Keywords: Learning-based control, Predictive control for nonlinear systems
Abstract: Learning has established a firm foothold in modern control. While integrating data-driven algorithms into autonomous systems offers unprecedented capabilities, deploying learning-based controllers in safety-critical domains poses significant risks. Optimization-based control frameworks -such as Model Predictive Control- leverage prediction to evaluate future trajectories and enforce physical constraints. However, classical concepts often struggle when operating in complex, unmodeled, or changing environments. This talk explores how the fundamental principle of model-based prediction can address key challenges in learning-based control. First, we revisit how safety can be guaranteed through prediction and investigate this mechanism beyond classical predictive control. Given that uncertainty remains the central challenge for prediction, the core of this presentation addresses how learning-based models can enhance predictive capabilities safely and efficiently. Specifically, we examine techniques for predicting uncertainty, adapting models online, and enabling safe exploration. Combining theoretical insights with computational methods and real-world applications, this talk highlights how the synergy of prediction, optimization, and learning supports safe, high-performance autonomy.

Keywords: Game theory
Abstract: Decision making in dynamic uncertain environments with multiple agents arises in many disciplines and application domains. A natural framework for modeling, optimization, and analysis of such multi-agent dynamical systems is the one provided by stochastic dynamic games, which accommodates different solution concepts depending on how the interactions among the agents are modeled, particularly whether they are in a cooperative mode (with the same objective functions, as in teams, where one seeks global optimality) or in a noncooperative mode (with different objective functions, where the solution concept depends on whether the roles of the agents are symmetric (Nash equilibrium) or asymmetric (Stackelberg equilibrium)) or a mix of cooperative and noncooperative behavior. What makes such problems, with (strategic) interactions among the agents, challenging is the asymmetric nature of the information different agents acquire (and do not share or only partially share (selectively) with others, even within teams). The complexity here (labeled C1) is different from the one that arises in stochastic control (or stochastic teams) where an agent who acts later does not have access to the measurements of the other agents who have acted before him (or equivalently when a controller in a stochastic control problem with partial/imperfect state measurements has limited memory, resulting in what is known as nonclassical information, requiring signaling. Of course, in a multi-agent system within a game-theoretic framework one can have (in addition to asymmetry in information) also limited memory for each agent, who now also have to deal with stochastic control problems with nonclassical information in computing their best-response functions, which compounds the difficulty (labeled C2). Both C1 and C2 constitute major challenges in multi-agent decision making, whose resolutions even for games with some specific structures would be a major contribution to the fields of control and game theory. This “Highlight Talk” will introduce open problems in this landscape, including ones where there is a possibility of agents receiving additional information at some cost, and how C1 and C2 arise in games with a high population of agents.

Keywords: Switched systems, Data driven control, Identification
Abstract: We study real-time identification of active subsystems in a switched linear system, along with the detection of the unknown switching instants. Immediately after a switch, the limited data generated by the new subsystem is consistent with infinitely many candidate models, making unique identification impossible. We extend the geometric transfer identification paradigm introduced in N.N. Mukesh et al. 2025 to select progressively more accurate candidate models from these infinite sets at each time instant. To achieve faster identification, we show that, generically, the traditional persistency of excitation requirement of n+m+nm data points can be reduced to just n+m steps for successful subsystem identification, where n and m denote the system order and number of inputs, respectively. This avoids the need for online input design and allows for shorter dwell-time assumptions. We further prove that, upon switching, a generic input renders the newly acquired data inconsistent with the previously active subsystem, even though infinitely many models remain consistent with the data. This property enables generic instantaneous switch detection. A robust numerical switch detection scheme is proposed and demonstrated for varying noise levels.

Keywords: Data driven control, Differential-algebraic systems, Numerical algorithms
Abstract: We derive a numerically stable method to compute an image representation of an unknown linear system only from data, leveraging a continuous-time version of Willems et al.'s fundamental lemma. To this end, we use derivatives approximated by algebraic differentiators. Our novel image representation avoids solving differential-algebraic equations and significantly reduces computational complexity by eliminating redundant degrees of freedom corresponding to the number of unknown quantities to be identified. Simulation results confirm the effectiveness of the proposed approach, even in the presence of severe measurement disturbances.

Keywords: Adaptive control, Data driven control
Abstract: This paper studies adaptive data-driven control (ADDC) for a class of non-square nonlinear systems with unknown input matrices and disturbances. For such systems, existing adaptive control methods often rely on prior structural information on the input matrix, whereas existing nonlinear direct data-driven control (DDC) methods are typically limited to local guarantees in the presence of disturbances. To address these challenges, we develop an ADDC framework that integrates offline data-driven learning with online adaptive compensation. The proposed framework is first established for systems with constant input matrices and is further extended to systems with time-varying input matrices. It is shown that, whenever the associated offline data-based optimization problem is feasible, the resulting controller ensures that all closed-loop signals are globally uniformly ultimately bounded (GUUB), without requiring prior knowledge of the input matrix.

Keywords: Data driven control
Abstract: We provide a practical relaxation of Willems' fundamental lemma for discrete-time linear time-invariant (single-input-single-output) systems. Instead of maintaining conventional Willems' persistency of excitation condition in the behavioral theory, we reformulate the problem in terms of signal generators, hence going back to the dynamical systems theory. We discuss the relationship between the persistency of excitation order and the dimension of the signal generator. Furthermore, we identify a necessary and sufficient condition on the signal generator that can generate informative input--output data for almost all systems and initial conditions. This formulation accommodates both a broad range of conventional persistently exciting input designs and a class of shorter inputs that violate Willems' condition, including sinusoidal sequences with fewer frequencies. Finally, the signal generator perspective allows a natural extension to continuous-time systems.

Keywords: Safety-critical control, Network analysis and control, Nonlinear systems
Abstract: Synthesizing control barrier functions (CBFs) for complex nonlinear systems remains difficult, particularly when safety constraints have high relative degree with respect to the input. In this work, we study the class of composite port-Hamiltonian systems as a network of interconnected subsystems, and this network admits a natural graph structure. We propose a novel graph-theoretic framework for the CBF synthesis problem. The framework addresses the problem of CBF construction for complex nonlinear systems by offering a relative-degree constraint induced by graph distance and a barrier reshaping rule informed by the graph topology. Furthermore, we perform a feasibility analysis of the reshaped barrier under a bounded input constraint and identify the sufficient conditions for feasibility. Lastly, the proposed framework is validated on an LC ladder network, where the CBF feasibility on a capacitor charge constraint depends on where the input enters the network.

Keywords: Data driven control, Maritime control, Safety-critical control
Abstract: Safe autonomous navigation in restricted maritime environments require control decisions that respect environmental and traffic constraints. The maritime Automatic Identification System (AIS) data contain vessel trajectories capturing global navigation of various types of vessels and their voyages. This presents a significant opportunity to build data-driven action sets for autonomous navigation and decision making. This letter develops a primitive-restricted receding-horizon control framework for decision making in marine vessels operating in restricted waterways. Navigation is formulated as a constrained receding-horizon optimization problem over a time-varying sailable domain defined by geometric, environmental, and maneuvering constraints. The admissible control space is restricted to a finite library of COLREGs compatible maneuver primitives learned offline from the AIS vessel trajectories and captures observed vessel behaviors. A residual correction layer computes and adjusts inputs to satisfy control Lyapunov and barrier conditions, ensuring safety while preserving primitive structure. Under standard recursive feasibility assumptions, the closed-loop system guarantees forward invariance of the feasible set and a Lyapunov-like decrease in the cost. The framework integrates data-derived maneuver primitives with formal safety guarantees for reliable maritime navigation and was validated through comprehensive simulations in various challenging maritime scenarios.

Keywords: Safety-critical control, Robotics, Autonomous robots
Abstract: In hierarchical quadruped navigation, high-level body-twist commands are tracked imperfectly by the low-level locomotion controller, especially on rough or slippery terrain, making nominal-command-level safety certificates unreliable.We propose a context-aware robust safety filter that explicitly accounts for this execution mismatch. A terrain-context descriptor and a tracking-residual descriptor are combined to construct an online anisotropic uncertainty set that bounds the execution mismatch between commanded and realized body twist.Using this set, we derive a robust barrier-tightening condition and formulate a minimally invasive quadratic-program shield.We establish one-step forward safety under calibrated uncertainty bounds, monotone safe-set contraction, and robustness to calibration conservatism. Simulations in Isaac Gym across mixed terrains and hardware experiments on a Unitree A1 show near-zero collision rates with substantially reduced intervention relative to fixed and isotropic baselines, and zero-collision realworld traversal using simulation-calibrated coefficients.

Keywords: Fault tolerant systems, Autonomous vehicles, Safety-critical control
Abstract: Proprioception is a human sense that provides feedback from muscles and joints about body position and motion. This key capability keeps us upright, moving, and responding quickly to slips or stumbles. In this paper we discuss a proprioception-like feature (machine proprioceptive feedback – MPF) for motion control systems. A distinguishing feature is that an unexpected response of one actuator, or one agent in a multi-agent system, is compensated by other actuators/agents through fast feedback loops that react only to the unexpected portion. The actuators/agents are connected by safety requirements encoded with Control Barrier Functions. The paper analyzes nature and degree of impairment that can be managed and offers two options – full-MPF and split- MPF – with different wiring architectures as well as different stability and safety properties. Multi-vehicle interchange lane- swap traffic simulations confirm the analytical results.

