Keywords: Biomedical, Compartmental and Positive systems, Control applications
Abstract: A novel interval predictor-based controller is presented to solve the Bispectral Index (BIS) regulation problem in anesthetic procedures where propofol and remifentanil are employed together. The resulting control scheme does not require observing or filtering the drug concentrations on the patient's effect--site from the BIS signal. Knowing a feasible interval of initial conditions is enough to ensure the convergence of the regulation errors to some compact sets around the origin despite perturbations in the pharmacodynamics and pharmacokinetics models. Some simulations, considering different in silico patients, are included to illustrate the implementability of the methods.

Keywords: Biological systems, Biomedical, Emerging control applications
Abstract: Can border controls and travel restrictions suppress epidemics? This is an important and recurring question for public health policymaking and pandemic preparedness. Although there is a consensus that infections imported from external locations are critical to sustaining local epidemic growth and driving the endemic equilibria of the disease, there remains ongoing debate on the effectiveness of interventions aimed at curbing importations. Most studies contributing to this debate rely on complex metapopulation models that preclude generalisable insights and formal control principles are rarely used. Here we demonstrate how classical control theory applied to an analytic but flexible and widely used transmission model provides compelling evidence that border and travel restrictions fail to stabilise spread. These restrictions always enter as precompensators and hence fail to shift the epidemic poles. Consequently, regions cannot respond to emergent outbreaks in isolation. We find that coordinating interventions across both the local and external regions converts precompensation into feedback control and derive new criteria for overall stability. We further develop formulae specifying how border controls shape performance, such as disease equilibria and total infections. During growing epidemic phases, cooperative control is crucial for stability. Once stability is assured, border control can be sufficient to meet performance targets.

Keywords: Model/Controller reduction, Optimization, Uncertain systems
Abstract: Zonotopes are a widely used set representation in set-based computations due to their compact representation size and their closure under many relevant set operations. However, certain set operations, such as the Minkowski sum, increase the zonotope order, which in turn increases the computational cost of further computations. To address this issue, various order reduction techniques have been proposed, most of which focus on overapproximating the original zonotope. While overapproximations are crucial for safety verification, some applications - such as reachset-conformant identification and backward reachability analysis - require underapproximations (also referred to as inner-approximations). Besides providing a comprehensive survey of existing underapproximative order reduction methods, we propose four novel reduction methods in this paper. We analyze the computational cost of all methods and evaluate the tightness of the resulting underapproximations through numerical experiments on more than 2000 randomly generated zonotopes. The results demonstrate that our proposed methods achieve a favorable balance between computational efficiency and approximation accuracy, making them well-suited for applications in control, estimation, and system identification.

Keywords: Lyapunov methods, Data driven control, Neural networks
Abstract: We consider the problem of verifying safety for continuous-time dynamical systems. Developing upon recent advancements in data-driven verification, we use only a finite number of sampled trajectories to learn a barrier certificate, namely a function which verifies safety. We train a safety-informed neural network to act as this certificate, with an appropriately designed loss function to encompass the safety conditions. In addition, we provide probabilistic generalisation guarantees from discrete samples of continuous trajectories, to unseen continuous ones. Numerical investigations demonstrate the efficacy of our approach and contrast it with related results in the literature.

Keywords: Reduced order modeling, Modeling, Model/Controller reduction
Abstract: While approximating dynamical systems, one may be interested in preserving physical insights of specific states of the underlying system, which can be achieved by fixing the output map of the approximated model. In this paper we derive a class of reduced-order models that achieve moment matching while enforcing an output map chosen by the designer. We show that such models can be constructed even without the knowledge of the underlying system by using data generated from some experiments. In doing so, we highlight how the proposed method can be utilized to enforce input-output behavior, such as passivity, negative imaginary, and/or finite gain, in the reduced-order model, thus providing provable guarantees on various user-specified requirements. We demonstrate this aspect through several examples.

Keywords: Reinforcement learning, Optimal control
Abstract: This paper proposes tackling safety-critical stochastic Reinforcement Learning (RL) tasks with a sample-based, model-based approach. At the core of the method lies a Model Predictive Control (MPC) scheme that acts as function approximation, providing a model-based predictive control policy. To ensure safety, a probabilistic Control Barrier Function (CBF) is integrated into the MPC controller. To approximate the effects of stochasticies in the optimal control formulation and to fulfil the probabilistic CBF condition, a sample-based approach with guarantees is employed. Furthermore, to counterbalance the additional computational burden due to sampling, a learnable terminal cost formulation is included in the MPC objective. An RL algorithm is deployed to learn both the terminal cost and the CBF constraint. Results from a numerical experiment on a constrained LTI problem corroborate the effectiveness of the proposed methodology in reducing computation time while preserving control performance and safety.

