Keywords: Robust control, Safety-critical control, Optimal control
Abstract: Recent developments in data-driven control, such as reinforcement learning, have spurred a renewed interest in optimal control and its approximate, near-optimal solutions, including value iteration (VI) and policy iteration (PI). As the community pushes to implement these algorithms on safety-critical systems, foundational questions regarding the stability, robustness, and safety of the resulting control laws become paramount. Intriguingly, even in the absence of learning, significant gaps remain in our fundamental understanding of stability and robustness for large classes of costs and dynamical models. This lecture presents a comprehensive overview of recent advancements in guaranteeing the stability of various optimal and near-optimal control laws for discrete-time linear and nonlinear systems. We will focus precisely on the intersection of Bellman’s dynamic programming principles and Lyapunov stability theory, with the ultimate goal of establishing a unified framework for simultaneous stability and near-optimality analysis. Finally, we will demonstrate how these theoretical insights directly apply to popular algorithmic techniques like VI and PI.

Keywords: Machine learning and control, Nonlinear systems, Identification for control
Abstract: This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for ordinary differential equations (ODEs) and partially for partial differential equations (PDEs), its extension to delay differential equations (DDEs) remains limited due to the infinite-dimensional phase space of DDEs. We propose a finite-dimensional Koopman approximation framework based on history discretization and a suitable reconstruction operator, enabling a tractable representation of the Koopman operator via kernel-based extended dynamic mode decomposition (kEDMD). Deterministic error bounds are derived for the learned predictor, decomposing the total error into contributions from history discretization, kernel interpolation, and data-driven regression. Additionally, we develop a kernel-based reconstruction method to recover discretized states from lifted Koopman coordinates, with provable guarantees. Numerical results demonstrate reliable prediction of nonlinear delay systems, with potential relevance to future control applications.

Keywords: Data driven control, Stability of linear systems, Large-scale systems
Abstract: Data-informativity has gained much attention as a data-driven approach that enables the direct assess- ment of system dynamics properties, such as stability, from collected data. Existing studies on data-informativity focus exclusively on data provided as time-series trajectories. In contrast, many practical applications, such as single- cell RNA sequencing, involve snapshot data, where the temporal evolution of individual entities is not trackable and only population distributions at discrete observation times are available. Motivated by this background, we propose a novel framework of data-informativity of snapshot data for stability. Although a sufficient condition for this setting can be derived by extending existing results, it requires enumerating all possible temporal evolutions, resulting in a computational burden of factorial order with respect to the number of data points. To overcome this issue, we derive computationally tractable criteria based on the snapshot data variance.

Keywords: Optimal control, Data driven control, Estimation
Abstract: Neural ordinary differential equations (NODEs) have emerged as a powerful means for modeling of different dynamic systems, owing to their continuous-depth structure matching dynamic systems, rich representation capacity, and high data and training efficiency. However, optimal control of NODEs has received limited attention, and conventional gradient-based optimal control approaches are inadequate because of the nonlinearity and nonconvexity inherent in NODEs. To fill in this gap, we study model predictive control of NODEs and propose a new perspective: inferring the best control actions based on the control objective and enabling the inference by ensemble sampling-based smoothing. With this perspective, we first derive a probabilistic inference problem in the form of state smoothing that holds an equivalence to the optimal control problem. Then, we develop a continuous-time ensemble Kalman smoothing approach to accomplish the inference. We finally validate the approach on a soft robot manipulator control problem that uses a NODE as its model. We compare our results with the well-known model predictive path integral controller, showing that our proposed method provides both high computational performance and control accuracy.

Keywords: Safety-critical control, Robotics, Constrained control
Abstract: Backup-set-based safety filters certify safety under input constraints by validating finite-horizon rollouts of input-admissible backup policies. To reduce conservativeness and possible deadlock behavior, practical systems often require multiple backup maneuvers, yet hard switching among backups can produce undesirable command changes. This work proposes a gradient-free safety filter that integrates multiple backup policies through a hierarchical convex blending architecture. Safety is evaluated using implicit barriers computed from backup rollouts, and a preferred backup mode is selected among safe candidates. An event-based anchor update and an interpolation rule of blending weights ensure continuity of the filtered input despite discrete changes in the preferred mode. The proposed safety filter satisfies convex input constraints whenever the nominal and backup inputs are admissible, and it guarantees forward invariance of the union safe set. Quadrotor collision-avoidance simulations with multiple obstacles demonstrate reduced conservativeness and continuous control input.

Keywords: Safety-critical control
Abstract: Ensuring safety is a critical requirement for autonomous systems, yet providing formal guarantees for nominal controllers remains a significant challenge. In this paper, we propose a modular sampling-based safety filter to ensure the safety of arbitrary nominal control inputs. At each timestep, the filter evaluates the safety of the nominal input by leveraging control sequence samples generated via Stein Variational Model Predictive Control (SV-MPC). This approach approximates a safety-conditioned posterior distribution over control sequences, enabling the filter to effectively capture multimodal safe regions in complex, non-convex environments. The filter guarantees safety by overriding the nominal input when all sampled control sequence candidates are deemed unsafe. By leveraging the scenario approach, the proposed method provides a probabilistic guarantee on its restrictiveness. We validate the filter through collision avoidance tasks in both single- and multi-vehicle settings, demonstrating its efficacy in navigating cluttered environments where nominal controllers may fail.

Keywords: Safety-critical control, Predictive control for nonlinear systems, Robust control
Abstract: Predictive Safety Filters (PSFs) enforce hard constraints by minimally modifying a proposed input using finite-horizon certification. Tube-free robustifications based on open-loop Lipschitz propagation can yield horizon-growing deviation bounds that destroy feasibility for moderate horizons.

We derive a contraction-based tube-free robustness margin for disturbed discrete-time nonlinear systems under an ancillary tracking law. The resulting deviation bound saturates to an ultimate limit and is incorporated via analytic state/input/domain tightenings without set-difference operations. We prove robust constraint satisfaction and backup-plan recursive feasibility. Monte Carlo inverted-pendulum results show horizon-robust certification: the certifiable action set remains non-vanishing and fallback stays near zero, unlike the Lipschitz baseline.

Keywords: Game theory, Uncertain systems, Optimization
Abstract: Correlated equilibria enable a coordinator to influence the self-interested agents by recommending actions that no player has an incentive to deviate from. However, the effectiveness of this mechanism relies on accurate knowledge of the agents’ cost structures. When cost parameters are uncertain, the recommended actions may no longer be incentive compatible, allowing agents to benefit from deviating from them. We study a chance-constrained correlated equilibrium problem formulation that accounts for uncertainty in agents' costs and guarantees incentive compatibility with a prescribed confidence level. We derive sensitivity results that quantify how uncertainty in individual incentive constraints affects the expected coordination outcome. In particular, the analysis characterizes the value of information by relating the marginal benefit of reducing uncertainty to the dual sensitivities of the incentive constraints, providing guidance on which sources of uncertainty should be prioritized for information acquisition. The results further reveal that increasing the confidence level is not always beneficial and can introduce a tradeoff between robustness and system efficiency. Numerical experiments demonstrate this tradeoff: the proposed algorithm reduces realized coordination cost by up to 35% at intermediate confidence levels, while the proposed information-gain metric consistently identifies effective uncertainty sources to reduce.

Keywords: Multi-agent learning, Cooperative control
Abstract: Multi-vehicle coordination in urban environments suffers from the curse of dimensionality, motivating the use of representation learning in multi-agent reinforcement learning (MARL). However, compact latent representations may discard the geometric and dynamical information required for explicit safety certification, giving rise to latent safety aliasing. To address this challenge, we propose a cross-space safe MARL architecture that learns scalable coordination in latent space while enforcing safety-critical execution in physical space. At the core of our method is a Decision-Sufficient Interaction Abstraction (DSIA), which extracts a compact decision-sufficient physical subsystem around the ego vehicle. This compact subsystem supports scalable learning while preserving the geometry and dynamics required for execution-level safety certification. On top of this retained subsystem, a nominal policy models perform coordination learning in a further latent space, whereas a Control Barrier Function (CBF) enforces hard collision-avoidance constraints directly in physical space, with backup-mediated recovery when the online safety filter becomes unacceptable. Theoretical analysis shows how DSIA and latent abstraction errors translate into certified robustness margins for the physical safety layer, bounds value distortion under MARL non-stationarity, and establishes conditional forward invariance of the executed closed loop under a constructive local recoverability design. Experiments in dense urban driving scenarios demonstrate efficient coordination together with strong collision avoidance performance.

Keywords: Cooperative control, Agents-based systems, Safety-critical control
Abstract: This paper presents a collaborative pace regulation strategy for aerial-ground robot teams deployed in an obstacle-rich environment, as a way of explicitly calling out the benefit of combining qualitatively different capabilities. In particular, an aerial robot, equipped with the appropriate sensors for obstacle detection and estimation, assists a ground robot with inadequate sensing to avoid obstacles and complete its task efficiently. Using its sensor measurements, the aerial robot estimates the dimensions of each obstacle with sensor accuracy that decreases as altitude increases. We propose a safety-critical pace control framework that ensures obstacle avoidance while satisfying inter-robot collaboration constraints, enabling the ground robot to adjust its speed based on the distance to nearby obstacles. We demonstrate the proposed framework through case studies in which the aerial and ground robots collaborate to reach the target location, highlighting an improvement in performance compared to fixed-altitude collaboration baselines.