Keywords: Autonomous vehicles, Embedded systems, Safety-critical control
Abstract: Runtime safety filters for automated driving must enforce obstacle-avoidance under state and actuator limits while remaining lightweight enough for real-time computation. We consider a reference-relative lateral evasion formulation in which an obstacle-side constraint becomes active when the ego vehicle reaches a critical distance to a front vehicle. To prevent late activation, we define a conservative activation index using future speed bounds and construct a time-varying viability sequence with a controlled-invariant terminal set. This yields an offline-computed certificate that ensures that a safe evasive maneuver exists and supports a minimally invasive online supervisor that filters nominal curvature commands only when necessary. We compare four monitoring implementations that trade-off exactness, memory, and runtime. In the experimental evaluation, two of the implementations achieve no violations with lower online computation than baseline approaches.

Keywords: Safety-critical control, Stability of nonlinear systems, Constrained control
Abstract: We propose a constricting Control Barrier Function (CBF) framework for prescribed-time control of control-affine systems with input constraints. Given a system starting outside a target safe set, we construct a time-varying safety tube that shrinks from a relaxed set containing the initial condition to the target set at a user-specified deadline. Any controller rendering this tube forward invariant guarantees prescribed-time recovery by construction. The constriction schedule is bounded and tunable by design, in contrast to prescribed-time methods where control effort diverges near the deadline. Feasibility under input constraints reduces to a single verifiable condition on the constriction rate, yielding a closed-form minimum recovery time as a function of control authority and initial violation. The framework imposes a single affine constraint per timestep regardless of state dimension, scaling to settings where grid-based reachability methods are intractable. We validate on a 16-dimensional multi-agent system and a unicycle reach-avoid problem, demonstrating prescribed-time recovery with bounded control effort.

Keywords: Game theory, Machine learning and control, Multi-agent learning
Abstract: Computing per-player feedback strategies in N-player adversarial differential games is computationally challenging as the associated coupled Hamilton-Jacobi-Bellman system is high-dimensional and generally lacks classical solutions. We address this by approximating viscosity solutions using physics-informed neural networks within a policy iteration scheme with a vanishing-viscosity annealing schedule. Theoretically, we establish an explicit varepsilon-Nash guarantee by bounding per-player regret via computable residuals and prove our method reaches this stopping criterion in finite time. For two-player zero-sum games, we further establish a computable bound on approximation error for the value functions. Numerical experiments on pursuit-evasion scenarios illustrate the tightness of these computed bounds and the framework's scalability to high-dimensional environments.

Keywords: Learning in Game theory, Multi-agent learning, Statistical learning
Abstract: A standard linear regression setting can be viewed as a sender–receiver interaction, where the receiver predicts an outcome based on features reported by the sender. When the sender withholds features to serve a private objective, one expects the prediction accuracy to deteriorate due to missing information. We show this intuition is not always correct. If the receiver accounts for strategic omission, and there is sufficient alignment between the sender and the receiver, a linear model adapted to such behavior achieves strictly lower mean-squared error than the best linear model with full feature access.

This result has important implications for disclosure policies in self-reporting environments, such as financial markets, where deciding between voluntary and mandatory reporting affects model performance. We derive necessary and sufficient conditions under which voluntary reporting yields better performance. When these underlying dynamics are unknown, we propose a joint-selection learning algorithm that simultaneously learns the optimal disclosure regime and its corresponding optimal predictor. Importantly, this is achieved at the same rate as if the optimal disclosure regime were known a priori, up to big-O order.

Keywords: Learning in Game theory, Multi-agent learning, Stochastic systems
Abstract: Randomized exploration is central to bandit learning, multi-agent reinforcement learning, and zeroth-order policy search, yet its independence and privacy are usually only treated as technical assumptions. We show that these properties are critical for security purposes and demonstrate how an adversarial agent can exploit privileged information on another agent’s exploration. We analyze a deceiver-victim pair in the minimal two-player strongly monotone setting, where a deceptive player obtains leaked signals that are merely correlated with the victim's exploration. We show that, by coupling their own exploratory action with this information, the deceptive player injects an externality that steers the learning dynamics to a new steady state, called the deceptive Nash equilibrium (DNE). We prove that the deceptive bandit learning (DBL) dynamics converge to an arbitrarily small neighborhood of the DNE while retaining optimal convergence rates. Interestingly, our analysis attains these optimal rates while relaxing second-order smoothness conditions from standard bandit optimization literature. We characterize conditions under which deception strictly shifts the steady state and its effect on the deceiver's cost, illustrating the results in a resource-allocation game.

Keywords: Game theory, Optimization algorithms, Data driven control
Abstract: Nash equilibrium computation in multi-agent decision-making can be challenging when a decision-maker has explicit access to its own optimization model but not to that of another agent. This paper studies a class of two-player constrained games with decoupled feasible sets under an asymmetric information structure: Player 1 knows its own objective and constraints but represents Player 2's response behavior through a best-response correspondence, a single-valued response map, or an approximation thereof. The equilibrium notion remains the standard Nash equilibrium, and the asymmetry concerns only the information available for computing it. We propose a projected gradient-response iteration that does not require explicit knowledge of Player 2's objective or optimality conditions. Under suitable regularity conditions, we establish the existence of a Nash equilibrium under set-valued best-response information, uniqueness under a single-valued Lipschitz continuous response map, and global linear convergence of the proposed iteration. We further analyze the inexact case and show that a uniformly bounded response-map error of size ε yields an explicit O(ε) ultimate bound around the Nash equilibrium associated with the exact response map. Numerical results corroborate the predicted convergence behavior and error scaling.

Keywords: Game theory, Optimization, Autonomous systems
Abstract: Effectively interpreting strategic interactions among multiple agents requires us to infer each agent's objective from limited information. Existing inverse game-theoretic approaches frame this challenge in terms of a "level-1" inference problem, in which we take the perspective of a third-party observer and assume individual agents share complete knowledge of one another's objectives. However, this assumption breaks down in decentralized, real-world scenarios like urban driving and bargaining, in which agents may act based on conflicting views of one another's objectives. We demonstrate the necessity of inferring agents' different estimates of each other's objectives through empirical examples, and by theoretically characterizing the prediction error of level-1 inference on fictitious gameplay data from linear-quadratic games. To address this fundamental issue, we propose a framework for level-2 inference to address the question: "What does each agent believe about other agents' objectives?" We prove that the level-2 inference problem is non-convex even in benign settings like linear-quadratic games, and we develop an efficient gradient-based approach for identifying local solutions. Experiments on a synthetic urban driving example show that our approach uncovers nuanced misalignments that level-1 methods miss.

Keywords: Intelligent systems, Optimization, Game theory
Abstract: Actionable recourse studies whether individuals can modify feasible features to overturn unfavorable outcomes produced by AI-assisted decision-support systems. However, many such systems operate in competitive settings, such as admission or hiring, where only a fraction of candidates can succeed. A fundamental question arises: what happens when actionable recourse is available to everyone in a competitive environment? This study proposes a framework that models recourse as a closed-loop adaptive process among candidates under a risk-based selection rule. Rejected individuals exert effort to improve actionable features along directions implied by the decision rule, while the selection benchmark evolves endogenously as many candidates adjust simultaneously. This creates endogenous selection, in which both the decision rule and the selection threshold are determined by the population's current feature state. This interaction generates a closed-loop dynamical system linking candidate selection and actionable recourse. We show that the initially selected candidates determine both the benchmark and the direction of improvement, thereby amplifying initial disparities and producing persistent performance gaps across the population.

Keywords: Optimization, Game theory, Optimal control
Abstract: This paper introduces a performative scenario optimization framework for decision-dependent chance-constrained problems. Unlike classical stochastic optimization, we account for the feedback loop where decisions actively shape the underlying data-generating process. We define performative solutions as self-consistent equilibria and establish their existence using Kakutani’s fixed-point theorem. To ensure computational tractability without requiring an explicit model of the environment, we propose a model-free, scenario-based approximation that alternates between data generation and optimization. Under a contraction condition and a uniform scenario-approximation condition, we prove almost-sure convergence of a stochastic fixed-point iteration with logarithmically growing sample sizes. We illustrate the framework through an AI safety application involving performative guardrails against Large Language Model (LLM) jailbreaks, where the numerical results exhibit stable co-evolution of the guardrail and the induced adversarial distribution.

Keywords: Stochastic optimal control, Uncertain systems, Chemical process control
Abstract: This paper presents an output-feedback generalized polynomial chaos expansion (gPCE)-based shrinking-horizon stochastic nonlinear model predictive control framework with iterative risk allocation (IRA) for batch processes subject to parametric uncertainty, stochastic disturbances, and a joint chance constraint (JCC). The framework integrates four components: (i) a structural identifiability and observability analysis based on extended Lie derivatives for the augmented state-space model; (ii) gPCE combined with conditional probability rules to separately quantify and propagate parametric and disturbance uncertainties through the nonlinear dynamics; (iii) a gPCE-based ensemble Kalman filter (EnKF) that updates the posterior distributions of states and parameters from noisy measurements; and (iv) a JCC reformulation via Boole's and Chebyshev's inequalities with IRA to redistribute the risk budget among constraints and reduce the conservatism of fixed uniform allocation. The method is validated on a semi-batch polypropylene glycol reactor with two uncertain parameters; the optimized risk allocation reduces batch time by approximately 38% compared with fixed allocation while maintaining the prescribed probabilistic safety level.