Keywords: Statistical learning, Reinforcement learning, Game theory
Abstract: In this paper, we expand the Bayesian persuasion framework to account for unobserved confounding variables in sender-receiver interactions. While traditional models typically assume that belief updates follow Bayesian principles, real-world scenarios often involve hidden variables that impact the receiver’s belief formation and decision-making. We conceptualize this as a sequential decision-making problem, where the sender and receiver interact over multiple rounds. In each round, the sender communicates with the receiver, who also interacts with the environment. Crucially, the receiver’s belief update is affected by an unobserved confounding variable. By reformulating this scenario as a Partially Observable Markov Decision Process (POMDP), we capture the sender’s incomplete information regarding both the dynamics of the receiver’s beliefs and the unobserved confounder. We prove that finding an optimal observation-based policy in this POMDP is equivalent to solving for an optimal signaling strategy in the original persuasion framework. Furthermore, we demonstrate how this reformulation facilitates the application of proximal learning for off-policy evaluation (OPE) in the persuasion process. This advancement enables the sender to evaluate alternative signaling strategies using only observational data from a behavioral policy, thus eliminating the necessity for costly new experiments.

Keywords: Cooperative control, Autonomous systems, Robotics
Abstract: In this paper, we propose an equilibrium-driven controller that enables a marsupial carrier-passenger robotic system to achieve smooth carrier-passenger separation and then to navigate the passenger robot toward a predetermined target point. To achieve smooth separation and navigation, we design a third-order potential gradient for the passenger's controller as a function of the carrier-passenger and carrier-target distances in the moving carrier robot's coordinate frame, which introduces three equilibrium points in the closed-loop error system, each corresponding to one of the following three scenarios: the passenger robot is (i) staying on the carrier robot, (ii) positioned between the carrier robot and the target, and (iii) reaching the target. Initially, the passenger robot is confined to the carrier robot, namely within the attraction region of the equilibrium point~(i). By appropriately decreasing the carrier-target distance, the equilibrium point (ii) vanishes, and the attraction and repulsion regions of equilibrium points (i) and (iii) change accordingly. This transition guides the passenger robot to leave the equilibrium point (i) and approach the equilibrium point (iii), which enables a smooth carrier-passenger separation and seamless navigation to the target. Furthermore, rigorous convergence analysis is also provided. Finally, 2D and 3D simulations are conducted to demonstrate the effectiveness and adaptability of the proposed controller facing obstacle in the surroundings.

Keywords: Cooperative control, Intelligent systems, Agents-based systems
Abstract: The safe optimal coordination control problem is addressed for partially-unknown input-constrained air-ground systems under hybrid cyberattacks. Adversaries can launch denial-of-service attacks to prevent data transmission and channel manipulation attacks to tamper with interaction data. A unified distributed observer-based optimal control framework is first proposed for the heterogeneous vehicles. To achieve consensus under hybrid cyberattacks, the Zeno-free switching-type self-triggered observer is constructed based on only viable faulting neighborhood data. Then, optimal input-constrained control policies are learned via an on-policy actor-critic neural network-based learning algorithm. Sufficient conditions to guarantee the stability of the closed-loop system under the modeled hybrid cyberattacks are established. Numerical examples validate the effectiveness of the developed approach.

Keywords: Distributed control, Control of networks, Cooperative control
Abstract: In recent years, numerous extended rigidity theories have been developed by considering different types of local constraints, to adapt to formation control in different scenarios. Among them, the signed angle constraint has attracted considerable interest for its exceptional ability to stabilize coordinate-free formations with high degrees of freedom. Unfortunately, the combinatorial aspects of signed angle rigidity remain largely unexplored. In this paper, we study signed angle rigidity theory in the context of frameworks and prove its complete equivalence to bearing rigidity theory in the plane for the first time. Building on this equivalence, we propose a distributed formation controller based on signed angle measurements only, which achieves global stability as long as the formation framework is infinitesimally signed angle rigid. A simulation example demonstrates the effectiveness of our results.

Keywords: Estimation, Cooperative control, Autonomous systems
Abstract: This paper introduces a framework of localizing and tracking a non-cooperative target by using two pursuers which are assumed to have measurements of self-displacements and interior angles of the triangle formed by the target and the pursuers. First, based on the geometric relationship between the target and pursuers, an {measurement} model is derived from the pursuers' measured interior angles and self-displacements. Combined with the state-transition model, a linear time-varying Kalman filter is designed to estimate the relative position and velocity between the target and the pursuers. Then, a fully actuated control law is designed by using the parametric design approach to achieve the target tracking task, which dynamically adjusts pursuers' trajectories. Finally, simulations demonstrate the proposed framework’s localization and tracking performance for targets with dynamic maneuvering capability.

Keywords: Variable-structure/sliding-mode control
Abstract: The paper deals with a well-posedness analysis for discontinuous infinite-dimensional systems, which can be regularized by means of the conventional (finite-dimensional) Filippov method. The study is inspired by sliding mode control theory. Sliding mode controllers for infinite-dimensional systems with finite- and infinite-dimensional sliding surfaces are designed. Theoretical results are supported by an example of an output-based sliding mode control for heat system.