Keywords: Robotics, Optimal control, Safety-critical control
Abstract: This paper presents a safety-critical centralized nonlinear model predictive control (NMPC) framework for cooperative payload transportation by two quadrupedal robots. The interconnected robot–payload system is modeled as a discrete-time nonlinear differential–algebraic system, capturing the coupled dynamics through holonomic constraints and interaction wrenches. To ensure safety in complex environments, we develop a control barrier function (CBF)-based NMPC formulation that enforces collision avoidance constraints for both the robots and the payload. The proposed approach retains the interaction wrenches as decision variables, resulting in a structured DAE-constrained optimal control problem that enables efficient real-time implementation. The effectiveness of the algorithm is validated through extensive hardware experiments on two Unitree Go2 platforms performing cooperative payload transportation in cluttered environments under mass and inertia uncertainty and external push disturbances.

Keywords: Event-triggered/resource-aware control, Communication networks
Abstract: Safe multi-agent coordination typically assumes what real-world, deployed, resource-constrained robots cannot provide: continuous, perfect state sharing. Robust control strategies must be complemented with robust communication strategies to deliver resilient deployments. In this work, we propose a unified control/communication strategy that provides safe control to guarantee inter-agent safety under intermittent communication and demonstrate its effectiveness in a pursuit-evasion scenario. Each agent computes the reachable set of neighboring agents based on the last state information received, then solves for a safe control input based on control barrier functions to ensure agents avoid collision. We prove that inter-agent collision avoidance is guaranteed provided communication staleness remains bounded. As the reachable set inflates between state transmissions, each agent reasons about when to preemptively transmit its state information to neighboring agents based on novel metrics characterizing uncertainty risk and kinematic risk. We implement and simulate a variety of pursuit-evasion scenarios and show that preemptive communication reduces messages by 77.5% compared to periodic and event-triggered baselines with zero collisions.

Keywords: Air traffic management, Multi-agent learning, Reinforcement learning
Abstract: We address robust separation assurance for small Unmanned Aircraft Systems (sUAS) under GPS degradation and spoofing via Multi-Agent Reinforcement Learning (MARL). In cooperative surveillance, each aircraft (or agent) broadcasts its GPS-derived position; when such position broadcasts are corrupted, the entire observed air traffic state becomes unreliable. We cast this state observation corruption as a zero-sum game between the agents and an adversary: with probability R, the adversary perturbs the observed state to maximally degrade each agent’s safety performance. We derive a closed-form expression for this adversarial perturbation, bypassing the iterative inner optimization of adversarial training entirely and enabling linear-time evaluation in the state dimension. We show that this expression approximates the exact minimizer of the value function over the modeled uncertainty set with second-order accuracy. We further bound the safety performance gap between clean and corrupted observations, showing that it degrades at most linearly with the corruption probability under Kullback-Leibler regularization. Finally, we integrate the closed-form adversarial policy into a MARL policy gradient algorithm to obtain a robust counter-policy for the agents. In a high-density sUAS simulation, we observe near-zero collision rates under corruption levels up to 35%, outperforming a baseline policy trained without adversarial perturbations.

Keywords: Predictive control for linear systems, Data driven control
Abstract: This work presents a modification of Data-enabled Predictive Control (DeePC) for linear time-invariant (LTI) systems that enlarges the positively invariant terminal ellipsoid by augmenting Hankel matrices online with the latest available input-output (IO) data. Under a slight modification of the terminal region semi-definite program (TR-SDP), we establish a lower bound on the relative growth of the terminal volume in terms of online Hankel window data and TR-SDP variables. To avoid solving the TR-SDP in real time, this bound is approximated via a pseudoinverse characterization of the TR-SDP variable, yielding a computationally-efficient event-trigger condition that rests on an approximation rather than the bound itself. We then study the single-input–single-output (SISO) case, where one further modification to the TR-SDP renders the trigger exact: growth of the terminal region is guaranteed whenever a user-defined threshold is exceeded. Numerical validation on simulated multi-input-multi-output (MIMO) and SISO battery systems for optimal charging shows both triggers firing during periods of high system activity, followed by consistent growth of the terminal region produced by the TR-SDP.

Keywords: Data driven control, Predictive control for linear systems, Robust control
Abstract: This paper presents a new data-driven robust predictive control law, for linear systems affected by unknown-but-bounded process disturbances. A sequence of input-state data is used to construct a suitable uncertainty representation based on interval matrices. Then, the effect of uncertainty along the prediction horizon is bounded through an operator leveraging matrix zonotopes. This yields a tube that is exploited within a variable-horizon optimal control problem, to guarantee robust satisfaction of state and input constraints. The resulting data-driven predictive control scheme is proven to be recursively feasible and practically stable. A numerical example shows that the proposed approach compares favorably to existing methods based on zonotopic tubes.

Keywords: Data driven control, Linear systems
Abstract: We consider the problem of data informativity for quadratic stabilization and H_{infty} control of continuous linear time invariant systems with delays using state feedback leveraging the matrix S-lemma. The control laws are given as a solution of linear matrix inequalities derived from data. We also consider the case where there are missing entries in data matrices and the goal is to design stabilizing data-driven control laws from data corrupted by these missing entries. The proposed results are demonstrated via numerical simulations. The numerical experiments show that using interpolation methods to recover missing entries may lead to data-driven controllers for a perturbed model rather than the true model.

Keywords: Data driven control, Predictive control for nonlinear systems, Constrained control
Abstract: In this paper, a novel data-driven Model Predictive Control scheme is conceived for a class of constrained discrete-time nonlinear systems. By taking advantage of the capabilities made available by behavioral approach, reinforcement learning and set-theoretic ideas, the receding horizon controller is formally derived by customizing reachability analysis to the data-driven scenario. The constrained optimization problem is formulated through Fundamental Lemma arguments applied to local linear descriptions of the nonlinear dynamics.

Keywords: Robust control, Data driven control
Abstract: Modern control synthesis relies on accurate models to design high-performance controllers, but obtaining such models is often costly, motivating renewed interest in data-driven approaches. Frequency-response-based synthesis methods are attractive since they use easily obtainable frequency data and allow flexible tuning. These methods formulate controller design as an optimization over the full frequency spectrum; however, practical implementation requires considering only a finite set of frequency points. This sampling step removes explicit stability and performance guarantees. By analyzing inter-frequency behavior, bounds on spectral errors can be established. Using these bounds, this paper proposes a novel algorithm for SISO controller design based on finite frequency-response data that guarantees closed-loop stability and robust performance.

Keywords: Data driven control, Identification, AI/LLM and control
Abstract: We study trajectory-level data attribution for the plug-in stochastic LQR cost hat J(mathcal D)=tr(P(hattheta)hat W), in which both the dynamics (A,B) and the process-noise covariance are estimated from the same identification data. Our target is the leave-one-trajectory-out (LOTO) shift Deltahat J_k, and we develop a first-order influence approximation that isolates the identification-to-control coupling through a three-level hierarchy: (i) the model-side surrogate IFm_k:=H^{-1}g_k, which is the emph{exact} ridge-LS parameter shift rather than a numerical Newton step; (ii) the fixed-covariance score IFfixed_k=zeta_Sigma^topIFm_k; and (iii) the stochastic score IFstoch_k, obtained from IFm_k by adding a residual-channel gradient h together with an exact direct-removal covariance correction. Theorem~ref{thm:decomp} decomposes Deltahat J_k into a leading first-order term and three explicit remainders. The new covariance remainder admits an algebraic bound and is free of Lyapunov amplification. Experiments on a DC motor, a mass--spring--damper with heterogeneous noise, and a quadrotor UAV hover task show near-perfect agreement with exact LOTO retraining on linear plants and on the linearized hover regime, so the score serves as a practical substitute for retraining in linear stochastic LQR.

Keywords: Uncertain systems, Data driven control, Robust control
Abstract: We establish sufficient conditions for robust positive invariance under state- and input-dependent disturbances with anisotropic covariance structure. The proposed ans"{a}tze maps a fixed ellipsoidal template through a GP-derived positive-definite matrix field, subsuming scalar homothetic scaling while retaining finite graph-based verification. The resulting LMI conditions couple the learned field to Schur-stable dynamics; an isotropic fallback with inflation factor r=1/(1-gamma_{mathrm{cl}}) proves admissibility. During each learning epoch the field is frozen, so online tube evaluation is one GP covariance query and a small matrix square root, with no online set iteration or LMI solve. Quadrotor simulations show a 195times reduction in 3D velocity-tube volume and a 2.1{times}10^5 reduction in the joint 7D velocity-control subspace relative to homothetic scaling.

