for signal-based fixed-point theorems that aid in predicting self-sustained oscillations. Our examples demonstrate the utility of periodic monotonicity preservation in relay feedback systems.