Keywords: Variable-structure/sliding-mode control, Robust control, Nonlinear systems
Abstract: This paper develops a nonsingular predefined-time terminal sliding mode control scheme based on smooth sliding surfaces with artificial time-delays. The proposed approach can achieve predefined-time control for perturbed chains of integrators with matched and mismatched disturbances. Especially, for double integrators, an initial-condition-based sufficient condition is provided to preserve the prescribed-time stability in the presence of bounded matched disturbances.

Keywords: Markov processes, Reinforcement learning, Computer/Network Security
Abstract: With the growing sophistication of cybersecurity threats, artificial intelligence driven defense solutions have gained significant attention, particularly reinforcement learning based approaches, which make sequential decisions based on the latest network information. Despite their success in adaptability, scalability, and real-time response, these methods remain highly vulnerable to adversarial deception—strategic manipulations that distort the defender’s perception of the network security state. This paper introduces a budget-constrained adversarial model, in which an attacker deploys decoys to mislead the defender about the true state of network compromises, disrupting effective and timely decision-making. Deception is formulated as an augmented Markov Decision Process, allowing an intelligent adversary to account for the defender’s perception of network compromises and anticipate defensive actions. An optimal deception policy is derived, enabling the strategic placement of decoys to maximize long-term security degradation while evading detection. A worst-case theoretical bound is established to quantify the long-term impact of deception on network security. Numerical experiments demonstrate that even minimal decoy-based deception significantly weakens network security, particularly against deterministic defense policies.

Keywords: Reinforcement learning, Statistical learning, Decentralized control
Abstract: Recently, there has been a surge of interest in decentralized learning approaches to tackle complex collaborative tasks in multi-agent systems. One of the most promising approaches is multi-agent reinforcement learning (MARL). Yet, as the number of agents becomes larger, the sample complexity in MARL increases exponentially, making scalability a fundamental issue. Networked MARL algorithms can address this issue by leveraging a communication network for information exchange between the agents. For homogeneous network MARL, previous research established a regret upper-bound sqrt{MH^4SAT}. Recent approaches rely on global knowledge about the structure of the communication network, which poses a serious limitation when it is not known or changes depending on the task. In this paper, we overcome this limitation by proposing a novel networked MARL algorithm with an upper-confidence bound (UCB) exploration strategy, called provably efficient local-information networked (PrELIN) MARL, that does not require any global information but only relies on the local interactions between the agents. Furthermore, we derive the regret and sample complexity for our algorithm and show that the regret bound may still remain sublinear.

Keywords: Statistical learning, Stochastic systems
Abstract: We derive a finite-sample probabilistic bound on the parameter estimation error of a system identification algorithm for Linear Switched Systems. The algorithm estimates Markov parameters from a single trajectory and applies a variant of the Ho-Kalman algorithm to recover the system matrices. Our bound guarantees statistical consistency under the assumption that the true system exhibits quadratic stability. The proof leverages the theory of weakly dependent processes. To the best of our knowledge, this is the first finite-sample bound for this algorithm in the single-trajectory setting.

Keywords: Statistical learning, Data driven control, Optimization
Abstract: We investigate the Probably Approximately Correct (PAC) property of scenario decision algorithms, which refers to their ability to produce decisions with an arbitrarily low risk of violating unknown safety constraints, provided a sufficient number of realizations of these constraints are sampled. While several PAC sufficient conditions for such algorithms exist in the literature---such as the finiteness of the VC dimension of their associated classifiers, or the existence of a compression scheme---it remains unclear whether these conditions are also necessary. In this work, we demonstrate through counterexamples that these conditions are not necessary in general. These findings stand in contrast to binary classification learning, where analogous conditions are both sufficient and necessary for a family of classifiers to be PAC. Furthermore, we extend our analysis to stable scenario decision algorithms, a broad class that includes practical methods like scenario optimization. Even under this additional assumption, we show that the aforementioned conditions remain unnecessary. Furthermore, we introduce a novel quantity, called the dVC dimension, which serves as an analogue to the VC dimension for scenario decision algorithms. We prove that the finiteness of this dimension is a PAC necessary condition for scenario decision algorithms. This allows to (i) guide algorithm users and designers to recognize algorithms that are not PAC, and (ii) contribute to a comprehensive characterization of PAC scenario decision algorithms.

Keywords: Learning, Estimation, Statistical learning
Abstract: In this brief paper, we present a naive aggregation algorithm for a typical learning problem with expert advice setting, in which the task of improving generalization, i.e., model validation, is embedded in the learning process as a sequential decision-making problem. In particular, we consider a class of learning problem of point estimations for modeling high-dimensional nonlinear functions, where a group of experts update their parameter estimates using the discrete-time version of gradient systems, with small additive noise term, guided by the corresponding subsample datasets obtained from the original dataset. Here, our main objective is to provide conditions under which such an algorithm will sequentially determine a set of mixing distribution strategies used for aggregating the experts' estimates that ultimately leading to an optimal parameter estimate, i.e., as a consensus solution for all experts, which is better than any individual expert's estimate in terms of improved generalization or learning performances. Finally, as part of this work, we present some numerical results for a typical case of nonlinear regression problem.

