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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Keywords: Autonomous vehicles, Autonomous systems, Cooperative control
Abstract: Emerging mobility systems are an example of Cyber-Physical Systems (CPSs) in which multiple autonomous agents (vehicles) interact with each other as well as with the infrastructure resources (road side units, traffic lights, etc). Control-theoretic and optimization methods provide a rich framework for managing these complex mixed-traffic socioeconomic multi-agent systems. Given the complexity involved and the abundance of data now available, it is essential to integrate learning-based methods not only to design optimal controllers with safety guarantees, but to also gain an understanding of human driving behavior, as well as user preferences for the mobility options that intelligent transportation systems provide. The three objectives of this tutorial paper are: (1) Set the stage for emerging mobility systems consisting of both autonomous and human-driven vehicles in a mixed traffic environment by formulating basic optimal control problems for autonomous vehicles that seek to jointly optimize travel time, energy, and comfort while ensuring that safety constraints are always satisfied. (2) Present methods for solving the formulated problems using a combination of optimization techniques and Control Barrier Functions (CBFs) that provide safety guarantees, as well as state of the art learning-based methods to design effective controllers for mixed traffic transportation systems. (3) Address the societal issues accompanying emerging mobility systems, including new metrics that incorporate accessibility and fairness in a transportation network consisting of both autonomous and human-driven vehicles.

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

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

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

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

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

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

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

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

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

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

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

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

Keywords: Nonlinear systems, PID control
Abstract: We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the output has a single-peaked period. Under the assumption that the linear system is stable and has an impulse response that is strictly monotonically decreasing on its infinite support, we take a novel approach in using the framework of total positivity to address our main question. It is shown that unimodal self-oscillations can only exist if the number of positive and negative elements in a period coincides. Based on this result, we derive conditions for the existence of such oscillations, determine bounds on their periods, and address the question of uniqueness.

Keywords: Compartmental and Positive systems, Stability of nonlinear systems, Decentralized control
Abstract: Almost every bounded trajectory of a strongly monotone system converges to an equilibrium. Relying on this, we derive a component-wise sufficient condition for multi-stability of monotone networks. We first show that a network is strongly monotone if each monotone subsystem is excitable and transparent, and every interconnection preserves monotonicity in a strong sense. Next, all trajectories of a network are bounded if each subsystem is input-to-state stable (ISS), and every interconnection function is bounded; we derive a sufficient condition for ISS tailored to monotone systems. Finally, we present a component-wise instability condition of an equilibrium for a network based on linearization, where instability guarantees the existence of multiple attracting equilibria.

Keywords: Reinforcement learning, Learning, Machine learning
Abstract: Domain randomization (DR) enables sim-to-real transfer by training controllers on a distribution of simulated environments, with the goal of achieving robust performance in the real world. Although DR is widely used in practice and is often solved using simple policy gradient (PG) methods, understanding of its theoretical guarantees remains limited. Toward addressing this gap, we provide the first convergence analysis of PG methods for domain-randomized linear quadratic regulation (LQR). We show that PG converges globally to the minimizer of a finite-sample approximation of the DR objective under suitable bounds on the heterogeneity of the sampled systems. We also quantify the sample-complexity associated with achieving a small performance gap between the sample-average and population-level objectives. Additionally, we propose and analyze a discount-factor annealing algorithm that obviates the need for an initial jointly stabilizing controller, which may be challenging to find. Empirical results support our theoretical findings and highlight promising directions for future work, including risk-sensitive DR formulations and stochastic PG algorithms.

Keywords: Intelligent systems, Identification
Abstract: Identifying high-emission vehicles is a crucial step in regulating urban pollution levels and formulating traffic emission reduction strategies. However, in practical monitoring data, the proportion of high-emission state data is significantly lower compared to normal emission states. This characteristic long-tailed distribution severely impedes the extraction of discriminative features for emission state identification during data mining. Furthermore, the highly nonlinear nature of vehicle emission states and the lack of relevant prior knowledge also pose significant challenges to the construction of identification models.To address the aforementioned issues, we propose a Set-Valued Transformer Network (SVTN) to achieve comprehensive learning of discriminative features from high-emission samples, thereby enhancing detection accuracy. Specifically, this model first employs the transformer to measure the temporal similarity of micro-trip condition variations, thus constructing a mapping rule that projects the original high-dimensional emission data into a low-dimensional feature space. Next, a set-valued identification algorithm is used to probabilistically model the relationship between the generated feature vectors and their labels, providing an accurate metric criterion for the classification algorithm. To validate the effectiveness of our proposed approach, we conducted extensive experiments on the diesel vehicle monitoring data of Hefei city in 2020. The results demonstrate that our method achieves a 9.5% reduction in the missed detection rate for high-emission vehicles compared to the transformer-based baseline, highlighting its superior capability in accurately identifying high-emission mobile pollution sources.