Keywords: Autonomous vehicles, AI/LLM and control
Abstract: In this paper, we introduce VisioPath, a novel framework combining vision-language models (VLMs) with model predictive control (MPC) to enable safe autonomous driving in dynamic traffic environments. The proposed approach leverages a bird’s-eye view video processing pipeline and zero-shot VLM capabilities to obtain structured information about surrounding vehicles, including their positions, dimensions, and velocitie, while providing semantically-informed initial trajectory guesses that warm-start the optimizer and enable contextually-aware navigation decisions (e.g., yielding to emergency vehicles). Using this rich perception output, we shape elliptical collision-avoidance potential fields around other traffic participants, which are seamlessly integrated into a finite-horizon optimal control problem for trajectory planning. The resulting trajectory optimization is solved via differential dynamic programming and is embedded in an event-triggered MPC loop. To ensure collision-free motion, a safety verification layer is incorporated in the framework that provides an assessment of potential unsafe trajectories. Extensive simulations in SUMO and CARLA simulators demonstrate that VisioPath outperforms other baseline approaches, such as conventional MPC, A*, RRT and CBF methods, across multiple metrics. By combining modern AI-driven perception with the rigorous foundation of optimal control, VisioPath represents a significant step forward in safe trajectory planning for complex traffic systems.

Keywords: Autonomous vehicles, Multi-agent learning, Reinforcement learning
Abstract: Urban carpooling in congested road networks requires decision-making frameworks capable of handling timevarying traffic conditions and multiple autonomous vehicles (AVs). This work models autonomous carpooling as a multiagent sequential decision problem formulated as a DecentralizedPartially Observable Markov Decision Process (Dec-POMDP). A two-layer architecture is adopted: an upper-layer policy optimized for decentralized task selection, and a lower-layer routing module computing shortest paths on the road graph. Realistic traffic dynamics are incorporated using TomTom-derived congestion data within a SUMO simulation environment. Numerical experiments show improved mission efficiency and the emergence of congestion-aware behaviors.

Keywords: Safety-critical control, Machine learning and control, Autonomous systems
Abstract: Reachability computations that rely on approximate or learned models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing reasonable probabilistic guarantees may require many samples, which can be costly. To remedy this, we propose that calibration of reachable sets be performed using active learning strategies. In order to produce a probabilistic guarantee on the active learning, we adapt the Pick-to-Learn algorithm, which produces generalization bounds for standard supervised learning, to the active learning setting. Our method, Approximate Pick-to-Learn, treats the process of choosing data samples as maximizing an approximate error function. Conformal prediction is used to ensure that the approximate error is close to the true model error. We demonstrate our technique for a simulated drone racing example in which learning is used to provide an initial guess of the reachable tube. Our method requires fewer samples to calibrate the model and provides more accurate sets than the baselines while also producing a novel generalization bound.

Keywords: Automotive control, Control applications
Abstract: Limit-of-handling scenarios such as drifting can be exploited to enhance the overall safety of autonomous vehicles. This paper presents a control strategy that stabilizes the vehicle while performing a drift maneuver. The proposed controller is based on a linear quadratic regulator (LQR) architecture, augmented with control barrier functions (CBFs) that are shown to be able to overcome the LQR sensitivity to model uncertainties by limiting both the longitudinal slip and the vehicle yaw rate. The validation is carried firstly through simulations, showing the impact of the CBFs when dealing with a mismatch in tire-road friction, and secondly on a 1:5-scale electric prototype. The results demonstrate the controller's ability to induce and regulate a drift maneuver, even in the presence of significant model uncertainties.

Keywords: Optimization algorithms, Machine learning and control, Optimization
Abstract: We study a hierarchical federated learning (FL) problem arising in over-parameterized learning and ill-posed optimization, where clients seek a solution that minimizes a secondary loss function among multiple optimal solutions of a primary distributed learning problem. First, when the inner-level objective is convex and the outer-level objective is convex or strongly convex, we propose a self-tuned regularized federated averaging method (StR-FedAvg). Second, for nonconvex outer-level objectives, we develop a two-loop FL scheme employing an inexact projected first-order method and StR-FedAvg with an iteratively updated regularization parameter. We establish communication complexity guarantees for both settings and preliminary experiments validate our theoretical findings.

Keywords: Optimization algorithms, Machine learning, Optimization
Abstract: Composite federated learning is essential for incorporating structured regularization, yet it suffers from excessive local computational overhead and weak convergence guarantees in non-convex settings. To overcome these limitations, we propose FedPACE, a novel proximal-decoupled alternating direction method of multipliers (ADMM) framework. FedPACE decouples the non-smooth regularization via a single server-side proximal evaluation, enabling clients to perform multiple local updates using lightweight closed-form expressions rather than exact subproblem solvers. Theoretical analysis shows that FedPACE achieves a vanishing expected ergodic squared KKT-stationarity measure through a variance-reduced momentum mechanism. After a one-time full-gradient initialization, the method uses constant-size mini-batches and attains a communication complexity of O(epsilon^{-3/2}) for general non-convex composite optimization. Experiments on CIFAR-10 show that FedPACE achieves higher test accuracy and more stable convergence than representative baselines under heterogeneous data distributions.

Keywords: Optimization algorithms, Optimization, Machine learning and control
Abstract: Federated learning (FL) is a communication-efficient collaborative learning framework that enables model training across multiple agents with private local datasets. While the benefits of FL in improving global model performance are well established, individual agents may behave strategically, balancing the learning payoff against the cost of contributing their local data. Motivated by the need for FL frameworks that successfully retain participating agents, we propose an incentive-aware federated averaging method in which, at each communication round, clients transmit both their local model parameters and their updated training dataset sizes to the server. The dataset sizes are dynamically adjusted via a Nash equilibrium-seeking update rule that captures strategic data participation. Under a strongly monotone game setting, we analyze the proposed method under convex and nonconvex global objective settings and establish performance guarantees for the resulting incentive-aware FL algorithm. Furthermore, under a merely monotone game setting, we consider a welfare loss minimization framework and establish asymptotic convergence of the scheme. Numerical experiments on the MNIST and CIFAR-10 datasets demonstrate that agents achieve competitive global model performance while converging to stable data participation strategies.

Keywords: Optimization algorithms, Optimization, Multi-agent learning
Abstract: Decentralized primal-dual methods are widely used for solving decentralized optimization problems, but their updates often rely on the potentially crude first-order Taylor approximations of the objective functions, which can limit convergence speed. To overcome this, we replace the first-order Taylor approximation in the primal update of EXTRA, which can be interpreted as a primal-dual method, with a more accurate multi-cut bundle model, resulting in a fully decentralized bundle EXTRA method. The bundle model incorporates historical information to improve the approximation accuracy, potentially leading to faster convergence. Under mild assumptions, we show that a KKT residual converges to zero. Numerical experiments on decentralized least-squares problems demonstrate that, compared to EXTRA, the bundle EXTRA method converges faster and is more robust to step-size choices.

Keywords: Multi-agent learning, Optimization algorithms, Control Systems Privacy
Abstract: We address nonconvex learning problems over undirected networks. In particular, we focus on the challenge of designing an algorithm that is both communication-efficient and that guarantees the privacy of the agents' data. The first goal is achieved through a local training approach, which reduces communication frequency. The second goal is achieved by perturbing gradients during local training, specifically through gradient clipping and additive noise. We prove that the resulting algorithm converges to a stationary point of the problem within a bounded distance. Additionally, we provide theoretical privacy guarantees within a differential privacy framework that ensure agents' training data cannot be inferred from the trained model shared over the network. We show the algorithm's superior performance on a classification task under the same privacy budget, compared with state-of-the-art methods.

Keywords: Optimization, Multi-agent learning
Abstract: Decentralized optimization plays a central role in multi-agent systems, yet most existing convergence analyses rely on restrictive Lipschitz smoothness assumptions that fail to capture the gradient growth observed in practical problems. In this work, we study the convergence of gradient tracking under (L0,L1)-smoothness, a generalized condition that allows the Hessian norm to grow with the gradient norm. Unlike prior approaches that use gradient clipping or normalization– which slows down convergence–we show that the standard gradient tracking method, without any algorithmic modification, inherently prevents gradient explosion along the optimization trajectory and achieves linear convergence for strongly convex objectives. Our analysis provides explicit stepsize conditions based on the generalized smoothness parameters and recovers the O(1/L2) stepsize order under conventional Lipschitz smoothness as a special case. Numerical experiments on a regularized ℓp minimization problem further highlight the necessity of our analysis: stepsizes chosen according to classical L-smoothness theory lead to divergence, while the proposed theory accurately predicts stable convergence.