Keywords: Decentralized control, Iterative learning control, Optimization
Abstract: Data centers are hitting a bottleneck in available power as the demand for computations increases, and sustainable power management has emerged as a key challenge in green computing. We propose algorithms to scalably manage power across servers and solutions to guarantee and hasten convergence in the power trajectory. This makes power use more efficient and stable, and provides a broad class of pricing functions to discourage excessive power consumption. A foundational framework is established to optimizing power-aware servers. We provide proofs of convergence with guarantees on rates. Simulations support our theory.

Keywords: Decentralized control, Optimal control, Building and facility automation
Abstract: What is the performance cost of using simple, decoupled control policies in inherently coupled systems? Motivated by industrial refrigeration systems, where centralized compressors exhibit economies of scale yet traditional control employs decoupled room-by-room temperature regulation, we address this question through the lens of multi-location inventory control. Here, a planner manages multiple inventories to meet stochastic demand while minimizing costs that are coupled through nonlinear ordering functions reflecting economies of scale. Our main contributions are: (i) a surprising equivalence result showing that optimal stationary base-stock levels for individual locations remain unchanged despite coupling when restricting attention to decoupled strategies; (ii) tight performance bounds for simple decoupled policies relative to optimal coupled policies, revealing that the worst-case ratio depends solely on the degree of nonlinearity in the ordering cost function; and (iii) an analysis of a practical online algorithm that achieves competitive performance without solving complex dynamic programs. Numerical simulations demonstrate that while decoupled policies significantly outperform their worst-case guarantees in typical scenarios, they still exhibit meaningful suboptimality compared to fully coordinated strategies. These results provide actionable guidance for system operators navigating the trade-off between control complexity and operational efficiency in coupled systems.

Keywords: Network analysis and control, Large-scale systems, Computational methods
Abstract: Optimal sensor placement is essential for state estimation and effective network monitoring. As known in the literature, this problem becomes particularly challenging in large-scale undirected or bidirected cyclic networks with parametric uncertainties, such as water distribution networks (WDNs), where pipe resistance and demand patterns are often unknown. Motivated by the challenges of cycles, parametric uncertainties, and scalability, this paper proposes a sensor placement algorithm that guarantees structural observability for cyclic and acyclic networks with parametric uncertainties. By leveraging a graph-based strategy, the proposed method efficiently addresses the computational complexities of large-scale networks. To demonstrate the algorithm's effectiveness, we apply it to several EPANET benchmark WDNs. Most notably, the developed algorithm solves the sensor placement problem with guaranteed structural observability for the L-town WDN with 1694 nodes and 124 cycles in under 0.1 seconds.

Keywords: Control of networks, Optimization, Lyapunov methods
Abstract: We consider a distributed cloud service deployed at a set of distinct server pools. Arriving jobs are classified into heterogeneous types, in accordance with their setup times which are differentiated at each of the pools. A dispatcher for each job type controls the balance of load between pools, based on decentralized feedback. The system of rates and queues is modeled by a fluid differential equation system, and analyzed via convex optimization. A first, myopic policy is proposed, based on task delay-to-service. Under a simplified dynamic fluid queue model, we prove global convergence to an equilibrium point which minimizes the mean setup time; however queueing delays are incurred with this method. A second proposal is then developed based on proximal optimization, which explicitly models the setup queue and is proved to reach an optimal equilibrium, devoid of queueing delay. Results are demonstrated through a simulation example.

Keywords: Optimization algorithms
Abstract: Optimization algorithms for time-varying cost functions extend classical methods, which cannot track dynamic minima. However, they typically assume access to the partial derivative of the cost function with respect to time. This is an assumption not satisfied in many situations where, although the time-varying parameters can be measured, either their time-derivatives or their model are unknown.

Distributed optimization algorithms for time-varying costs typically inherit these limitations and introduce additional challenges, such as requiring each node to measure the time-varying parameters its local cost depends on. This work addresses these issues by first developing a centralized time-varying optimization algorithm that ensures convergence to a bounded neighborhood of the optimal trajectory. We then extend it to a distributed framework, relaxing the aforementioned measurement requirements. The effectiveness of our approach is validated through numerical examples of varying complexity.

Keywords: Algebraic/geometric methods, Optimization algorithms, Optimal control
Abstract: A fundamental issue at the core of trajectory optimization on smooth manifolds is handling the implicit manifold constraint within the dynamics. The conventional approach is to enforce the dynamic model as a constraint. However, we show that this approach leads to significantly redundant operations, as well as being heavily dependent on the state space representation. Specifically, we propose an intrinsic successive convexification methodology for optimal control on smooth manifolds. This so-called iSCvx is then applied to a representative example involving attitude trajectory optimization for a spacecraft subject to non-convex constraints.