Keywords: Predictive control for nonlinear systems, Optimal control, Process Control
Abstract: The Output Sensitivity Modification (OSM) strategy is a newly proposed method that redefines what constitutes a `solution' of a dynamic optimization problem by defining a set of halting conditions, in order to obtain solutions with a preferred sensitivity structure. The OSM strategy was originally derived for single shooting, and in this paper, we extend the method to simultaneous transcription: multiple shooting and direct collocation. We prove equivalence to the single shooting approach under mild regularity assumptions. A benchmark Continuous Stirred Tank Reactor (CSTR) is used for numerical examples, where we impose a sensitivity structure that promotes decoupling between reactant inlet flow rate and reaction temperature. The benchmark illustrates the equivalence and efficacy of the extension to simultaneous transcription. The problems are solved via Newton's method applied to a residual vector formulation of the halting conditions, using the Fischer-Burmeister function for complementarity. In addition, we propose a heuristic in which we use the unmodified optimum to warm-start the Newton iterations, which proved effective on the CSTR benchmark.

Keywords: Autonomous robots, Robotics, Predictive control for nonlinear systems
Abstract: Sampling-based motion planning such as Model Predictive Path Integral (MPPI) control has become attractive for robotics due to its ability to handle nonlinear dynamics and non-smooth objectives without gradient information, while leveraging parallel rollout computation for real-time performance. However, in real-world robotic systems, the optimized control input is often applied after a non-negligible planning delay, causing a mismatch between the state used in forward simulation and the actual state at control execution, which can significantly degrade planning accuracy and may even lead to unsafe behavior such as collisions. This paper proposes Closed-Loop MPPI with Initial-State Sampling (CLIS-MPPI), which explicitly addresses execution-time state mismatch by modeling planning delay as a distribution over plausible execution-time initial states, performing rollout optimization from sampled initial states, and applying a rollout-based local feedback correction during control execution. The proposed method is validated through real-world experiments on a 6-DoF UR5e manipulator in a narrow-passage task involving obstacle avoidance and end-effector target reaching. Across 5 real-world runs of the same task, standard MPPI collided in 2 runs, whereas CLIS-MPPI remained collision-free in all 5 runs. Averaged over all collision-free runs for each method (3 for MPPI and 5 for CLIS-MPPI), CLIS-MPPI reduced the average task completion time from 25.4 s to 24.4 s and the average end-effector path length from 0.456 m to 0.425 m. It also reduced the overall joint-position and joint-velocity root mean square errors (RMSEs) from 0.100 rad and 0.108 rad/s to 0.017 rad and 0.011 rad/s, respectively. These results demonstrate improved safety, planning-execution consistency, and motion smoothness.

Keywords: Optimal control, Optimization algorithms, Predictive control for nonlinear systems
Abstract: Model Predictive Path Integral (MPPI) control is a widely used sampling-based method for trajectory optimization, yet its convergence properties remain only partially understood. This paper provides a direct convergence analysis using variational optimization. By lifting constrained trajectory optimization to a Kullback-Leibler (KL) regularized problem over decision distributions, we derive a reduced free-energy objective defined over a parametric sampling family. For general parametric families, we derive gradient and Hessian representations of this reduced objective and analyze preconditioned gradient descent on the sampling-distribution parameters. In the fixed-covariance Gaussian case, the classical MPPI update is recovered exactly as a unit-step preconditioned gradient update. We prove descent and stationarity guarantees for the exact expectation-based iteration when the Hessian of the reduced objective is bounded in the metric induced by the preconditioner. For the Gaussian family, we further show that the preconditioned Hessian is governed by the covariance of the Gibbs-tilted distribution relative to the covariance of the sampling distribution, yielding a covariance-dependent sufficient condition for the descent of exact unit-step MPPI. Numerical experiments illustrate the theory and the effect of key hyperparameters.

Keywords: Optimization algorithms, Predictive control for nonlinear systems, Human-in-the-loop control
Abstract: Natural disasters such as hurricanes and wildfires can have devastating consequences that affect large populations. Among all relief measures, evacuation is crucial for saving lives and reducing panic as well as asset losses. Existing studies have extensively explored evacuation route planning, which focuses on pre-disaster route recommendations with the assumption that people must comply with those recommendations. In contrast, dynamic evacuation routing, which accounts for the behaviors of distributed evacuation groups and the stochastic unfolding of disasters, has received little attention. This paper proposes an approach that iteratively infers evacuees' compliance in the route recommendation and integrates the inference into a dynamic route recommendation model. In numerical experiments, this approach demonstrates superior effectiveness in reducing evacuation time and road congestion.

Keywords: Robust control, Learning-based Control, Stability of nonlinear systems
Abstract: In this paper, we propose a learning framework for synthesizing a robust controller for dynamical systems evolving on a Lie group. A robust control contraction metric (RCCM) and a neural feedback controller are jointly trained to enforce contraction conditions on the Lie group manifold. Sufficient conditions are derived for the existence of such an RCCM and neural controller, ensuring that the geometric constraints imposed by the manifold structure are respected while establishing a disturbance-dependent tube that bounds the output trajectories. As a case study, a feedback controller for a quadrotor is designed using the proposed framework. Its performance is evaluated using numerical simulations and compared with a geometric controller.

Keywords: Information theory and control, Learning-based Control, Automotive control
Abstract: Q-decomposition Double Deep Q-Network (DDQN) enhances the transparency of the black-box DDQN by decomposing the global reward signal across subagents, thereby improving the explainability and interpretability of the learned policy. Despite prior convergence guarantees for multi-agent SARSA and linear DQN, the convergence of Q-decomposed DDQN has not been formally established. In this paper, we prove that the Q-decomposed linear DDQN converges almost surely to the fixed point of the projected Bellman operator, and that

under GLIE exploration and sufficiently wide networks, this

fixed point coincides with the globally optimal Q-function.

Numerical results validate the theoretical findings, with Q-decomposition achieving 97.4% of the optimal solution obtained via dynamic programming.

Keywords: Stochastic optimal control, Stochastic systems, Optimization algorithms
Abstract: We study the problem of online feedback optimization for stochastic linear plants and quadratic performance costs in the presence of an unknown disturbance and persistent white noise. For this problem, we introduce a novel two-timescale control architecture consisting of a static feedback term and a dynamically tuned feedforward term. Through singular perturbation analysis, we show that the steady-state mean of the system converges to the feasible optimizer of the problem, independently of the feedback term, and the steady-state covariance converges to the standard LQR baseline up to a small bias of order O(epsilon), where epsilon is the learning rate of the optimization dynamics. In this sense, our results highlight a novel separation principle that justifies a sequential design approach for stochastic feedback optimization: the feedback term may be designed offline via LQR techniques to minimize the covariance penalty, e.g., using a Riccati equation, while the dynamic feedforward leverages a gradient-based architecture that rejects the unknown disturbance from the steady-state mean, all while incurring only an O(epsilon)- optimality gap. Numerical simulations are provided to validate the theory.

Keywords: Multi-agent learning, Stochastic optimal control, Game theory
Abstract: The last-iterate convergence of gradient-based learning in games is generally more challenging than the ergodic counterpart. Recent advances have explored the ideas of optimism, extra-gradient, and mirror-prox to tame gradient dynamics and avoid cycling behaviors. When analyzed in the mirror descent framework, a primal-dual first-order method that generalizes gradient descent by exploiting the problem geometry, these ideas share the same spirit: the current gradient update is based on a prediction of the current feedback (that is not realized yet) rather than the previous one, leading to predictive mirror descent (PMD). However, it remains unclear how to design such a prediction to induce desired convergence rates, which is the central question of this work. Inspired by the Brezis-Ekeland variational principle, we first establish an equivalence between PMD’s finite-time primal-dual path (mirror path) in convex games and the closed-loop Nash equilibrium path of a finite-horizon stochastic mirror differential game (SMDG) whose stage cost is based on the Fenchel conjugate of the prediction term. To answer the question above, we study the terminal-time bounds of the equilibrium path in expectation and with high probability in SMDG, which, through the equivalence, translate to the last-iterate convergence rate in PMD. Our proposed equilibrium characterization of gradient dynamics, under the lens of variational analysis, offers a unified approach to designing PMD in games.

Keywords: Stochastic systems, Markov processes, Uncertain systems
Abstract: Sequential decision-making in high-dimensional binary systems is challenging when the factored dependency structure governing state transitions is unknown and must be learned simultaneously with the transition probabilities. We address this problem through Bayes-adaptive reinforcement learning in binary Factored Markov Decision Processes (FMDPs) in which both the dependency structures and the local transition probabilities are unknown and must be learned online. We employ a Bayesian framework with independent priors over finite candidate parent sets and Beta priors for Bernoulli transition parameters. This choice enables exact, closed-form posterior updates via Beta-Bernoulli conjugacy, without requiring sampling or variational approximations. To overcome the intractability of the exact Bayesian information state, we introduce a compressed representation comprising the physical state, posterior-structure beliefs, and posterior-predictive transition probabilities. We prove this representation is sufficient for computing one-step predictive distributions and establish a suboptimality bound for the optimal compressed policy relative to the Bayes-optimal policy. A deep Q-network (DQN) is used to learn a policy over this reduced-dimensional compressed space. Numerical experiments demonstrate that our approach achieves strong control performance compared to competing methods.

Keywords: Learning, Identification for control, Learning-based Control
Abstract: In this paper, we present an online learning approach for two-player zero-sum linear quadratic games with unknown dynamics. We develop a framework combining regularized least squares model estimation, high probability confidence sets, and surrogate model selection to maintain a regular model for policy updates. We apply a shrinkage step at each episode to identify a surrogate model in the region where the generalized algebraic Riccati equation admits a stabilizing saddle point solution. We then establish regret analysis on algorithm convergence, followed by a numerical example to illustrate the convergence performance and verify the regret analysis.