Keywords: Optimization, Machine learning, Sensor fusion
Abstract: Learning-enabled control systems increasingly rely on multiple sensing modalities (e.g., vision, audio, language, etc.) for perception and decision support. A key challenge is that multi-modal sensor training dynamics are often imbalanced: fast-to-learn sensing channels dominate optimization, while slower channels remain underutilized, degrading reliability under sensing perturbations. Existing balancing strategies are largely heuristic and can require computationally intensive subroutines. In this paper, we reformulate multi-modal sensor learning as a multi-objective optimization (MOO) problem that explicitly prioritizes the worst-performing modality while retaining the nominal multi-modal sensor fusion objective. We then propose a simple gradient-based method, MIMO (multi-modal sensor learning via MOO), for the resulting formulation. We provide convergence guarantees and evaluate the method on standard multi-modal benchmarks. Results show improved balanced performance over state-of-the-art balanced multi-modal learning and MOO baselines, together with up to ~20x reduction in subroutine computation time, highlighting the suitability of MIMO for resource-constrained control pipelines.

Keywords: Process Control, Optimization algorithms, Optimization
Abstract: Benders decomposition is a widely used method for solving large-scale mixed-integer optimization problems. However, a key computational bottleneck is the repeated solution of an increasingly complex master problem across iterations. In this paper, we propose a feasibility-aware imitation learning framework that predicts the integer variable assignments of the master problem while accounting for feasibility with respect to admissible assignments and accumulated Benders feasibility cuts. The agent is trained via behavioral cloning and subsequently fine-tuned using a feasibility-based logit adjustment, and deployed with explicit feasibility checks and a time-limited solver to preserve finite convergence. Application to a prototypical case study shows that the proposed method reduces solution time relative to existing imitation learning approaches for accelerating Benders decomposition, while preserving solution accuracy.

Keywords: Optimal control, Optimization algorithms, Machine learning and control
Abstract: This paper presents i-LiftProj, a first-order optimization framework for nonlinear optimal control based on a spectrally normalized invertible Koopman lifting. Building on the recently proposed LiftProj framework, which performs ADMM dynamics projections in a lifted linear space, we replace the unconstrained autoencoder with an augmented Invertible ResNet whose ambient lifting map is bi-Lipschitz by construction. We also replace the learned decoder with a fixed-point inverse of the learned ambient diffeomorphism, thereby removing learned-decoder approximation error from the projection step. Since the lifted linear model remains approximate, we analyze i-LiftProj through a surrogate dynamics manifold induced by the learned lifting rather than identifying it with the true nonlinear dynamics manifold. Under standard smoothness and strong-convexity assumptions on the convex ADMM subproblem, we derive an asymptotic residual-floor bound whose size is explicitly controlled by the lifting condition number and by the mismatch between the true dynamics manifold and its lifted linear surrogate. Numerical experiments on a 6-DoF rocket powered descent guidance problem show that i-LiftProj preserves solution quality and constraint satisfaction while yielding smoother residual reduction than the LiftProj baseline.

Keywords: Adaptive control, Learning-based Control, Robust control
Abstract: This paper studies the integration of reinforcement learning and adaptive control for nonlinear systems with parametric uncertainty. A feedback policy is assumed to be obtained offline for a nominal parameterized model using reinforcement learning and then deployed online on a plant whose parameters may differ from the nominal values. To compensate for this mismatch, we introduce an adaptive mechanism that updates the parameter supplied to the learned policy in real time using a projection and dead-zone structure. For nonlinear input–affine systems with unknown constant parameters, we prove uniform exponential stability of the coupled tracking and parameter-estimation error dynamics under suitable excitation and small-gain conditions. In addition, an explicit and adjustable bound on the optimality-gap with respect to the parameter-matched learned policy is derived. A nonlinear tracking example illustrates how online adaptation reduces performance degradation caused by parameter mismatch.

Keywords: Learning-based Control, Adaptive control, Numerical algorithms
Abstract: Adaptive inverse Gaussian-process (GP) control may use approximate linear solves and inverse forms under per-step matrix-access budgets. For an anchored adaptive update with finitely many scalar atoms and nonnegative kernel weights, this paper derives deterministic certificates relating primitive errors to parameter and input perturbations. An exact-gradient companion on the implemented controller's dictionary stream isolates the effect of numerical errors on that stream. Valid residual and inverse-form certificates yield gradient-error radii and a propagated parameter envelope. In an exact-arithmetic matrix-access model, residual solves and scalar Lanczos Gauss/Gauss--Radau brackets instantiate these certificates; nested allocations give nonincreasing budget-labeled bounds on a fixed realized stream. A conditional tracking-error inequality explains their use in a separate robustness analysis, and a nonlinear tracking example quantifies the gap between observed perturbations and their certificates at three budgets.

Keywords: Reinforcement learning, Iterative learning control, Robotics
Abstract: In this paper, we propose a cost-matching approach for optimal humanoid locomotion within a Model Predictive Control (MPC)-based Reinforcement Learning (RL) framework. A parameterized MPC formulation with centroidal dynamics is trained to approximate the action-value function obtained from high-fidelity closed-loop data. Specifically, the MPC cost-to-go is evaluated along recorded state–action trajectories, and the parameters are updated to minimize the discrepancy between MPC-predicted values and measured returns. This formulation enables efficient gradient-based learning while avoiding the computational burden of repeatedly solving the MPC problem during training. The proposed method is validated in simulation using a commercial humanoid platform. Results demonstrate improved locomotion performance and robustness to model mismatch and external disturbances compared with manually tuned baselines.

Keywords: Optimization algorithms, Numerical algorithms, LMIs
Abstract: This paper proposes a new numerical technique for handling infinite-dimensional Differential Linear Matrix Inequalities defined over a compact time interval. To this end, we use an interpolation of rational matrix functions and an extended robust version of Finsler’s Lemma to convert a polynomial time-dependent constraint over a finite time interval into an efficient, tractable Linear Matrix Inequality. The proposed approach is subsequently employed to derive a new set of computationally efficient sufficient LMI conditions for the design of an mathcal{H}_{infty} state-feedback controller for sampled-data systems.

Keywords: Optimization, Optimization algorithms, Power systems
Abstract: Convex programs with a large number of constraints arise naturally in control and engineering. An optimal solution of such a problem is typically determined by a small subset of the constraints, called a basis. Instead of the original problem, Clarkson's algorithm iteratively searches for a basis and solves the corresponding subproblem. Its efficiency is often limited by the rapid growth of the intermediate subproblems. We propose a Basis-Retaining Clarkson's (BRC) algorithm that retains the active basis from one iteration to the next, and a heuristic variant, Violation-Restricted BRC (VR-BRC), which samples exclusively from violated constraints. We establish light tail bounds on violation counts, motivating the use of smaller sampling sizes than the Clarkson's Algorithm. We evaluate our method on six benchmarks including both theoretical and real-world optimization problems, and demonstrate vastly improved runtime compared to the Clarkson's Algorithm, its variants, and full solvers.

Keywords: Optimization algorithms, Numerical algorithms, Computational methods
Abstract: Standard parallel DIRECT evaluates the potentially optimal intervals selected in each iteration as a synchronized batch. When evaluation runtimes are heterogeneous, this iteration-level barrier leaves workers idle while they wait for stragglers. We propose asyncDIRECT, which replaces the synchronized batch with an asynchronous size sweep over the hyperrectangle-size classes. At each size-class step, the lower-bound criterion for potential optimality is reevaluated using the available results, while the DIRECT subdivision rule is retained. Evaluations are initiated asynchronously, allowing the sweep to proceed without a global wait. We compare asyncDIRECT with iteration-synchronous DIRECT under controlled evaluation-time variability and on standard benchmark functions, focusing on wall-clock run time and attained objective values.

Keywords: Reduced order modeling, Optimization, Linear systems
Abstract: We revisit the problem of approximating a linear time-invariant LTI model by a reduced-order model (ROM) in an H_2-optimal sense. A widely used method for computing such ROMs is the iterative rational Krylov algorithm (IRKA). However, in practice, the stability of the resulting ROM is not generally guaranteed. In this work, we develop a novel framework that can be used to obtain H_2-optimal models of single-input single-output LTI systems while enforcing stability of the ROM. We use Malmquist-Takenaka orthogonal expansions in the corresponding H_2-spaces and their connection to hyperbolic geometry to develop an equilibrium function. We show that the poles of an H_2-optimal ROM transfer function are defined by the zeros of this equilibrium function. The resulting nonlinear root-finding problem is solved using a Newton-type method formulated on the products of Poincar'e disk manifolds, where updates are performed along hyperbolic geodesics ensuring that the stability constraint is satisfied at every iteration. We present numerical experiments on benchmark systems for both discrete- and continuous-time LTI MOR problems, including examples where IRKA produces unstable reduced models while the proposed method preserves stability throughout the iteration.