Keywords: Optimization algorithms, Numerical algorithms, Machine learning
Abstract: This paper studies properties of fixed points of generalised Extra-gradient (GEG) algorithms applied to min- max problems. We discuss connections between saddle points of the objective function of the min-max problem and GEG fixed points. We show that, under appropriate step-size selections, the set of local saddle points (local Nash equilibria) is a subset of locally stable fixed points of GEG. Convergence properties of the GEG algorithm are obtained through a stability analysis of a discrete-time dynamical system. The results when compared to existing methods are illustrated through numerical examples.

Keywords: Optimization algorithms, Robust control
Abstract: We propose a novel approach for analyzing dynamic regret of first-order online convex optimization (OCO) algorithms for strongly convex and Lipschitz-smooth objectives. Crucially, we provide a general analysis that is applicable to a wide range of first-order algorithms that can be expressed as an interconnection of a linear dynamical system in feedback with a first-order oracle. By leveraging Integral Quadratic Constraints (IQCs), we derive a semi-definite program which, when feasible, provides a regret guarantee for the online algorithm. For this, the concept of variational IQCs is introduced as the generalization of IQCs to time-varying monotone operators. Our bounds capture the temporal rate of change of the problem in the form of the path length of the time-varying minimizer and the objective function variation. In contrast to standard results in OCO, our results do not require neither the assumption of gradient boundedness, nor that of a bounded feasible set. Numerical analyses showcase the ability of the approach to capture the dependence of the regret on the function class condition number.

Keywords: Game theory, Machine learning, Cooperative control
Abstract: We consider a game with N cooperative players that have a global objective. Simple distributed algorithms such as gradient play often converge to a Nash equilibrium (NE). However, a NE typically suffers from poor global performance. Converging to the global optimum requires explicit communication and coordination. In this paper, we propose a new approach to improve the performance at NE. Our method uses machine learning offline training to design games with efficient NE. In particular, we use a dataset of games with parameters coming from a certain distribution (e.g., uniformly random player locations). We then train a deep neural network (DNN) where the input is the local measurement available to the player and the output is the reward parameters that best approximate the global objective. We demonstrate our approach for two %three classes of games: energy games and wireless power control games. Our approach offers significant performance boosts while requiring no communication between the players and no complexity increase in real-time.

Keywords: Mean field games, Large-scale systems, Nonlinear systems
Abstract: The paper studies a nonlinear mean field game (MFG) model based on McKean-Vlasov (MV) approximation, which involves multiple major agents and multiple populations of minor agents. Since the interactions occur not only between major–minor agents but also among major–major agents and minor–minor populations, complicating equilibrium existence analysis, we first cast the MFG as two sets of adjoint stochastic McKean–Vlasov equations coupled via the mean field behavior. Subsequently, a new norm on the product probability measure space is constructed to prove that one set of equations exists solutions, while the existence of solutions to the other set is proved based on Pontryagin stochastic maximum principle. Then, within the established product normed space, Banach's fixed point theorem is utilized to prove the existence of equilibrium for this MFG, which is manifested as solutions to two sets of coupled equations. Finally, an epsilon-Nash equilibrium is proved for the finite agent situation, in which epsilon to 0 while all population sizes go to infty, and a numerical experiment under certain settings is carried out.

Keywords: Autonomous vehicles, Predictive control for linear systems, Robotics
Abstract: This paper presents a safe model predictive control (SMPC) framework designed to ensure the satisfaction of hard constraints, for systems perturbed by an external disturbance. Such safety guarantees are ensured, despite the disturbance, by online softening a subset of adjustable constraints defined by the designer. The selection of the constraints to be softened is made online based on a predefined priority assigned to each adjustable constraint. The design of a learning-based algorithm enables real-time computation while preserving the original safety properties.

Simulations results, obtained from an automated driving application, show that the proposed approach provides guarantees of collision-avoidance hard constraints despite the unpredicted behaviors of the surrounding environment.

Keywords: Constrained control, Autonomous systems, Autonomous vehicles
Abstract: This paper takes a step towards addressing the difficulty of constructing Control Barrier Functions (CBFs) for parallel safety boundaries. A single CBF for both boundaries has been reported to be difficult to validate for safety, and we identify why this challenge is inherent. To overcome this, the proposed method constructs separate CBFs for each boundary. We begin by presenting results for the relative degree one case and then extend these to higher relative degrees using the CBF backstepping technique, establishing conditions that guarantee safety. Finally, we showcase our method by applying it to a unicycle system, deriving a simple, verifiable condition to validate the target CBFs for direct implementation of our results.

Keywords: Optimization, Cooperative control, Autonomous vehicles
Abstract: This paper presents a persistent control methodology for a sustainably powered host/agent network that executes tip-and-cue oceanographic observing operations within a spatiotemporally evolving environment. Specifically, a renewably powered host vessel simultaneously serves as a recharging platform for an autonomous aerial vehicle (AAV), while also performing broad surveillance of an evolving mission domain. When the AAV is on board the host vessel, the mission trajectory (termed the “nominal” trajectory) is selected based on a clarity-driven ergodic planner. When a location of interest (termed a “tip” location) is detected by the host vessel, the AAV is dispatched to provide detailed observation of that location. This necessitates a replanning operation (of the “rendezvous” trajectory) wherein a rendezvous point is selected to maximize the mutual long-horizon benefit to the host and agent. Because the mutually beneficial rendezvous point will, in general, deviate from the original ergodic trajectory, another replanning operation (of the nominal trajectory) is completed on rendezvous. In this paper, we demonstrate the efficacy of the combination of the ergodic trajectory planner and rendezvous planner for a solar-powered host vessel (the SeaTrac SP-48 ASV) and a quadrotor (Agilicious) agent vehicle. In particular, the combined control system is shown to significantly outperform a line-transect strategy and an ergodic controller wherein the rendezvous point is constrained to lie on the nominal mission trajectory.