Keywords: Robotics, Learning, Identification for control
Abstract: Accurate modeling of robot dynamics is essential for model-based control, yet remains challenging under distributional shifts and real-time constraints. In this work, we formulate system identification as an in-context meta-learning problem and compare deterministic and generative sequence models for forward dynamics prediction. We take a Transformer-based meta-model, as a strong deterministic baseline, and introduce to this setting two complementary diffusion-based approaches: (i) inpainting diffusion (Diffuser), which learns the joint input–observation distribution, and (ii) conditioned diffusion models (CNN and Transformer), which generate future observations conditioned on control inputs. Through large-scale randomized simulations, we analyze performance across in-distribution and out-of-distribution regimes, as well as computational trade-offs relevant for control. We show that diffusion models significantly improve robustness under distribution shift, with inpainting diffusion achieving the best performance in our experiments. Finally, we demonstrate that warm-started sampling enables diffusion models to operate within real-time constraints, making them viable for control applications. These results highlight generative meta-models as a promising direction for robust system identification in robotics.

Keywords: Reinforcement Learning, Markov processes, Neural networks
Abstract: We study the convergence properties of Temporal Difference (TD) dynamics when the value function approximation belongs to a class of nonlinear functions satisfying a geometric notion of homogeneity, extending prior results in the literature. Our theoretical results are illustrated using an example, motivated by neural networks, that is homogeneous only in the generalized sense.

Keywords: Reinforcement learning, Robust control, Process Control
Abstract: Reinforcement Learning (RL) policies trained in simulation often exhibit degraded performance when deployed on physical systems due to the sim-to-real gap. This work investigates Curriculum Learning (CL) over simulation fidelity as a strategy for improving sim-to-real transfer in a color mixing task validated on physical hardware. We propose a four-level curriculum that progresses from simple linear in- terpolation to physically grounded spectral mixing with tinting effects. We systematically compare five switching strategies that govern transitions between these fidelity levels. Our approach combines the sample efficiency of simpler models with the transfer benefits of realistic dynamics. Curriculum-based training achieves comparable or superior real-world performance; however, transfer quality strongly depends on the switching strategy. Success-rate-based switching with slow, conservative progression uniquely achieves 50% success on the challenging C4 target and the lowest average real-world distance, whereas fast-progression variants of the same criterion do not improve over direct high-fidelity training. Reward-based switching attains the best simulation curriculum score but not the best real-world transfer, underlining that simulation performance alone does not reliably predict transfer quality.

Keywords: Stability of nonlinear systems, Optimization, Optimization algorithms
Abstract: This paper studies equality-constrained minimization problems through the lens of feedback control. We introduce a unified control-theoretic framework by showing that a PID feedback law acting on the dual variable induces the emph{PID saddle-point flow} (PID-SPF), a broad class of saddle-point dynamics associated with the augmented Lagrangian. This framework recovers several classical primal-dual flows as special cases. We prove that the equilibria of the proposed flow coincide with the stationary points of the original problem. Our analysis reveals how the feedback gains affect the optimization: integral action enforces constraint satisfaction, proportional action introduces the augmented Lagrangian structure, and derivative action modifies the geometry of the primal dynamics by inducing a state-dependent Riemannian metric. Moreover, for convex problems with affine constraints, we establish global exponential convergence by leveraging contraction theory for all admissible PID gains, providing in the process explicit bounds on the convergence rate. Finally, we validate our theoretical results on numerical examples including an application to bilevel optimization.

Keywords: Optimization algorithms, Stability of nonlinear systems, Lyapunov methods
Abstract: In this paper, an input-to-state Lyapunov function for the RMSProp optimization algorithm is introduced. Global asymptotic stability of the RMSProp algorithm for constant step sizes and robustness properties with respect to arbitrary bounded time-varying step size rules are established.

Keywords: Extremum seeking, Nonlinear output feedback, Optimization
Abstract: We study the problem of global extremum seeking in the presence of local extrema. We investigate two different perturbation-based methods: 1) a well-known classical extremum seeking scheme for steady-state output optimization, and 2) a source seeking scheme for a two-dimensional point mass. In each of these two scenarios, the closed-loop system involves a damped double integrator subject to an oscillatory force. An averaging analysis reveals that the respective averaged system is again a damped double integrator, but now subject to a potential force. The potential force is given by the gradient of a locally averaged objective function. Such a function is less prone to have undesired local extrema and is therefore better suited for global optimization. We provide sufficient conditions for semi-global practical uniform asymptotic stability of the closed-loop systems. The sufficient conditions only involve assumptions on the averaged objective function but not the original one.

Keywords: Optimization algorithms, Stability of nonlinear systems, Game theory
Abstract: It is well known that mirror descent may diverge or cycle on merely monotone variational inequalities. In this paper, we propose Target Mirror Descent (TMD), a unified framework that stabilizes monotone flows via a target point correction mechanism in the dual update. By appropriate design choices, the TMD framework recovers the proximal point algorithm, extragradient methods, splitting methods, Brown-von Neumann-Nash dynamics, forward-backward-forward dynamics, and discounted mirror descent as special instances. Thus, we establish a unified perspective on these landmark algorithms and their convergence. Beyond unification, we leverage the TMD framework to correct an equilibrium misalignment in discounted mirror descent and to generalize its higher-order extension beyond interior solutions. Moreover, a key structural feature of TMD is the explicit decoupling of the mirror map from the target determination, which enables geometric ensembles: multiple TMD instances solve the same problem in parallel using distinct mirror maps, while sharing a common dual update.We show that such an ensemble rigorously reduces to a single TMD with a synthesized mirror map, and thus inherits these convergence guarantees.

Keywords: Extremum seeking, Game theory, Optimization
Abstract: The nested Extremum Seeking (nES) algorithm is a model-free optimization method that has been shown to converge to a neighborhood of a Nash equilibrium. In this work, we demonstrate that the same nES dynamics can instead be made to converge to a neighborhood of a Stackelberg (leader--follower) equilibrium by imposing a different scaling law on the algorithm's parameters. For the two--level nested case, using Lie--bracket averaging and singular perturbation arguments, we provide a rigorous stability proof showing semi-global practical asymptotic convergence to a Stackelberg equilibrium. The results reveal that equilibrium selection, Nash versus Stackelberg, depends on the hierarchical scaling of parameters and the induced time-scale structure. We demonstrate the effect using a simple quadratic example and the canonical Fish War game. The Stackelberg variant of nES provides a model-free framework for hierarchical optimization in multi-time-scale systems, with potential applications in power grids, networked dynamical systems, and tuning of particle accelerators.

Keywords: Linear parameter-varying systems, Estimation, Uncertain systems
Abstract: This letter proposes a two-step interval state estimation framework for discrete-time linear parameter-varying (LPV) systems subject to mixed unknown-but-bounded (UBB) uncertainties. First, a stabilizing LPV observer is utilized to generate a stable nominal center trajectory. Second, the estimation error bounds are propagated using ellipsotope set arithmetic, which flexibly unites the geometric advantages of ellipsoids and zonotopes to tightly enclose the reachable set of the error dynamics under mixed-norm constraints. To ensure computational tractability during the set propagation, order reduction strategies are employed. Finally, the feasibility and performance of the introduced method are validated through simulation on a longitudinal LPV model of a Boeing 747 aircraft.

Keywords: Predictive control for nonlinear systems, Data driven control
Abstract: We consider nonlinear model predictive control (MPC) schemes without stabilizing terminal conditions, where the model used in the optimization step is generated based on input-output data only. We establish exponential stability for sufficiently long prediction horizons assuming exponential stabilizability and a proportional error bound. Moreover, we verify the imposed condition on the approximation using kernel interpolation and demonstrate the practical applicability to nonlinear systems by numerical simulations.

Keywords: Iterative learning control, Robust control, Data driven control
Abstract: Conformal prediction (CP) has been used to obtain a probabilistic bound on the error between a learned dynamics model and the true system. This bound can then be embedded into robust control Lyapunov function (CLF) and control barrier function (CBF) frameworks. However, such an approach does not retain stability/safety guarantees because of the distribution shift between the closed-loop trajectory distribution under the deployed CLF/CBF policy and the trajectory distribution from which the CP bound and its guarantees were derived. To address this issue, we propose an episodic framework that iteratively updates the robust conformal CLF/CBF policy while maintaining stability/safety guarantees across episodes. We achieve this by (1) using adversarially robust conformal prediction, and (2) quantifying a distribution shift budget that allows us to control how much the model error can increase across policy updates. This distribution shift budget is derived via a closed-loop trajectory sensitivity analysis, yielding an implicit and an explicit update rule for the CP bound. We analyze convergence of our algorithm which we also demonstrate on three case studies. To the best of our knowledge, these are the first results that provide stability/safety guarantees for robust conformal CBF/CLF policies.

Keywords: Model/Controller reduction, Data driven control, Formal Verification/Synthesis
Abstract: This paper develops a direct data-driven framework for constructing reduced-order models (ROMs) of discrete-time linear dynamical systems with unknown dynamics and process disturbances. The proposed scheme enables controller synthesis on the ROM and its refinement to the original system via an interface function designed using noisy data. To achieve this, the notion of simulation functions (SFs) is employed to establish a formal relation between the original system and its ROM, yielding a quantitative bound on the mismatch between their output trajectories. To construct such relations and interface functions, we rely on data collected from the unknown system. In particular, using noise-corrupted input--state data gathered along a single trajectory of the system, and without identifying the original dynamics, we propose data-dependent conditions, cast as a semidefinite program, for the simultaneous construction of ROMs, SFs, and interface functions. Through a case study, we demonstrate that data-driven controller synthesis on the ROM, combined with controller refinement via the interface function, enables the satisfaction of complex logic specifications.