Keywords: Predictive control for linear systems, Machine learning and control
Abstract: Computing the Lipschitz constant of the solution map of a multi-parametric quadratic program is important to the analysis of optimization-based control. This problem is governed by three factors: the parameter dimension, the number of decision variables, and the number of constraints. While empirical evidence has long suggested exponential complexity, a rigorous complexity-theoretic proof has been lacking. In this paper, we fill this gap by proving that this problem is not only NP-hard but also APX-hard. This rules out any polynomial-time approximation scheme unless P=NP. Furthermore, we reveal that: (a) the problem becomes polynomial-time solvable when the number of constraints or decision variables is fixed; and (b) NP-hardness persists even in the scalar parameter case. These results confirm empirical observations and show that the complexity stems from the combinatorial explosion of critical regions as constraints and decision variables grow, rather than from the parameter dimension.

Keywords: Adaptive systems, Estimation, Identification
Abstract: This paper presents a method to improve the convergence speed of the conventional adaptive observer proposed in Q. Zhang, 2002, for a class of state–affine nonlinear systems with unknown constant parameters. The proposed adaptive observer combines an additional Luenberger–type observer with a high–order sliding–mode observer to enhance state estimation. Furthermore, it incorporates new filtering mechanisms and a fixed–time parameter estimation algorithm. Under an interval–excitation condition, the resulting observer guarantees fixed–time stability of the adaptive estimation error, ensuring that both the state and parameter estimation errors converge to zero within a fixed time. To the best of our knowledge, this is the first adaptive observer achieving such performance. Simulation results demonstrate the performance of the proposed method.

Keywords: Reinforcement learning, Markov processes, Filtering
Abstract: We study model-based learning of finite-window policies in tabular partially observable Markov decision processes (POMDPs). A common approach to learning under partial observability is to approximate unbounded history dependencies using finite action-observation windows. This induces a finite-state Markov decision process (MDP) over histories, referred to as the superstate MDP. Once a model of this superstate MDP is available, standard MDP algorithms can be used to compute optimal policies, motivating the need for sample-efficient model estimation. Estimating the superstate MDP model is challenging because trajectories are generated by interaction with the original POMDP, creating a mismatch between the sampling process and target model. We propose a model estimation procedure for tabular POMDPs and analyze its sample complexity. Our analysis exploits a connection between filter stability and concentration inequalities for weakly dependent random variables. As a result, we obtain tight sample complexity guarantees for estimating the superstate MDP model from a single trajectory. Combined with value iteration, this yields approximately optimal finite-window policies for the POMDP.

Keywords: Machine learning and control, Supervisory control, Switched systems
Abstract: We study supervisory switching control for partially-observed linear dynamical systems. The objective is to identify and deploy a suitable controller for the unknown system by periodically selecting among a collection of N candidate controllers, some of which may destabilize the underlying system. While classical estimator-based supervisory control guarantees asymptotic stability, it lacks quantitative finite-time performance bounds. Conversely, current non-asymptotic methods in both online learning and system identification require restrictive assumptions that are incompatible in a control setting, such as system stability, which preclude testing potentially unstable controllers. To bridge this gap, we propose a novel, non-asymptotic analysis of supervisory control that adapts multi-armed bandit algorithms to a control-theoretic setting. The proposed data-driven algorithm evaluates candidate controllers via scoring criteria that leverage system observability to isolate the effects of state history, enabling both detection of destabilizing controllers and accurate system identification. We present two algorithmic variants with dimension-free, finite-time guarantees, where each identifies the matching controller in O(N log^2 N) steps, while simultaneously achieving finite L_2-gain with respect to system disturbances.

Keywords: Machine learning, Supervisory control, Power systems
Abstract: Power System State Estimation (PSSE) converts geographically distributed measurements into the voltage magnitudes and phase angles needed for grid monitoring and control. Learned estimators can perform this mapping rapidly, but model-aware False Data Injection Attacks (FDIAs) may corrupt their inputs while retaining AC plausibility and residual-based stealth. Physics-Informed Neural Networks (PINNs) limit candidate states through power-flow consistency; however, their robustness depends on balancing supervised and physics losses whose scales and gradient contributions evolve during training. This paper proposes a PINN that jointly learns homoscedastic uncertainty parameters and uses them to adapt the two objectives. The formulation assigns trainable log-uncertainties to the active-power, reactive-power, voltage, and angle losses while safeguarding against an underweighted physics objective. The estimator is trained only on clean steady-state data and is evaluated, without adversarial retraining, under baseline state-distortion and stricter residual-profile-matching regimes on the IEEE~118-bus system. Accuracy is measured against the uncompromised system state. Relative to a fixed-weight PINN, dynamic weighting reduces overall Mean Absolute Error (MAE) by 55% while also improving voltage- and angle-estimation accuracy. The results show that learning the physics/data balance from clean data improves robustness to unseen FDIAs.

Keywords: Observers for Linear systems, Agents-based systems, Sensor networks
Abstract: While unknown input observers have been extensively studied in centralized settings, their distributed counterparts remain largely unexplored, particularly in discrete time. Building upon the model-based approach of (Disaro', Fattore, and Valcher, IEEE Transactions on Automatic Control, 2026), we derive necessary and sufficient data-driven conditions for the existence of distributed unknown input observers directly from collected data, without requiring an explicit system model. The same data are then used to design the observer, with the final step relying on decentralized dynamic output feedback theory applied to data-derived matrices.

Keywords: Data driven control, Robust control, Uncertain systems
Abstract: This paper develops a method to construct robust positively invariant (RPI) tube sets from finite noisy input-state data of an unknown linear time-invariant (LTI) system, yielding tubes that can be directly embedded in tube-based robust data-driven predictive control. Data-consistency uncertainty sets are constructed under process/measurement noise with polytopic/ellipsoidal bounds. In the measurement-noise case, we provide a deterministic and data-consistent procedure to certify the induced residual bound from data. Based on these sets, a robustly stabilizing state-feedback gain is certified via a common quadratic contraction, which in turn enables constructive polyhedral/ellipsoidal RPI tube computation. Numerical examples quantify the conservatism induced by noisy data and the employed certification step.

Keywords: Optimal control, Robotics, Vision-based control
Abstract: Active perception in uncertain environments requires robots to navigate safely while acquiring informative observations to reduce map uncertainty. These objectives inherently conflict, as informative viewpoints often lie near uncertain regions with higher collision risk. To address this challenge, we develop a conflict-aware active perception and control framework for robotic systems operating in environments represented by 3D Gaussian Splatting (3DGS). Safety is enforced using a Control Barrier Function (CBF) derived from an Average Value-at-Risk (AVaR) collision-risk metric that accounts for geometric uncertainty and guarantees forward invariance of a safe set. To improve perception, we propose a risk-aware Expected Information Gain (EIG) formulation for selecting the next-best-view and introduce perception barrier functions that align the camera orientation with the local information-ascent direction. To obtain a tractable formulation of the conflicting safety and perception objectives, we propose a unified safety-critical, perception-aware quadratic program that enforces safety as a hard constraint while relaxing the perception constraint through slack variables. Simulation results demonstrate that the proposed method improves both safety and information acquisition compared to existing 3DGS-based approaches.

Keywords: Identification for control, Indirect adaptive control, Autonomous vehicles
Abstract: Accurate dynamics models are critical for the design of predictive controllers for autonomous mobile robots. Physics-based models are often too simple to capture relevant real-world effects, while data-driven models are data-intensive and slow to train. We introduce an approach for fast adaptation of neural robot dynamic models that combines offline training with efficient online updates. Our approach learns an incremental neural dynamics model offline and performs low-rank second-order parameter adaptation online, enabling rapid updates without full retraining. We demonstrate the approach on a real quadrotor robot, achieving robust predictive tracking control in novel operational conditions.

Keywords: Machine learning and control, Cyber-Physical Security
Abstract: State-space model (SSM) for time-series forecasting have demonstrated strong empirical performance on benchmark datasets, yet their robustness under adversarial perturbations is poorly understood. We address this gap through a control-theoretic lens, focusing on the recently proposed Spacetime SSM forecaster. We first establish that the decoder-only Spacetime architecture can represent the optimal Kalman predictor when the underlying data-generating process is autoregressive - a property no other SSM possesses. Building on this, we formulate robust forecaster design as a Stackelberg game against worst-case stealthy adversaries constrained by a detection budget, and solve it via adversarial training. We derive closed-form bounds on adversarial forecasting error that expose how open-loop instability, closed-loop instability, and decoder state dimension each amplify vulnerability - offering actionable principles towards robust forecaster design. Finally, we show that even adversaries with no access to the forecaster can nonetheless construct effective attacks by exploiting the model's locally linear input-output behavior, bypassing gradient computations entirely. Experiments on the Monash benchmark datasets highlight that model-free attacks, without any gradient computation, can cause at least 33% more error than projected gradient descent with a small step size.