Keywords: Stochastic systems, Information theory and control, Estimation
Abstract: The causal conditional (CC) directed information (DI) can test the Granger causality for stochastic processes. However, for point process networks, the CCDI has only been developed for a trivariate network. In this work, we develop the general multivariate CCDI under Kramer’s framework by developing the CC likelihood, which is characterized by marginal intensity functions. We establish several Granger causality equivalences, unifying and generalizing existing results. Further, for Hawkes networks, we develop an estimation method of CCDI requiring only one point process trajectory, by developing an analytical formula for the marginal intensity functions, and an ergodic theorem for the CCDI.

Keywords: Algebraic/geometric methods, Stochastic systems, Numerical algorithms
Abstract: In this paper, we study the numerical simulation of stochastic differential equations (SDEs) on the special orthogonal Lie group SO(n). We propose a geometry-preserving numerical scheme based on the stochastic tangent space parametrization (S-TaSP) method for state-dependent multiplicative SDEs on SO(n). The convergence analysis of the S-TaSP scheme establishes a strong convergence order of O(delta^((1-epsilon)/2)), which matches the convergence order of the previous stochastic Lie Euler-Maruyama scheme while avoiding the computational cost of the exponential map. Numerical simulation illustrates the theoretical results.

Keywords: Predictive control for nonlinear systems, Optimal control
Abstract: In this work, we propose a Model Predictive Control (MPC) formulation incorporating two distinct horizons: a prediction horizon and a constraint horizon. This approach enables a deeper understanding of how constraints influence key system properties such as suboptimality, without compromising recursive feasibility and constraint satisfaction. In this direction, our contributions are twofold. First, we provide a framework to estimate closed-loop optimality as a function of the number of enforced constraints. This is a generalization of existing results by considering partial constraint enforcement over the prediction horizon. Second, when adopting this general framework under the lens of safety-critical applications, our method improves conventional Control Barrier Function (CBF) based approaches. It mitigates myopic behaviour in Quadratic Programming (QP)-CBF schemes, and resolves compatibility issues between Control Lyapunov Function (CLF) and CBF constraints via the prediction horizon used in the optimization. We show the efficacy of the method via numerical simulations for a safety critical application.

Keywords: Data driven control, Nonlinear systems, Predictive control for nonlinear systems
Abstract: This paper extends the Willems' Fundamental Lemma to nonlinear control-affine systems using the Koopman bilinear realization. This enables us to bypass the Extended Dynamic Mode Decomposition (EDMD)-based system identification step in conventional Koopman-based methods and design controllers for nonlinear systems directly from data. Leveraging this result, we develop a Data-Enabled Predictive Control framework for nonlinear systems with unknown dynamics. A case study demonstrates that our direct data-driven control method achieves improved optimality compared to conventional Koopman-based methods. Furthermore, in examples where an exact Koopman realization with a finite-dimensional lifting function set of the controlled nonlinear system does not exist, our method exhibits advanced robustness to finite Koopman approximation errors compared to existing methods.

Keywords: Stability of nonlinear systems, Nonlinear systems, LMIs
Abstract: Scaled relative graphs offer a graphical tool for analysis of nonlinear feedback systems. Of specific interest for stability analysis is the scaled graph, a special case of the scaled relative graph, related to non-incremental system properties. Although recently substantial progress has been made in scaled graph analysis, at present their use in multivariable feedback systems is limited by conservatism. In this paper, we aim to reduce this conservatism by introducing multipliers and exploit system structure in the analysis with scaled graphs. In particular, we use weighted inner products to arrive at a weighted scaled graph and combine this with a commutation property to formulate a stability result for multivariable feedback systems. We present a method for computing the weighted scaled graph of Lur'e systems based on solving sets of linear matrix inequalities, and demonstrate a significant reduction in conservatism through an example.

Keywords: Linear parameter-varying systems, Stability of nonlinear systems, Observers for nonlinear systems
Abstract: This paper investigates the observer-based stabilization problem for a class of disturbance-affected Nonlinear Parameter-Varying (NLPV) systems. We introduce a novel observer-controller framework that leverages Linear Matrix Inequality (LMI) conditions to guarantee robust performance. Unlike previous works that focus solely on state estimation, our approach integrates a controller based on the estimated states to ensure asymptotic stability and optimal disturbance attenuation. Through the deployment of the parameter-dependent Lyapunov (PDL) function and mathcal{H}_infty criterion, a new LMI condition is synthesized to achieve the objective. Further, due to the judicious use of a variant of Young's inequality, the reformulated Lipschitz property, and the matrix multiplier method presented in our previous works, the established LMI encompasses extra degrees of freedom from a feasibility point of view. The performance of the method is validated through simulations on a nonlinear time-varying pendulum system, demonstrating enhanced noise attenuation and faster convergence compared to existing approaches.