Keywords: Reduced order modeling, Model/Controller reduction, Modeling
Abstract: We present an error-bound analysis for model reduction by moment matching. The problem of minimizing the 2-norm of the approximation error is reformulated as the minimization of the 2-norm of an equivalent cascade system. For a prescribed set of interpolation points, we first pose a constrained optimization problem and then derive a family of feasible solutions to a restricted version of this problem. Building on this formulation, we introduce a relaxed optimization problem that admits an explicit feasible solution, providing an approximate solution to the original nonconvex constrained problem. We further show that this approximation is equivalent to the least-squares solution associated with minimizing the 2-norm of one of the two subsystems in the cascade representation. The proposed approach provides a priori error bounds for the optimization problem, and its approximate closed-form feasible solution eliminates the need for iterative procedures. The theoretical findings and error bounds are validated and discussed through a numerical example.

Keywords: Safety-critical control, Uncertain systems, Model Validation
Abstract: Signal Temporal Logic (STL) is an expressive language for specifying behaviors of dynamical systems from continuous signals. However, a limitation of standard STL is its inherently deterministic semantics, which prevents it from accommodating uncertainty. Existing approaches to overcome this limitation are computationally costly and limit real-time capability, requiring repeated trajectory sampling or redesign of probability distributions over atomic propositions whenever the atomic propositions or specifications change. We introduce pacSTL, a framework that combines Probably Approximately Correct (PAC)-bounded reachable set predictions with an interval extension of STL. pacSTL computes lower and upper bounds on atomic robustness values by solving optimization problems over PAC-bounded reachable sets and propagates the bounds through the temporal logic operators. The resulting evaluation yields a PAC-bounded robustness interval at the specification level. We demonstrate the efficiency and relevance of pacSTL by verifying a quadrotor flight scenario and runtime monitoring a maritime navigation encounter.

Keywords: Stochastic optimal control, Safety-critical control, Robotics
Abstract: Many safety-critical control systems operate under latent uncertainty that sensors cannot resolve at decision time. Such uncertainty, arising from unknown physical properties, disturbances, or unobserved geometry, affects dynamics, task feasibility, and safety margins. Standard methods optimize expected performance and offer limited protection against rare but severe outcomes, while robust formulations treat uncertainty conservatively without exploiting its probabilistic structure. We consider systems with measured state and an unknown, time-invariant parameter represented by a belief distribution. We propose a risk-sensitive belief-space Model Predictive Path Integral (MPPI) controller that plans under this belief, regularizes performance using Conditional Value-at-Risk (CVaR), and imposes a CVaR constraint on a trajectory safety margin over the horizon. For the exact risk-constrained formulation underlying this controller, we establish three properties: (1) the CVaR constraint implies a probabilistic safety guarantee, (2) the controller recovers the risk-neutral optimum as the objective risk weight tends to zero, and (3) a union-bound argument extends the per-horizon guarantee to cumulative safety over repeated solves. In contact-rich MuJoCo simulations of vision-guided dexterous stowing, where a manipulator inserts a grasped object into an occupied slot with pose uncertainty exceeding prescribed lateral clearance requirements, our method achieves 82% success with zero contact violations at high risk aversion, compared with 55% and 50% for a risk-neutral configuration and a CCMPPI baseline, both of which incur nonzero exterior contact forces. Project page: https://clintonenwerem.com/belief-cvar-mppi/.

Keywords: Extremum seeking, Distributed parameter systems, Backstepping
Abstract: This letter presents a gradient-based extremum seeking control (ESC) framework for real-time optimization of unknown static scalar maps subject to input actuation dynamics governed by a reaction–advection–diffusion (RAD) partial differential equation (PDE). The optimizing map depends on a distributed-effect input, namely the spatial integral of the PDE state, rather than on a pointwise or boundary value. Since advection and reaction distort the probing signal and complicate the closed-loop design, we first solve a trajectory-generation boundary-value problem to construct an explicit boundary probing signal. We then apply infinite-dimensional backstepping to the resulting PDE--ODE error cascade and, via a spatially weighted Lyapunov functional, establish local exponential stability of the averaged closed-loop system under an explicit bound on the reaction coefficient. Finally, infinite-dimensional averaging yields practical convergence of the closed-loop trajectories to a small neighborhood of the unknown extremum. Simulations validate the proposed method.

Keywords: Optimal control, Variational methods, Numerical algorithms
Abstract: We address optimal control of semilinear evolution equations on Banach spaces with finitely many control channels, a framework encompassing many infinite-dimensional dynamical systems arising in applications. For this setting, we derive an exact and global formula quantifying the increment of the cost functional with respect to an arbitrary reference control. This identity enables the design of monotone descent algorithms that require no linearization or step-size tuning. We establish the existence of optimal controls and propose a practical sample-and-hold realization of the descent step. The effectiveness of the method is demonstrated on a controlled reaction-diffusion equation.

Keywords: Distributed control, Cooperative control, Control of networks
Abstract: In practical multi-agent systems, agents are self-interested and may require incentives to exchange information or resources with others. Examples include energy exchange among independently operated microgrids and participatory sensing, where individuals share data collected by their own mobile devices. In such systems, it is natural to consider that agents can be modeled as systems driven by the exchange of valuable resources. In our previous work, we have formulated a model of such value exchange multi-agent systems where each agent, modeled as a first-order integrator, possesses tokens and exchanges them for information. Furthermore, we have provided a necessary and sufficient condition for consensus of the system with a specific value exchange rule. As a next step, we aim to clarify the common properties of exchange rules that guarantee consensus. To this end, we introduce the notion of fairness, which requires that agents exchange with all their neighbors simultaneously, and we show that the fairness of all agents is a necessary and sufficient condition for consensus independently of the network topology.

Keywords: Quantized systems, Distributed control, Networked control systems
Abstract: This paper investigates the consensus problem for continuous-time multi-agent systems under coarse information constraints imposed by quantized communication. We propose a distributed error-feedback quantization mechanism in which each agent maintains a local auxiliary error-feedback dynamic based on its own state information. Only the quantized auxiliary variables are exchanged over the network. We demonstrate that this mechanism enables global asymptotic consensus under any quantization resolution. Finally, a numerical example is provided to validate the effectiveness of the proposed approach.

Keywords: Networked control systems, Sensor networks, Agents-based systems
Abstract: Distributed optimization offers significant advantages over centralized methods in terms of scalability and robustness when solving large-scale problems. In this paper, we propose a novel decentralized optimization algorithm that integrates Inexact Consensus ADMM (IC-ADMM) with a finitetime decentralized quantized communication algorithm. The proposed method enjoys three main benefits: (i) it operates on directed communication graphs, (ii) it requires only quantized local information instead of exact values, and (iii) it does not rely on solving the local subproblems exactly. Under the assumption that each node’s local objective is μ-strongly convex and L-smooth, the algorithm is guaranteed to achieve global linear convergence to a neighborhood of the optimal solution. Extensive numerical experiments demonstrate its advantages over existing methods in terms of convergence speed and communication efficiency.

Keywords: Networked control systems, Decentralized control, Optimal control
Abstract: Despite longstanding interest, controller synthesis remains challenging for networks of heterogeneous, nonlinear agents. Moreover, the requirements for computational scalability and information privacy have become increasingly critical. This paper introduces a dissipativity-based distributed controller synthesis framework for networks with heterogeneous agents and diverse performance objectives, leveraging the Network Dissipativity Theorem and iterative convex overbounding. Our approach enables the synthesis of controllers in a distributed way by achieving a network-wide consensus on agents' dissipativity variables while keeping sensitive subsystem information locally. The proposed framework is applied to full-state feedback controller synthesis.

Keywords: Cooperative control, Networked control systems
Abstract: Distributed consensus is a fundamental problem in multi-agent systems, where agents iteratively exchange information to agree on a common value using local communication. A discrete-time multi-agent consensus problem with probabilistic communication is considered. Instead of edge weights, each node is assigned a probability of broadcasting its state based on its centrality in the graph, which complicates the problem due to asymmetry. We have proved that exponential convergence is possible without traditional step-size assumptions. Moreover, the convergence rate is expressed explicitly in terms of node probabilities for a specific class of graphs using the Dobrushin coefficient. For arbitrary graphs, an upper and lower convergence bounds are derived in terms of node probabilities using Cheeger-type spectral bounds. Finally, we have shown how the convergence rate can be adjusted through node probabilities. Numerical examples validate the theoretical convergence results.

Keywords: Optimization, Stability of nonlinear systems, Optimization algorithms
Abstract: The Łojasiewicz inequality characterizes objective-value convergence along gradient flows and, in special cases, yields exponential decay of the cost. However, such results do not directly give rates of convergence in the state. In this paper, we use contraction theory to derive state-space guarantees for gradient systems satisfying generalized Łojasiewicz inequalities. We first show that, when the objective has a unique strongly convex minimizer, the generalized Łojasiewicz inequality implies semi-global exponential stability. We then give two curvature-based sufficient conditions, together with constraints on the Łojasiewicz rate, under which the nonconvex gradient flow is globally incrementally exponentially stable.