Keywords: Optimization, Large-scale systems, Modeling
Abstract: Monotone co-design provides a mathematical framework for managing the tightly coupled trade-offs between subsystem functionalities and resource requirements that arise in complex engineered systems. In many practical settings the underlying component models are already linear, yet existing solvers still resort to generic discretization, sacrificing both accuracy and complexity by ignoring the topological structure of the problem. This paper isolates the corresponding exact regime by introducing Linear Design Problems (LDPs), a class of co-design problems whose feasible functionality–resource sets are polyhedra over Euclidean posets. We show that queries on LDPs reduce exactly to Multi-Objective Linear Programs (MOLPs), thereby bridging monotone co-design semantics and polyhedral multiobjective optimization. Furthermore, we prove that the LDP class is closed under series, parallel, intersection, and feedback interconnections, so that any composition of linear components yields a system-level LDP. Exploiting this closure, we derive a monolithic lifted formulation that retains blockangular sparsity and resolves a system-level co-design query through a single MOLP. We validate the approach on a rigid gripper co-design benchmark whose every component is an LDP. The monolithic algorithm recovers the exact Pareto front with zero approximation error and orders-of-magnitude faster runtime, substantially outperforming the state-of-the-art codesign solver MCDPL in both accuracy and speed.

Keywords: Optimization, Large-scale systems, Modeling
Abstract: When designing systems with multiple conflicting objectives, efficiently discovering the full set of non-dominated solutions remains a fundamental challenge. In this paper, we introduce an online learning framework for multi-objective decision-making within the monotone co-design setting. An agent sequentially queries an expensive design problem to identify the set of non-dominated trade-offs while minimizing evaluations. The key mechanism is a generic family of optimistic evaluators, history-dependent bounds that enable safe early elimination of unpromising implementations and allow heterogeneous structural assumptions. We prove that the resulting rejection-sampling algorithm is sound and that the admissible region contracts monotonically as data accumulates, and instantiate the evaluators under monotonicity, Lipschitz continuity, and linear-parametric structure. Experiments on intermodal mobility systems and synthetic benchmarks demonstrate substantial gains over uniform sampling, Bayesian optimization, and evolutionary baselines.

Keywords: Optimal control, Predictive control for linear systems, Lyapunov methods
Abstract: Computational constraints permeate the controller design process, and yet are rarely treated as explicit design constraints. Towards addressing this gap, we propose a quantitative framework that captures the effects of common design approximations, such as model order reduction, temporal discretization, horizon truncation, and solver accuracy, on both controller performance and computational requirements. Our framework highlights that these approximations are tunable parameters within an overall controller design process. By leveraging incremental input-to-state stability, we show that bounding the aggregate effects of these approximations reduces to verifying a design-dependent sector bound on the difference between the deployed policy and an idealized baseline, with stability enforced via a small-gain condition. We operationalize these insights via a Design Meta-Problem in which the performance gap is minimized subject to stability, real-time compute, and timing constraints. Finally, we instantiate the framework on a receding horizon LQR case study, and demonstrate a principled near-optimal navigation of tradeoffs among sampling rate, model order, horizon length, and solver iterations.

Keywords: Optimization algorithms, Large-scale systems, Optimal control
Abstract: Block-structured quadratic programs (QPs) arise naturally in direct optimal control and must be solved efficiently and reliably to achieve reasonable performance of applied optimal control. While Alternating Direction Method of Multipliers (ADMM)-based QP solvers have gained popularity, existing approaches typically split the problem without fully exploiting the block structure inherent to optimal control QPs. We propose qpBAMM, an ADMM-based solver that splits the QP into a box-constrained QP and a projection onto linear dynamics, enabling a parallel gradient projection method and partial parallelization of the projection step. The resulting solver effectively exploits the block-structured QP arising from optimal control. Numerical results demonstrate significant advantages over two recent numerical solvers based on the Augmented Lagrangian method, particularly for optimal control problems with a high-dimensional state space.

Keywords: Optimization algorithms, Optimization
Abstract: Decentralized optimization over directed networks is frequently challenged by asymmetric communication and the inherent high variance of stochastic gradients, which collectively cause severe oscillations and hinder algorithmic convergence. To address these challenges, we propose the Stochastic Momentum Tracking Push-Pull (SMTPP) algorithm, which tracks the momentum term rather than raw stochastic gradients within the Push-Pull architecture. This design successfully decouples the variance reduction capacity from the algebraic connectivity of the graph.Although the inherent topology mismatch of directed graphs precludes exact convergence under persistent stochastic noise, SMTPP rigorously compresses this unavoidable steady-state error floor into a minimal neighborhood determined by network connectivity and gradient variance. Furthermore, SMTPP guarantees convergence on any strongly connected directed graph. Extensive experiments on non-convex logistic regression demonstrate that the algorithm is highly robust to network connectivity. By effectively dampening topology-induced oscillations, SMTPP achieves convergence rates and overall performance that closely match those of centralized baselines, regardless of whether the network is sparse or dense.

Keywords: Optimization, Optimization algorithms, Stochastic systems
Abstract: This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based augmented Lagrangian method that employs a Polyak-type gradient estimator and requires only one stochastic gradient evaluation per iteration. Under the standard stochastic oracle model and the smoothness condition of the expected objective, we establish a convergence guarantee in terms of the first-order KKT residual of the original constrained problem. In particular, the proposed method computes an epsilon-stationary solution in expectation within O(epsilon^{-4}) stochastic gradient evaluations. Numerical experiments further show that the proposed method achieves competitive iteration complexity and improved wall-clock efficiency compared with representative recursive-momentum baselines.

Keywords: Subspace methods, Nonlinear systems, Numerical algorithms
Abstract: Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image under the operator. To systematically minimize this error, we propose an algebraic framework for subspace pruning utilizing principal vectors. We establish the equivalence of this approach to existing consistency-based methods while providing a foundation for broader generalizations. To ensure scalability, we introduce an efficient numerical update scheme based on rank-one modifications, reducing the computational complexity of tracking principal angles by an order of magnitude. Finally, we demonstrate the effectiveness of our framework through numerical simulations.

Keywords: Subspace methods, Learning, Nonlinear systems
Abstract: Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning systematically discards geometrically misaligned directions to enhance this invariance proximity, yet existing techniques are largely restricted to standard Euclidean settings. To bridge this gap, this paper presents an approach for computing principal angles and vectors to enable Koopman subspace pruning within a Reproducing Kernel Hilbert Space (RKHS) geometry. We first outline an exact computational routine, which is subsequently scaled for large datasets using randomized Nyström approximations. Based on these foundations, we introduce the Kernel-SPV and Approximate Kernel-SPV algorithms for targeted subspace refinement via principal vectors.

Keywords: Identification for control, Data driven control, Nonlinear systems identification
Abstract: Koopman operator theory yields powerful tools for modeling, analysis, and control of nonlinear dynamical systems. Prominently, linear time-invariant (LTI) Koopman representations have been proposed to enable the application of linear control techniques, such as LQR and convex MPC. In this work, we investigate the implications of exact LTI Koopman representations for continuous-time nonlinear control systems. In particular, we show that, assuming a mild controllability condition and the inclusion of the coordinate maps, the dynamics of the underlying control system must be affine linear. Furthermore, we study the modeling bias introduced by the LTI structure and analyze its dependency on the choice of observables.

Keywords: Data driven control, Predictive control for nonlinear systems, Robust control
Abstract: Data-driven model predictive control (MPC) using Koopman operator theory is a promising approach for constrained control of unknown nonlinear systems. While linear Koopman realizations are commonly used due to their simplicity, bilinear Koopman realizations can provide significantly higher approximation accuracy for nonlinear control systems. However, robust MPC (RMPC) formulations that account for modeling errors in bilinear Koopman realizations remain limited. This paper proposes a RMPC framework for unknown nonlinear systems with general nonlinear constraints based on data-driven bilinear Koopman realizations. A central difficulty is that finite-dimensional Koopman predictors need not preserve the manifold of valid lifted states, so multi-step prediction in lifted coordinates may leave the region where one-step error certificates apply. We address this issue by reprojecting each predicted lifted state back onto the manifold, thereby obtaining an error-aware discrete-time control-affine predictor in the original state space without impractical assumptions. For this predictor, we develop a discrete-time robust control contraction metric based homothetic tube construction, and then formulate a tube-based RMPC problem with terminal ingredients. Under the proposed formulation, we prove robust satisfaction of the original nonlinear constraints by the true closed-loop trajectory, recursive feasibility, and convergence to a neighborhood of the target state. Numerical experiments demonstrate robust stabilization of nonlinear systems and the advantages of the proposed method over existing Koopman-based RMPC approaches in terms of performance.

Keywords: Discrete event systems, Fault diagnosis
Abstract: This paper studies the failure diagnosability of stochastic discrete-event systems (DES) under unreliable observations. In DES literature, diagnosability refers to the system property requiring each fault to be eventually detected. The uA-Diagnosability was proposed by Thorsley et al., 2008, which extends the A-Diagnosability to include unreliable sensor readings. In particular, a system is uA-Diagnosable if every failure can be eventually detected with arbitrary probability, even when the same event may produce different observations. This paper further studies uA-Diagnosability by showing that the problem of verifying if a system is uA-Diagnosable is PSPACE-Complete, and therefore likely its verification cannot be done with polynomial complexity. Moreover, a new testing condition based on language equivalence is provided, which requires exponential complexity with respect to the number of states. Next, a probabilistic testing algorithm with polynomial complexity is proposed, which may incur certain test errors. The test error bounds are then analytically studied and shown to be calibratable through a hyper-parameter. Lastly, the proposed probabilistic testing algorithm is modified to prioritize faulty states with less extensions to minimize the error bound, in the event that the total number of condition checks is limited.