Keywords: Stability of nonlinear systems, Markov processes, Delay systems
Abstract: In this paper, we utilize monotonicity to simplify contraction analysis of discrete-time nonlinear time-delay systems with parameters following stochastic processes. First, we extend the concept of almost sure monotonicity to the time-delay systems, which can be verified via analysis of the corresponding prolonged systems. Next, we introduce a novel notion of uniform incremental asymptotic stability (UIAS) in the first moment to the time-delay systems and develop its sufficient condition. By virtue of almost sure monotonicity, if this condition holds, the time-delay systems are UIAS in the first moment for any finite length of delay. Moreover, the proposed result suggests that UIAS in the first moment has a strong connection with stability of the averaged deterministic systems. We formalize this observation for almost surely cooperative systems by establishing the equivalence between UIAS and uniform incremental asymptotic mean stability.

Keywords: Stability of hybrid systems, Lyapunov methods, Hybrid systems
Abstract: We study the property of fixed-time stability (FxTS) for hybrid dynamical systems (HDS) that combine continuous-time and discrete-time dynamics, possibly modeled via set-valued maps. For such systems, we provide sufficient Lyapunov characterizations for certifying FxTS of general closed sets. In this work, FxTS of a closed set is defined to require two properties: Lyapunov stability and fixed time convergence. For fixed time convergence, the system's trajectories must converge to the set of interest within a finite hybrid time that is uniformly bounded over all initializations. Our main contributions are two-fold: we first show that if the HDS admits solutions that flow for sufficiently long time, as well as a suitable Lyapunov function with a sufficient ``fixed-time'' decrease along flows and nonincrease during jumps, then the HDS will exhibit FxTS. Afterwards, we extend this result by showing that, under a mild dwell time condition, FxTS can be established for HDS for which the Lyapunov function is allowed to mildly increase during jumps. While our theoretical results pave the way for the general analysis of a broad class of fixed-time stable hybrid algorithms and systems, we illustrate them using two representative cases: a hybrid system with dwell-time conditions on the jumps, and systems exhibiting arbitrarily fast switching between a finite number of fixed-time stable vector fields.

Keywords: Robotics, Stability of hybrid systems, Algebraic/geometric methods
Abstract: We enhance a recently proposed hybrid controller that asymptotically stabilizes a class of closed orbits (so-called oscillations) for mechanical control systems with underactuation degree one. The controller in question enforces virtual holonomic constraint (VHCs) within a parametric family and instantiates new VHCs at certain events so as to asymptotically stabilize the target orbit. In this paper we propose a novel feedback mechanism in the jump map of the hybrid controller ensuring the asymptotic stabilization of oscillations with guaranteed basin of attraction. We demonstrate the new controller with a four degrees-of-freedom robot mimicking a child on a swing. For this robot, we are able to stabilize a large range of oscillations with guaranteed basin of attraction.

Keywords: Stability of hybrid systems, Algebraic/geometric methods
Abstract: This paper develops the hybrid Lyapunov theorem for geometric hybrid dynamical systems, namely hybrid inclusions evolving on intrinsic C1-manifolds. We present various nonsmooth analysis notions, which aid in the formulation of sufficient conditions for existence of solutions. We also present topological definitions of uniform global stability, attractivity, and asymptotic stability of a nonempty, compact set A. Finally, the Lyapunov theorem provides relaxed conditions for uniform global asymptotic stability of the set A. An example illustrates the concepts and results.

Keywords: Optimal control, Numerical algorithms, Predictive control for nonlinear systems
Abstract: Direct collocation (DC) is a widely used method for solving dynamic optimization problems (DOPs), but its implementation simplicity and computational efficiency are limited for challenging problems. For DOPs involving singular arcs, DC solutions often exhibit significant fluctuations along the singular arc, accompanied by large residual errors between collocation points, where the dynamic constraints are enforced as equality constraints. In this paper, we introduce the direct transcription method of integrated residual regularized direct collocation (IRRDC). This approach enforces dynamic constraints using a combination of point-wise residual constraints (expressed as either equalities or inequalities) and a penalty term on the integrated residual error, which helps reduce errors between collocation points. IRRDC retains the implementation simplicity of DC while improving both solution accuracy and efficiency, particularly for challenging problem types. Through the examples, we demonstrate that for problems where traditional DC results in excessive fluctuations, IRRDC effectively suppresses fluctuations and yields solutions with greater accuracy - at least two orders of magnitude lower in various error measures in relation to the dynamic and path constraints.