Keywords: Uncertain systems, Robust control, Optimization
Abstract: This paper addresses the problem of Tikhonov regularization in cases where the structural information, represented by the regularization matrix or graph Laplacian, is subject to uncertainty. Unlike conventional methods that assume a perfectly known structure, we propose a robust framework where structural uncertainties are explicitly modeled using Linear Fractional Transformations (LFTs). We derive a theoretical error bound for the nominal Tikhonov solution under worst-case perturbations using mu-analysis from robust control theory, and a guaranteed upper bound on the worst-case estimation error via a Linear Matrix Inequality (LMI). The proposed method is applied to graph signal processing (GSP), specifically for signal recovery on graphs with uncertain edge weights, where independent edge weight uncertainties admit a closed-form robust solution equivalent to nominal Tikhonov regularization on an augmented graph. Numerical experiments demonstrate that our robust approach significantly outperforms standard Tikhonov regularization in the presence of structural uncertainties, providing a bridge between robust control theory and data-driven inverse problems.

Keywords: Energy systems, Control Systems Privacy, Distributed control
Abstract: Distributed energy systems with prosumers require new methods for coordinating energy exchange among agents. Coalitional control provides a framework in which agents form groups to cooperatively reduce costs; however, existing bottom-up coalition-formation methods typically require full information sharing, raising privacy concerns and imposing significant computational overhead.

In this work, we propose a limited information coalition-formation algorithm that requires only limited aggregate information exchange among agents. By constructing an upper bound on the value of candidate coalitions, we eliminate the need to solve optimisation problems for each potential merge, significantly reducing computational complexity while limiting information exchange. We prove that the proposed method guarantees cost no greater than that of decentralised operation.

Coalition strategies are optimised using a distributed approach based on the Alternating Direction Method of Multipliers (ADMM), further limiting information sharing within coalitions. We embed the framework within a model predictive control scheme and evaluate it on real-world data, demonstrating improved economic performance over decentralised control with substantially lower computational cost than full-information approaches.

Keywords: Learning in Game theory, Smart grid, Variational methods
Abstract: Demand-side management (DSM) enables distribution system operators (DSOs) to steer electricity consumption through dynamic prices, thereby leveraging users' flexibility for delivering grid services. The resulting hierarchical interaction between the DSO dynamically setting the prices and the users optimally responding to them can be formulated as a Stackelberg game. Efficiently designing these prices is challenging, as the users’ response models are unknown or difficult to estimate. In this paper, we propose a learning-based zeroth-order algorithm for incentive design, in which the iterative update of the price signals is efficiently assisted by a data-driven online estimation of the users' responses. The proposed method is then proven to converge to an equilibrium tariff while allowing the DSO to estimate the decision-making problems at the user level. Moreover, the method preserves users' privacy, as the update rule of the DSO is solely based on observations of communicated user actions. Numerical simulations employing real-world data illustrate the efficient convergence of our learning-based proposed method, while significantly reducing the number of required interactions between the DSO and the users with respect to the state-of-the-art approach.

Keywords: Learning in Game theory, Estimation, Variational methods
Abstract: Inverse dynamic game theory aims to learn the unknown objective functions of non-cooperative agents from their observed behavior. Existing inverse game formulations typically rely on noiseless, full-state observations and do not provide theoretical guarantees on the monotonicity of the learned pseudogradient operator. To address these theoretical and practical gaps in the context of linear-quadratic dynamic games, we introduce a tractable inverse Variational Inequality (VI) framework equipped with a Linear Matrix Inequality (LMI) constraint that guarantees strong monotonicity of the learned pseudogradient operator. To deploy this framework in environments corrupted by measurement noise, we propose a robust receding-horizon online learning scheme. By formulating the online update via Maximum A Posteriori (MAP) estimation, we derive an adaptive Tikhonov regularization penalty that optimally filters sensor noise. Furthermore, we utilize Hutchinson's trace estimator to maintain real-time computational tractability. Numerical simulations of a non-cooperative collision avoidance game showcase the proposed methodology, hereby demonstrating significant error variance suppression and superior trajectory prediction across different noise regimes.

Keywords: Distributed control, Agents-based systems, Power systems
Abstract: A privacy-preserving dynamic average consensus (DAC) algorithm is proposed that achieves consensus while preventing external eavesdroppers from inferring the reference signals and their derivatives. During the initialization phase, each agent generates a set of sinusoidal signals with randomly selected frequencies and exchanges them with its neighboring agents to construct a masking signal. Each agent masks its reference signals using this composite masking signal before executing the DAC update rule. It is shown that the developed scheme preserves the convergence properties of the conventional DAC framework while preventing information leakage to external eavesdroppers. Furthermore, the developed algorithm is applied to state-of-charge (SoC) balancing in a networked battery energy storage system to demonstrate its practical applicability. Simulation results validate the theoretical findings.

Keywords: Robust adaptive control, Lyapunov methods, Nonlinear systems
Abstract: Centralized networked control systems (NCSs) are a critical and evolving field of research used in military, commercial, and civilian operations including reconnaissance, formation flight, search and rescue, and teleoperation applications. While centralized NCSs can enhance system efficiency, coordination of agents in the network, and reduce computational loads on individual agents, communication (input/output) delays pose significant challenges to stability. These delays not only degrade tracking performance, but also pose a significant obstacle to overall system stability and coordination. Existing approaches often rely on linear models or known delays, making uncertain input and output delay compensation for systems with general nonlinear dynamics an open problem. This preliminary work develops a closed-loop control framework for follower agents with nonlinear control-affine dynamic models, which ensures trajectory tracking for each agent by compensating for unknown time-varying input and output delays induced by adversarial attacks or communication constraints within a centralized NCS. A Lyapunov–Krasovskii (LK) functional-based stability analysis is performed to ensure semi-global exponential trajectory tracking to an ultimate bound for each follower agent. Additionally, numerical simulations are performed to demonstrate the controller’s performance.

Keywords: Networked control systems, Robust control, Control of networks
Abstract: Communication-aware control is essential to reduce costs and complexity in large-scale networks. While many works focus on full state feedback or linear agents, this work proposes a method to design dissipativity-augmented output feedback controllers with reduced online communication. The contributions are threefold: a generalized well-posedness condition for the controller network, a convex relaxation for the constraints that infer stability of a network from dissipativity of its agents, and a synthesis algorithm integrating the Network Dissipativity Theorem, alternating direction method of multipliers, and iterative convex overbounding. The proposed approach yields a sparsely interconnected controller that is both robust and applicable to networks with heterogeneous nonlinear agents. The efficiency of these methods is demonstrated on heterogeneous networks with uncertain and unstable agents, and is compared to standard H-infinity control.

Keywords: Nonlinear output feedback, Resilient Control Systems, Control system architecture
Abstract: This paper addresses the problem of fixed-time output tracking for a class of nonlinear systems subject to denial-of-service (DoS) attacks.Under DoS attacks, the transmission of the reference signal may be intermittently interrupted during certain time intervals. This paper proposes a novel fixed-time convergent backstepping control framework, applicable to nonlinear systems such as unmanned aerial vehicle (UAV) formations and ground robots.The framework comprises a predictor-based filter with fixed-time convergence, a fixed-time backstepping controller, and a fixed-time extended state observer (ESO). In contrast to prior solutions, the design not only effectively addresses the state non-differentiability issue induced by DoS attacks but also achieves practical fixed-time convergence (with convergence time bounds independent of initial states), while actively enhancing convergence performance during DoS-induced communication suspensions. Theoretical proofs demonstrate practical fixed-time stability with convergence to a small neighborhood of the origin within a fixed-time bound, independent of initial conditions. Finally, the effectiveness of the proposed scheme is validated through UAV experiments under intermittent DoS attacks.

Keywords: Control of networks, Nonlinear output feedback, Algebraic/geometric methods
Abstract: We study synchronization of heterogeneous control-affine nonlinear agents interconnected through diffusive (relative-output) measurements. We separate the design into an edge-space step—specifying a stabilizing model evolution for relative outputs—and a lift step—realizing the prescribed edge motion using the agents' allowable input directions, constrained by the control-affine geometry of the agents. We introduce an admissibility notion that characterizes when an edge-driven diffusive design is feasible. We derive checkable combinatorial certificates that connect graph topology and actuation limits directly to admissibility, so that feasible edge dynamics can be verified in a practical and transparent way. The results are illustrated on synchronization of nonlinear oscillators.

Keywords: Network analysis and control, Algebraic/geometric methods, Nonlinear systems
Abstract: The parametric sensitivity of a network of nonlinear input-output systems is considered, where each node is modelled by a Chen-Fliess functional expansion. In this framework, communication between the nodes is only possible at the input-output level. The specific goal is to determine the forward output sensitivity to a network parameter for any admissible set of external inputs. These results could be used for training and optimization of such networks or for model reduction problems. The analysis requires a variational generalization of the Kawski-Sussmann universal control system, which is viewed in terms of a right-trivialized ODE on a formal Lie group.

Keywords: Power systems, Smart grid, Simulation
Abstract: Dynamic simulation of power systems having states that exhibit stiff behaviors requires a significant computational effort. Hybrid discretization methods have been proposed in the literature that employ an explicit method to discretize the non-stiff states and an implicit method to discretize the stiff states, with the goal of obtaining a larger stability domain compared to the explicit method and a lower computational burden compared to the implicit method. This paper presents two new findings. At first, it is shown via (a) a case study on a stiff linear system (developed by linearizing the IEEE 2-area 4-machine test system around a nominal operating point) and (b) theoretical analysis that, unlike the explicit and implicit methods, the stability domain of a hybrid discretization method is not invariant to the state space representation of a system, under a given state partitioning algorithm. A consequence of this result is that a hybrid discretization method can have a smaller stability domain than the underlying explicit method, even under a highly rational partition of the states, as shown through another case study in this paper. To assess whether this counter-intuitive phenomenon can be observed on a small scale system, theoretical results are presented that characterize the set of 2-dimensional systems for which the stability domain of a hybrid discretization method can be guaranteed to be (a) larger than that of the underlying explicit method regardless of the partition of the states and (b) smaller than that of the underlying explicit method at least under one of the partitions of the states. These results reveal that under certain conditions, having a wide separation between the stiff and non-stiff groups of eigenvalues is neither necessary nor sufficient to obtain computational benefits from application of hybrid discretization methods. The analysis presented in this paper can be useful in developing optimal state partitioning algorithms in the future.