Keywords: Discrete event systems
Abstract: In the inference-based decentralized diagnosis framework for discrete event systems, multiple local diagnosers perform multi-level inference against self-ambiguity and ambiguities of the others to jointly arrive at a correct diagnosis decision. For a chosen nonnegative integer N, the notion of N-inference diagnosability introduced by Kumar & Takai guarantees that the occurrence of any failure is detected within a finite number of steps, using N-level inference. The class of N-inference diagnosable systems expands monotonically as the parameter N increases. In the authors' recent work, a notion of non-uniformly bounded inference observability, which does not involve an upper bound of inference level, was introduced in the setting of decentralized supervisory control. Here we introduce a similar notion of non-uniformly bounded inference diagnosability for decentralized diagnosis, which is weaker than N-inference diagnosability for any nonnegative integer N. It serves as a necessary and sufficient condition for the existence of a decentralized diagnoser that correctly detects the occurrence of any failure within a fixed finite number of steps, using inference with unbounded level.

Keywords: Cyber-Physical Security, Automata, Discrete event systems
Abstract: Existing literature on timed opacity uses specific definitions for restricted subclasses of timed automata or limited observation models. This lack of a unified definition makes it difficult to establish formal relationships and compare the expressiveness of different opacity variants. This paper establishes a unified framework for timed opacity by introducing an observation model for timed automata with full delay observation and partial observation of events, locations, and clocks. Based on this model, we define the notion of evolution-based timed opacity. We then prove that evolution-based timed opacity strictly implies language-based timed opacity and establish a formal equivalence with execution-time opacity under constrained observations. This framework establishes a unified semantic hierarchy for characterizing the landscape of timed opacity.

Keywords: Smart grid, Power systems, Optimization algorithms
Abstract: Distribution networks are increasingly exposed to threats such as extreme weather, aging infrastructure, and cyber risks--resulting in more frequent contingencies and outages, a trend likely to persist. Dynamic networked microgrids (DNMGs) offer a promising solution to mitigate the impacts of such contingencies and enhance resiliency. However, distribution networks present unique challenges due to their unbalanced nature and the inherent uncertainty in both loads and generation. This paper develops an approach to reconfigure and control DNMGs building on our prior work on 1) two-stage mixed-integer robust optimization for configuring DNMGs and 2) a model-free, real-time optimal power flow algorithm to manage DNMG operations in the time between reconfigurations. A case study on a realistic network demonstrates the scalability of the combined approach. The case study also illustrates the ability to maintain power flow feasibility as loads vary and operating conditions change when the methods are used in tandem.

Keywords: Stochastic optimal control, Robust control, Game theory
Abstract: We study the Linear Quadratic Gaussian regulation problem in the face of worst-case noise distributions when these are mutually independent, zero-mean, stationary, and within a radius (as measured by the Wasserstein distance) of some reference Gaussian noise distributions. Compared with nonstationary ambiguity models, our stationary modeling choice reduces conservatism when the disturbances are stationary, as is often the case in practice. We first show optimality of linear output-feedback policies via the existence of a Nash equilibrium in an equivalent zero-sum game between a control engineer and a fictitious adversary that compete to minimize and maximize the control cost. Additionally, we show that Nash equilibria may fail to exist when the distributions are not restricted to have zero mean. We then propose an iterated best-response algorithm to compute Nash equilibria and thereby the optimal feedback policies. Our computational framework unifies two seemingly different viewpoints: game-theoretic iterated best response and Frank-Wolfe approaches. Finally, we illustrate the robustness of the proposed controller to unknown noise distributions on an inverted pendulum with physical parameters, a canonical control benchmark.

Keywords: Control over communications, Linear systems, Markov processes
Abstract: This paper studies the minimum rate required for a partially observable linear system with side information. The Linear Quadratic Gaussian(LQG) plant and the Gaussian-Markov source are considered. We show that a class of linear policies is sufficient for optimizing the conditional directed information lower bound. We also show that the resulting optimization problem is convex for the scalar case in both time-varying and time-invariant systems. Our results generalize the past works that consider the case with full or partial observation only, and the case with full observation and side information.

Keywords: Hybrid systems, Autonomous vehicles, Stochastic optimal control
Abstract: In this paper, we study the use of regime switching diffusions as a hybrid system modeling framework for computing a feedback control policy for a navigation task involving two Dubins vehicles. Initially, one vehicle transports the other, but in the second phase of the task they separate. One vehicle is tasked to reach a moving point target, while the other is tasked to reach a safe distance from the target. We demonstrate that the problem can be solved by a set of interdependent stochastic Hamilton-Jacobi-Bellman and Backward Kolmogorov equations associated with the regime switching diffusion. To enable the use of these equations, we also exploit Cantelli’s inequality to evaluate the probability of task success following separation. Finally, we compute the solution and validate it through a numerical simulation.

Keywords: Output regulation, Stability of linear systems, Predictive control for linear systems
Abstract: High-precision output tracking is a fundamental objective in control theory and engineering, typically achieved through model-based inversion. For non-minimum phase (NMP) systems, this task necessitates a stable inversion to prevent the divergence of unstable zero dynamics. However, the real-time implementation of stable inversion remains challenging under conventional frameworks, as they often rely on block-wise pre-computation over large time windows.This paper proposes an online stable inversion framework for NMP systems by enforcing a relative-degree-consistent terminal boundary condition within a receding-horizon Model Predictive Control (MPC) scheme. By integrating an LMI-based terminal controller with a terminal output equality constraint, the proposed approach ensures that the finite-horizon optimization remains consistent with the system's stability requirements. Through the derivation of an explicit MPC solution, conditions for terminal-controller stability and terminal-equality feasibility are provided. Furthermore, quantitative criteria for Finite-Time Stability (FTS) and Input-Output Finite-Time Stability (IO-FTS) are established. The effect of the prediction horizon is characterized subject to a compatible terminal-reference extension.The theoretical results are validated through a fourth-order DC motor case study, where the controller effectively manages inverse responses and maintains rigorously bounded tracking errors.

Keywords: Predictive control for nonlinear systems, Optimal control
Abstract: Operation at steady state is often not optimal when optimizing over an economic cost objective. In many cases, periodic operation yields better performance. Therefore, we derive asymptotic stability guarantees of an economic model predictive control scheme with terminal conditions for systems with optimal periodic operation for a more general setup than existing methods can handle. Moreover, we establish a non-averaged closed-loop performance bound by defining the closed-loop cost via a Cesàro summation instead of ordinary summation. Such a non-averaged performance bound provides new insights for systems with periodic optimal operation.

Keywords: Learning-based Control, Reinforcement learning, Uncertain systems
Abstract: Optimism in the face of uncertainty is a popular approach to balance exploration and exploitation in reinforcement learning. Here, we consider the online linear quadratic regulator (LQR) problem, i.e., to learn the LQR corresponding to an unknown linear dynamical system by adapting the control policy online based on closed-loop data collected during operation. In this work, we propose Intrinsic Rewards LQR (IR-LQR), an optimistic online LQR algorithm that applies the idea of intrinsic rewards originating from reinforcement learning and the concept of variance regularization to promote uncertainty-driven exploration. IR-LQR typically retains the structure of a standard LQR synthesis problem by only modifying the cost function, resulting in an intuitively pleasing, simple, computationally cheap, and efficient algorithm. This is in contrast to existing optimistic online LQR formulations that rely on more complicated iterative search algorithms or solve computationally demanding optimization problems. We show that IR-LQR achieves the optimal worst-case regret rate of sqrt{T}, and compare it to various state-of-the-art online LQR algorithms via numerical experiments carried out on an aircraft pitch angle control and an unmanned aerial vehicle example.

Keywords: Distributed parameter systems, Backstepping
Abstract: We develop a backstepping-based observer design for a class of ODE - continuum-PDE cascade systems, which can be viewed as the limit, of a finite collection of ODE - 2times 2 hyperbolic systems, as the number of individual PDE system components tends to infinity. We address a (practically motivated) case in which average (boundary) measurements, over the ensemble dimension, are available. Exponential stability of the estimation error system is shown by proving well-posedness of the kernel equations and constructing a Lyapunov functional. We also establish that the backstepping kernels derived coincide with the solution of a Sylvester equation, which has not been shown before (even for non-continuum PDE systems). We then introduce an implementation method, adopting a spectral-based approach for computing the observer dynamics, which we illustrate in a numerical simulation example.