Keywords: Network analysis and control, Linear systems
Abstract: This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the effect of nodal dynamics in the interconnected system, we propose a new quantitative index of network complexity rooted in the notion of McMillan degree of a linear system. First, we show that network systems with the same interconnection pattern share the same complexity index for almost all choices of their interconnection weights. Then, we investigate the dependence of the proposed index on the topology of the network and the degree of heterogeneity of the nodal dynamics. Specifically, we find that the index depends on the matching number of subgraphs identified by nodal dynamics of different nature, highlighting the joint impact of network architecture and component diversity on overall system complexity.

Keywords: Optimization algorithms, Large-scale systems, Networked control systems
Abstract: In this paper, we investigate the problem of decentralized consensus optimization over directed graphs with limited communication bandwidth. We introduce a novel decentralized optimization algorithm that combines the Reduced Consensus Augmented Lagrangian Alternating Direction Inexact Newton (RC-ALADIN) method with a finite time quantized coordination protocol, enabling quantized information exchange among nodes. Assuming the nodes' local objective functions are mu-strongly convex and simply smooth, we establish global convergence at a linear rate to a neighborhood of the optimal solution, with the neighborhood size determined by the quantization level. Additionally, we show that the same convergence result also holds for the case where the local objective functions are convex and L-smooth. Numerical experiments demonstrate that our proposed algorithm compares favorably against algorithms in the current literature while exhibiting communication efficient operation.

Keywords: Optimization algorithms, Large-scale systems, Networked control systems
Abstract: Distributed optimization and learning algorithms are designed to operate over large scale networks enabling processing of vast amounts of data effectively and efficiently. One of the main challenges for ensuring a smooth learning process in gradient-based methods is the appropriate selection of a learning stepsize. Most current distributed approaches let individual nodes adapt their stepsizes locally. However, this may introduce stepsize heterogeneity in the network, thus disrupting the learning process and potentially leading to divergence. In this paper, we propose a distributed learning algorithm that incorporates a novel mechanism for automating stepsize selection among nodes. Our main idea relies on implementing a finite time coordination algorithm for eliminating stepsize heterogeneity among nodes. We analyze the operation of our algorithm and we establish its convergence to the optimal solution. We conclude our paper with numerical simulations for a linear regression problem, showcasing that eliminating stepsize heterogeneity enhances convergence speed and accuracy against current approaches.

Keywords: Autonomous robots
Abstract: This paper addresses the problem of autonomous robot navigation in unknown, obstacle-filled environments with second-order dynamics by proposing a Dissipative Avoidance Feedback (DAF). Compared to the Artificial Potential Field (APF), which primarily uses repulsive forces based on position, DAF employs a dissipative feedback mechanism that accounts for both position and velocity, contributing to smoother and more natural obstacle avoidance. The proposed continuously differentiable controller solves the motion-to-goal problem while guaranteeing collision-free navigation by using the robot's state and local obstacle distance information. We show that the controller guarantees safe navigation in generic n-dimensional environments and achieves Almost Global Asymptotic Stability (AGAS) under certain curvature conditions. Designed for real-time implementation, DAF requires only locally measured data from limited-range sensors (e.g., LiDAR, depth cameras), making it particularly effective for robots navigating unknown workspaces. Simulations in 2D and 3D environments are conducted to validate the theoretical results and showcase the effectiveness of our approach.

Keywords: Robotics, Autonomous robots
Abstract: In this paper, we develop a fast mixed-integer convex programming (MICP) framework for multi-robot navigation by combining graph attention networks and distributed optimization. We formulate a mixed-integer optimization problem for receding horizon motion planning of a multi-robot system, taking into account the surrounding obstacles. To address the resulting multi-agent MICP problem in real time, we propose a framework that utilizes heterogeneous graph attention networks to learn the latent mapping from problem parameters to optimal binary solutions. Furthermore, we apply a distributed proximal alternating direction method of multipliers algorithm for solving the convex continuous optimization problem. We demonstrate the effectiveness of our proposed framework through experiments conducted on a robotic testbed.