Keywords: Stability of linear systems, Power systems, Networked control systems
Abstract: We propose a decentralized framework to analytically guarantee the small-signal stability of future power systems with grid-forming converters. Our approach leverages dynamic loop-shifting techniques to compensate for the lack of passivity in the network dynamics and establishes decentralized parametric stability certificates, depending on the local device-level controls and incorporating the effects of the network. By following practical tuning rules, we are able to ensure plug-and-play operation without centralized coordination. Unlike prior works, our approach accommodates coupled frequency and voltage dynamics, incorporates network dynamics, and does not rely on specific network configurations, offering a general and scalable solution for the integration of power-electronics-based devices into future power systems. We validate our theoretical stability results through numerical case studies in a high-fidelity simulation model.

Keywords: Stability of linear systems, Robust control, Numerical algorithms
Abstract: This paper presents a constructive approach to find inner approximations of semi-algebraic sets, which are usually employed in control theory to characterize the set of parameters that make the closed-loop system asymptotically stable. The inner approximation is governed by two parameters which control the scale and the smoothness of the approximation. It is shown that as these two parameters go to infinity, the approximation covers the whole semi-algebraic set. Furthermore, the Chebyshev center of the inner approximation converges to the one of the original semi-algebraic set. Two control applications of the proposed method are provided.

Keywords: Stability of nonlinear systems, Robust control
Abstract: This paper studies stabilization and its corresponding closed-loop region-of-attraction (ROA) for homogeneous polynomial dynamical systems whose nonlinear term admits an orthogonally decomposable (ODECO) tensor representation. While recent tensor-based results provide explicit solutions and sharp global characterizations for ODECO systems, closed-loop synthesis and computable ROA estimates are still often dominated by local linearization or Lyapunov/SOS (sum of squares) methods, which can be conservative and computationally demanding. We propose a structure-preserving linear feedback design that shares the ODECO eigenbasis of the system's tensor, thereby enabling closed-form trajectory expressions, explicit convergence/escape thresholds, and sharp ROA characterizations. Under mild conditions, we further derive robustness/ISS-type bounds for bounded disturbances. Numerical examples validate the theoretical results.

Keywords: Large-scale systems, Linear systems, Lyapunov methods
Abstract: This paper studies the stability of interconnected linear systems with periodic dynamics. While comparison-based Lyapunov methods provide tractable conditions for time-invariant systems, extending them to periodic settings is challenging due to harmonic interactions induced by time-varying coefficients. We develop a harmonic-domain comparison framework that represents periodic subsystems in an equivalent infinite-dimensional form while yielding finite-dimensional stability conditions based on comparison matrices. Classical norm-based interconnection bounds are shown to be conservative since they ignore spectral separation between subsystem energies and coupling dynamics. To address this issue, we introduce a frequency-weighted comparison framework that yields refined interconnection gains and less conservative stability conditions. The resulting criteria are expressed as nonsingular M-matrix conditions and computed via an LMI-based synthesis formulation. A numerical example illustrates the effectiveness of the approach.

Keywords: Control applications
Abstract: This article presents a robust control framework to enable dynamic docking of robotic floating satellite platforms actuated by multiple thrusters, ensuring safety while maintaining feasibility. Safety during docking is guaranteed through the integration of adaptive control barrier function (CBF) constraints. Unlike existing switching-based CBF formulations for docking, the proposed approach introduces a CBF that continuously adapts according to the Euclidean distance between the chaser and the target, enabling smoother and less conservative safety enforcement. Furthermore, the adaptive CBF formulation reduces constraint conservatism when necessary to ensure feasibility under thruster input limitations. A tube-based nonlinear model predictive control scheme is developed to achieve robust docking with a moving target under input and CBF constraints. Robustness to bounded disturbances is ensured through a Lyapunov-based invariant tube, which guarantees bounded tracking errors. The efficacy of the proposed framework is demonstrated through software-in-the-loop Gazebo simulations and real-time hardware experiments, achieving docking under on/off actuation and in the presence of external disturbances.

Keywords: Mechatronics, Robust control, Linear parameter-varying systems
Abstract: This paper presents a frequency-domain procedure that selects a nominal model and a design bandwidth from frequency response functions (FRFs) measured under multiple operating conditions, and the procedure is applied to a hybrid gantry system with actuator asymmetry and payload variations. FRFs measured under representative payload conditions reveal significant coupling between actuators. To obtain a decoupled representation suitable for controller design, canonical polyadic decomposition (CPD) is applied to the measured FRFs to derive approximately frequency-invariant transformation matrices. The transformed system is evaluated using the relative gain array (RGA) to determine a feasible control bandwidth where diagonal dominance is preserved. Candidate nominal models are then compared using a frequency-domain robust stability condition based on the small-gain theorem. The results show that the nominal model corresponding to a balanced payload configuration provides a wider achievable robust bandwidth than the other cases, making it a suitable nominal model for disturbance observer design under payload variations.

Keywords: Hybrid systems, Attack Detection, Cyber-Physical Security
Abstract: This paper investigates the stealthy attack detection for sensor-fusion cyber-physical systems with unknown-but-bounded noises through the control channel. The detection framework is particularly applicable to sensor-fusion scenarios in which multiple suspicious sensors contributing to the fused estimate may be compromised simultaneously. First, we construct an admissible output set using secure sensors and an attack output set for each attack hypothesis. Then, we introduce a receding-horizon optimization framework to design exposure inputs, namely bounded auxiliary control perturbations injected through the control channel, so as to enlarge the separation between the admissible output set and the attack output sets according to the separation tendency. A sufficient detection condition is further derived, showing that set separation guarantees detectability of the compromised sensors. Moreover, an offline exposure budget guidance is developed to support budget selection before online exposure starts. Simulations on a UAV navigation system under stealthy GNSS and LiDAR attacks validate the proposed method.

Keywords: Distributed parameter systems, Sampled-data control
Abstract: The L2 residue separation method has recently emerged as an effective approach for designing finite-dimensional controllers for PDEs while avoiding spillover caused by neglected modes. This paper extends the method to sampled-data control and shows that it enables implementation via a standard zero-order hold in the cases where existing approaches require a less practical generalized hold mechanism. Specifically, we consider a semilinear reaction-diffusion equation with unknown nonlinearity, boundary heat-flux actuation, and temperature measurements taken at the opposite boundary. For this system, we design a finite-dimensional output-feedback controller whose parameters are chosen to eliminate potential spillover. Stability under sample-and-hold actuation is established via a Lyapunov-Krasovskii functional. The framework naturally extends to additional delay effects, including fast-varying input and network-induced delays, through appropriate augmentations of the Lyapunov-Krasovskii functional.

Keywords: Backstepping, Quantized systems, Event-triggered/resource-aware control
Abstract: We develop an observer-based, event-triggered backstepping control design for linear, 2 × 2 hyperbolic systems in which the available boundary measurement is subject to quantization. The design relies on two main elements--a) an observer-based event-triggered control law that employs only quantized measurements and b) a switching strategy that adjusts online the quantizer's range/error. We establish semiglobal exponential stability (in sup-norm) of the closed-loop system via i) derivation of input-to-state stability estimates for the plant-observer interconnection with respect to quantization- and sampling-induced disturbances and ii) establishing that the state remains within the range of the quantizer (if it does so at initial time), while subsequently converging to the origin, with a proper design of the adjustable parameter of the quantizer.

We illustrate the design in numerical simulations, including a performance comparison with a fixed-range/error quantizer.

Keywords: Stability of nonlinear systems, Distributed parameter systems
Abstract: We study an axial dispersion tubular reactor model governed by a nonlinear parabolic equation with Robin-type boundary conditions and boundary feedback control. We derive sufficient conditions for the exponential stability of the steady-state solution of the closed-loop system and provide an explicit estimate of the decay rate. In addition, numerical simulations are presented to illustrate the sharpness of the obtained decay rate for different choices of the feedback gain parameter.

Keywords: Networked control systems, Game theory, Robust control
Abstract: This paper develops an incentive-based mixed H_2/H_infinity Stackelberg defense strategy to mitigate false data injection (FDI) attacks in networked control systems. An incentive-driven framework is proposed in which a defender designs incentive mechanisms to influence rational attackers and induce team-oriented defense behavior. To this end, existing stochastic mixed H_2/H_infinity control results for discrete-time systems, which mainly rely on state-feedback designs, are extended to static output-feedback (SOF) control despite the inherent nonconvexity. By incorporating incentive mechanisms into a hierarchical game-theoretic framework, FDI attacks are treated as disturbance inputs, and both disturbance attenuation and performance optimization are achieved under a team-oriented defense strategy. Numerical results demonstrate the effectiveness of the proposed approach in maintaining robust system performance.