Keywords: Distributed parameter systems, Differential-algebraic systems, Backstepping
Abstract: This paper considers the backstepping observer design for a class of general linear PDAE-DAE systems. Well-posedness of these infinite-dimensional descriptor systems is verified using the Weierstraß normal form assuming matrix pencils with index 1, which is obtained analytically. This results in a coupled hyperbolic-elliptic PDE-ODE system with algebraic constraints and vanishing transport velocities allowing to define an observer in state space form. This observer is systematically designed using a multi-step backstepping approach. It is shown that the resulting observer error dynamics are asymptotically stable. The novel observer design procedure is verified for an unstable PDAE-DAE system and validated in simulations.

Keywords: Distributed parameter systems, Stability of nonlinear systems, Lyapunov methods
Abstract: This paper studies in-domain regional stabilization of 2-D nonlinear Kuramoto-Sivashinsky equation on the square domain. The regional stabilization is guaranteed in the H2 stability framework because it employs 2-D Sobolev’s inequality with H2 bounds. This is different from the existing results for 1-D case with H1 stability. To cope with the unknown external disturbance, the active disturbance rejection control approach is employed. An extended state observer is constructed for the disturbance estimation in the framework of modal decomposition approach by using the first mode. The efficient linear matrix inequality conditions are provided for determining the upper bound on the domain of attraction that preserve H2 exponential stability of the closed-loop system. A numerical example illustrates the efficiency of our method.

Keywords: Game theory, Predictive control for nonlinear systems, Stability of nonlinear systems
Abstract: Game-theoretic MPC (or Receding Horizon Games) is an emerging control methodology for multi-agent systems that generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion. This control paradigm has recently received increasing attention in various application fields, including robotics, autonomous driving, traffic networks, and energy grids, due to its ability to model the competitive nature of self-interested agents with shared resources while incorporating future predictions, dynamic models, and constraints into the decision-making process. In this work, we present the first formal stability analysis based on dissipativity and monotone operator theory that is valid also for non-potential games. Specifically, we derive LMI-based certificates that ensure asymptotic stability and are numerically verifiable. Moreover, we show that, if the agents have decoupled dynamics, the numerical verification can be performed in a scalable manner. Finally, we present tuning guidelines for the agents' cost function weights to fulfill the certificates and, thus, ensure stability.

Keywords: Game theory, Linear systems
Abstract: This paper studies feedback Nash equilibria (FNE) in scalar discounted linear quadratic (LQ) games with N players. By explicitly incorporating the discount factor, we show that finite-cost equilibria may fail to stabilize the original system, motivating a distinction between FNE and stable FNE together with a sufficient stability condition. Based on a parametric characterization of the policies, we propose numerical methods for computing all equilibria. Particular attention is devoted to the symmetric game, where a closed-form expression of the symmetric FNE and conditions for the existence of up to M ≤ 2^N − 2 equilibria are derived. Numerical experiments illustrate how equilibrium multiplicity depends on the game configuration and highlight the emergence of finite-cost non-stabilizing equilibria.

Keywords: Predictive control for nonlinear systems, Observers for nonlinear systems, Robust control
Abstract: A joint guidance and robust observer-based output-feedback synthesis framework is developed for discrete-time nonlinear systems subject to bounded process disturbances and measurement noise. The method co-designs a reference trajectory, time-varying Luenberger observer and observer-based linear output-feedback gains, and coupled ellipsoidal funnels that certify conditioned-invariant bounds on tracking and estimation errors. Nonlinear residuals are bounded by incremental quadratic constraints (QCs) parameterized by local Lipschitz constants, estimated via sampling approaches. The coupled invariance and stability conditions are formulated as linear matrix inequality (LMI) surrogates and solved using sequential convex programming with proximal regularized sequential-convex-programming (prox-SCP) via a semidefinite programming (SDP). Simulations of a unicycle under persistent sensory noise and system disturbances demonstrate robust tracking and funnel-certified constraint satisfaction with respect to the jointly designed reference trajectory.

Keywords: Optimal control, Optimization, Linear systems
Abstract: This paper characterizes the capacity conditions under which advance order information (AOI) creates value in recycling-based additive manufacturing. A score–sort–allocate policy ranks orders by urgency, volume, and penalty exposure, and accepts them as capacity allows, yielding a prioritized demand target. We formulate an optimal control model driven by this target and analyze it via Pontryagin’s Minimum Principle. The key structural finding is that preview alters the optimal control when capacity sits idle ahead of a demand surge, while its value diminishes under saturation. An effective-horizon criterion identifies the shortest advance-commitment window worth acquiring and the length beyond which further commitment yields no cost-effective return. Numerical experiments across three demand–capacity regimes show that AOI value grows with available capacity, and a first-in-first-out (FIFO) baseline isolates the contribution of customer prioritization.

Keywords: Robust control, Constrained control, Computational methods
Abstract: Relaxed invariance concepts, such as innerouter approximations and K-invariant sets, have been explored in recent years to approximate control invariant sets. However, the practical use of these sets in the presence of disturbances faces a major drawback: the admissibility of input sequences cannot, in general, be verified. This is due to their closed-loop nature, which only ensures the existence of admissible control policies rather than specific sequences. This paper contributes by providing an openloop alternative definition of inner-outer approximations, while also establishing a method for their computation from the nominal dynamics by exploiting contractivity. Since restricting the approach to open-loop sequences can introduce conservatism, this work also proposes a computationally tractable construction method for closed-loop robust inner-outer approximations based on symbolic control tools. This methodology not only enables the computation of the inner-outer approximations but also provides the corresponding set of admissible control policies.

Keywords: Optimal control, Control applications, Biological systems
Abstract: Artificial microswimmers at low Reynolds number are modeled by driftless control systems arising from hydrodynamic constraints and internal shape actuation. These systems induce a sub-Riemannian structure in which actuation defines a horizontal distribution and locomotion is governed by its Lie algebra. We introduce a geometric formulation of articulated microswimmers that includes classical multi-link models as well as n-arm swimmers, with motion generated through iterated Lie brackets of the actuation fields. We analyze a three-arm microswimmer as a control system on a six-dimensional configuration manifold and prove that the associated distribution has non-generic growth vector (3,4,6) on a dense set. Fixing one arm orientation yields a two-input subsystem that realizes a Cartan (2,3,5) bracket-generating structure embedded within the three-arm dynamics. This subsystem admits abnormal extremals whose projections are the rigid singular curves of the associated Cartan distribution. This framework provides a geometric basis for analyzing efficient strokes and for guiding the design of artificial microswimmers.

Keywords: Nonlinear systems, Algebraic/geometric methods, Observers for nonlinear systems
Abstract: Many nonlinear dynamical systems exhibit symmetry, affording substantial benefits for control design, observer architecture, and data-driven control. While the classical notion of group invariance enables a cascade decomposition of the system into highly structured subsystems, it demands very rigid structure in the original system. Conversely, much more general notions (e.g., partial symmetry) have been shown to be sufficient for obtaining less-structured decompositions. In this work, we propose a middle ground termed “weak invariance”, studying diffeomorphisms (resp., vector fields) that are group invariant up to a diffeomorphism of (resp., vector field on) the symmetry group. Remarkably, we prove that weak invariance implies that this diffeomorphism of (resp., vector field on) the symmetry group must be an automorphism (resp., group linear). Additionally, we demonstrate that a vector field is weakly invariant if and only if its flow is weakly invariant, where the associated group linear vector field generates the associated automorphisms. Finally, we show that weakly invariant systems admit a cascade decomposition in which the dynamics are group affine along the orbits. Weak invariance thus generalizes both classical invariance and the important class of group affine dynamical systems on Lie groups, laying a foundation for new methods of symmetry-informed control and observer design.

Keywords: Nonholonomic systems, Switched systems, Delay systems
Abstract: The nonholonomic integrator is a famous example in feedback design - although it is small-time locally controllable to the origin, no continuous feedback law exists. Therefore, any stabilizing feedback laws must be either time-varying or discontinuous. A previously studied discontinuous feedback law stabilizes initial conditions lying between two paraboloids and has a sliding mode on the xy-plane.

We investigate the effect of introducing delays into this discontinuous feedback law. To a first-order analysis, the lag causes the sliding mode of the xy-plane to bifurcate into two switching regions where the resulting dynamics can be interpreted as a hybrid dynamical system with hysteresis. Counterintuitively, the presence of a delay can actually have a positive effect on both the size of the basin of attraction and the convergence rate of the controller.

We also consider the natural generalization of the nonholonomic integrator to higher dimensions.

Keywords: Lyapunov methods, LMIs, Stability of linear systems
Abstract: This paper addresses the admissibility problem of Takagi–Sugeno (T–S) fuzzy singular systems with time-varying delays based on the Lyapunov-Krasovskii functional (LKF) approach. In order to fully exploit the information from the decomposed state, an augmented vector composed of the decomposed state and its derivative is incorporated into the multiple integral terms of the LKF, which plays a key role in capturing the relationships among the state energies. Furthermore, cross information among the states of each decomposed subsystem is also incorporated into the construction of the LKF. The upper bound for integral terms in derivative of the LKF is then estimated in the form of linear matrix inequalities (LMIs) by utilizing free-matrix-based multiple integral inequality. A numerical example is provided to validate the superiority of the proposed criterion.