Keywords: Cyber-Physical Security, Game theory, Robust control
Abstract: This paper investigates an incentive-based Stackelberg game framework with mixed H_2/H_infty control constraints for defending networked control systems (NCSs) against false data injection (FDI) attacks. The defender--attacker interaction under a team-oriented defense objective is modeled as a hierarchical Stackelberg game, where the defender designs an H_2/H_infty control strategy while accounting for the Nash equilibrium behaviors of FDI attackers and external disturbances associated with two individual control inputs. An incentive mechanism is introduced to guide attackers toward actions consistent with the team-oriented defense objective. To characterize the resulting hierarchical Stackelberg equilibrium, the design problem with H_infty constraints is reformulated as a constrained optimization problem. Using a Lagrange multiplier approach, tractable equilibrium conditions are derived that provide a systematic framework for identifying feasible incentive gains and the corresponding Nash equilibrium. The proposed strategy achieves a balanced trade-off between defensive control effort and adversarial actions under prescribed H_infty performance constraints. Numerical simulations demonstrate the effectiveness and robustness of the proposed defense mechanism against FDI attacks.

Keywords: Estimation, Observers for Linear systems, Nonlinear output feedback
Abstract: This paper studies attack detection for discrete-time linear systems with stochastic process noise that produce both a vulnerable (i.e., attackable) linear measurement and a secured (i.e., unattackable) quadratic measurement. The motivating application of this model is a dynamic-game setting where the quadratic measurement is interpreted as a system-level utility or reward, and control inputs into the linear system are interpreted as control policies that, once applied, are known to all game participants and which steer the system towards a game-theoretic equilibrium (e.g., Nash equilibrium). To detect attacks on the linear channel, we develop a novel quadratic-utility-aware observer that leverages the secured quadratic output and enforces measurement consistency via a projection step. We establish three properties for this observer: feasibility of the true state, prox-regularity of the quadratic-constraint set, and a monotone error-reduction guarantee in the noise-free case. To detect adversarial manipulation, we compare linear and quadratic observer trajectories using a wild bootstrap maximum mean discrepancy (MMD) test that provides valid inference under temporal dependence. We validate our framework using numerical experiments of a pursuit–evasion game, where the quadratic observer preserves estimation accuracy under linear-sensor attacks, while the statistical test detects distributional divergence between the observers’ trajectories.

Keywords: Game theory, Queueing systems, Safety-critical control
Abstract: Modern Graphics Processing Unit (GPU)-backed services must satisfy strict latency service-level objectives (SLOs) while controlling spare-capacity costs. In multi-tenant GPU cloud platforms, this trade-off is inherently dynamic because workload demand is endogenous; specifically, pricing shapes the submissions of heterogeneous tenants, which subsequently impact congestion and delay. We formulate the joint pricing-and-scaling problem as a large-population Stackelberg game problem, and we derive an explicit equilibrium demand map. The resulting closed-loop model reveals a structural failure mode in which delay-insensitive workloads sustain a residual demand floor, making the backlog undrainable under bounded price and service capacity. This observation motivates a computable drainability guardrail that certifies uniformly negative backlog drift in the residual-demand regime. For any fixed price-capacity pair satisfying the drainability guardrail, we establish global convergence to a unique operating point under a checkable step-size condition. Building on this fixed-pair analysis, we further develop an optimizer agnostic action shield that provides a negative-drift certificate for shielded execution in the residual regime of the dynamic problem and show empirically that it improves safety and robustness for model-free reinforcement learning (RL) in this setting.

Keywords: Delay systems, Stability of linear systems
Abstract: This article describes the set of stabilizing parameters for a double integrator using two delayed feedback gains. The system is normalized so that the parameter space becomes 3-dimensional. A stability analysis for a given gain ratio is obtained using the stability crossing curves with two delays as the parameters. A global geometric description of the stable region is obtained by analyzing the evolution and bifurcation of stability crossing curves as the gain ratio changes.

Keywords: Communication networks, Delay systems, Stability of nonlinear systems
Abstract: We study the strong stability of Max-Weight scheduling in wireless queueing systems with both observation and control-input delays. In these systems, channel state information reaches an edge controller only after measurement and reporting latency, while the selected schedule is implemented after an additional actuation delay, creating a decision--execution mismatch. Although prior work has studied delayed state information and scheduling delays separately, a unified stability analysis under simultaneous observation and control-input delays remains lacking. We develop a Lyapunov--Foster framework for the resulting stochastic delayed difference inclusion. The main result gives an explicit sufficient condition for strong stability and a closed-form bound on the time-average backlog. The condition separates delayed-observation and delayed-execution effects through two penalty terms, clarifying how each delay mechanism reduces the available stability margin. Numerical experiments connect the sufficient condition to empirical behavior and indicate that, in the tested regimes, control-input delay has a stronger impact on backlog growth than observation delay.

Keywords: Delay systems, Chemical process control, Time-varying systems
Abstract: In the present paper, we give the global robust stability for a class of complex balanced chemical reaction networks satisfying the conditions of the Deficiency Zero Theorem, subjected to both arbitrary time delays and time-varying perturbations. We prove that if the system possesses no boundary equilibria and the time-varying perturbations are bounded and asymptotically decay to zero, any positive solution to the non-autonomous delay differential equation converges to a unique positive complex balanced equilibrium point of the unperturbed autonomous system, determined by the corresponding conservation quantities. To achieve this, we formulate a non-autonomous Lyapunov-Krasovskii functional and utilize Barbalat's lemma alongside the invariant properties of the omega-limit set. Finally, we provide a biochemical example of a reversible competitive inhibition network to demonstrate the validity and applicability of our theoretical results.

Keywords: Biomedical, Extremum seeking, Metabolic systems
Abstract: Automated insulin delivery (AID) systems are often tuned for the population and offer limited online adaptation to the inter- and intrapatient variability in insulin needs caused by meal patterns, physical activity, and fluctuations in insulin sensitivity. We present a real-time, data-driven personalization approach that adapts controller parameters using the subject's daily glycemic data. The adaptation is formulated as projected gradient descent on a daily risk metric, where the gradient estimation is designed to attenuate noise and metabolic variability. We use contraction theory to validate the optimization framework and convergence of the closed-loop system under adaptation. In silico experiments on the 100-adult cohort of the FDA-accepted UVA/Padova T1D simulator show that our method improves glycemic risk and increases time-in-range (TIR, 70-180mg/dL) by 2%, 3%, and 4% after 4, 8, and 17 weeks, respectively, under variability in meal timing, meal size, and insulin sensitivity.

Keywords: Optimization, Optimization algorithms
Abstract: This paper introduces the generalized quaternionic Stiefel manifold and studies its geometry for Riemannian optimization. We clarify its relationships with existing manifolds, especially the real generalized Stiefel manifold and the quaternionic Stiefel manifold, and derive explicit expressions for several geometric quantities on the proposed manifold. In particular, the generalized quaternionic Stiefel manifold is regarded as a real Riemannian manifold, and expressions for the tangent space, normal space, the orthogonal projection onto the tangent space, a retraction, and a vector transport on this manifold are derived. Some numerical experiments for the generalized quaternionic eigenvalue problem and a version of quaternionic canonical correlation analysis are performed by Riemannian optimization methods to demonstrate the viability of the proposed optimization framework.

Keywords: Optimization algorithms, Optimization, Numerical algorithms
Abstract: Nonconvex optimization underlies many modern machine learning and control tasks, where saddle points pose the dominant obstacle to reliable convergence in high-dimensional settings. Escaping these saddle points deterministically using continuous-time optimization remains an open challenge: gradient descent is blind to curvature, stochastic perturbation methods lack deterministic guarantees, and Newton-type approaches suffer from Hessian singularity. Adopting the perspective of viewing optimization algorithms as dynamical systems, we present Curvature-Regularized Gradient Dynamics (CRGD), which augments the objective with a smooth penalty on the negative Hessian eigenvalues, yielding an augmented cost that serves as an optimization Lyapunov function with user-selectable convergence rates to second-order stationary points. Numerical experiments confirm that CRGD converges to second-order stationary points, even in regimes where gradient descent fails.

Keywords: Statistical learning, Algebraic/geometric methods, Variational methods
Abstract: Bayesian inference on Lie groups is fundamental in robotics and control, where orientations and poses evolve on nonlinear manifolds, such as SO(3) and SE(3). For these problems, particle-based approximations are often required since closed-form solutions are often unavailable, and Euclidean methods do not transfer directly. Stein variational gradient descent (SVGD) provides a flexible framework for particle-based Bayesian inference using score-function information, but it often converges too slowly for practical use. This paper introduces momentum-accelerated Lie group SVGD for concentrated target distributions on Lie groups. Two accelerated schemes are derived by incorporating Polyak heavy-ball and Nesterov-type momentum into the Lie group SVGD updates. The resulting methods preserve the structure and computational complexity of standard Lie group SVGD while yielding improved convergence behavior. Simulation studies on SO(3) and SE(3), including a Bayesian fusion example, demonstrate faster convergence in comparison to standard Lie group SVGD. The proposed approach provides an effective extension of particle-based variational inference on Lie groups for control applications.

Keywords: Optimization algorithms, Optimization
Abstract: Proximal bundle methods (PBM) are a powerful class of algorithms for convex optimization. Compared to gradient descent, PBM constructs more accurate surrogate models that incorporate gradients and function values from multiple past iterations, which leads to faster and more robust convergence. However, for smooth convex problems, PBM only achieves an O(1/k) convergence rate, which is inferior to the optimal O(1/k^2) rate. To bridge this gap, we propose an accelerated proximal bundle method (APBM) that integrates Nesterov’s momentum into PBM.We prove that under standard assumptions, APBM achieves the optimal O(1/k2) convergence rate. Numerical experiments demonstrate the effectiveness of the proposed APBM.