Keywords: Optimal control, Constrained control, Systems biology
Abstract: In this letter, we study optimal vaccination in a heterogeneous metapopulation epidemic model with state and mixed control-state constraints and a linear cost on the control, which better reflects real‐world expenses compared to quadratic penalties. Within a general SIR / SEIR K-patch framework, we formulate the resulting control problem on a finite horizon, prove the existence of optimal control, and derive the necessary conditions via Pontryagin's maximum principle extended to handle both shipment and per-region capacity limits. We use Pontryagin's result to rule out the existence of singular arcs and obtain a complete characterization of the optimal policy as bang-bang, with at most one switching time per region per week. Numerical experiments on networks of 3 to 8 cities confirm that the predicted switching structure arises from the linear cost assumption, and we compare these findings with optimal quadratic-cost policies.

Keywords: Optimal control, Numerical algorithms
Abstract: An adversarial setting is considered where two agents influence in turn a dynamical system using continuous, scalar actions. One agent seeks to maximize an infinite-horizon value, while the other aims to minimize it, leading to a sequential noncooperative game. To search for the minimax-optimal solution, we introduce Minimax Optimistic Planning for Continuous actions (MOPC), an algorithm that iteratively refines the most promising regions of the space of action sequences. Our analysis shows that MOPC provides computable bounds on the solution quality. Furthermore, we prove these bounds converge at well-characterized rates as computation grows, where the convergence rates are driven by a measure of problem complexity. We show how to pose in our framework -- and thereby near-optimally solve -- a class of problems in which opinions in a social network are influenced by two competing marketers. In experiments on such problems, MOPC outperforms uniform allocation over time.

Keywords: Hybrid systems, LMIs, Formal Verification/Synthesis
Abstract: We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex formulation of optimal control based on occupation measures, resulting in a convex relaxation resembling the discrete shortest-paths linear program that can be solved efficiently to global optimality. This approach improves scalability to large numbers of discrete modes compared to the NP-hard mixed- integer formulation. We use this to plan trajectories under linear temporal logic specifications, comparing the computed cost lower bound to a nonconvex optimization approach with fixed mode sequence. In our numerical experiments, we find that this bound is typically in the vicinity of the nonconvex solution. While the method inherits the limitations of semidefinite programming, the runtime speedup is significant compared to the often intractable mixed-integer formulation. Our implementation is available at https://github.com/ebuehrle/hpoc.

Keywords: Quantum information and control, Robust control, Uncertain systems
Abstract: Robust control design in open quantum systems under parametric uncertainty is essential for practical quantum applications. In this work, we propose an efficient algorithm for identifying robust control solutions in high-dimensional quantum systems. The algorithm reduces the computational complexity by utilizing the Suzuki-Trotter expansion to accelerate the solution of system dynamics. Our simulation results demonstrate that the proposed algorithm can achieve control solutions of high fidelity and robustness with improved efficiency.

Keywords: Quantum information and control
Abstract: The estimation of all the parameters in an unknown quantum state or measurement device, known as quantum state tomography (QST) and quantum detector tomography (QDT), is fundamental to the characterization and control of quantum systems. This paper presents a unified state space framework for QST and QDT based on observable measurement results at different evolution moments, applicable to both closed and Markovian open quantum systems. We derive lower bounds on the number of sampling points required for a unique estimation and analyze the computational complexity and mean squared error (MSE) scaling. As the estimator may yield unphysical results, we introduce new correction techniques to enforce physicality, which may also improve the infidelity scaling. The effectiveness of the proposed methods is validated through numerical simulations.

Keywords: Quantum information and control, Emerging control applications
Abstract: We develop a method for controlling the ensemble states of a two-level quantum system on the Bloch sphere. A spectrum of resonance frequencies parametrizes the ensemble. The evolution of the ensemble states under externally applied controls is uniquely determined by their respective resonance frequencies. Therefore, the control fields must be designed to simultaneously evolve the ensemble states across the domain of resonance frequencies. The objective is to evolve the discretized quantum ensemble states from an arbitrary initial dispersion to a targeted final configuration on the Bloch sphere. The proposed method holds potential for broad applicability in areas such as nuclear magnetic resonance (NMR), electron spin resonance (ESR), quantum computing and information processing, sampling-based learning control (SLC), quantum sensing and metrology, and quantum error correction.

Keywords: Data driven control, Nonlinear systems identification, Robust control
Abstract: We derive novel deterministic bounds on the approximation error of data-based bilinear surrogate models for unknown nonlinear systems. The surrogate models are constructed using kernel-based extended dynamic mode decomposition to approximate the Koopman operator in a reproducing kernel Hilbert space. Unlike previous methods that require restrictive assumptions on the invariance of the dictionary, our approach leverages kernel-based dictionaries that allow us to control the projection error via pointwise error bounds, overcoming a significant limitation of existing theoretical guarantees. The derived state- and input-dependent error bounds allow for direct integration into Koopman-based robust controller designs with closed-loop guarantees for the unknown nonlinear system. Numerical examples illustrate the effectiveness of the proposed framework.

Keywords: Data driven control, Cooperative control, Output regulation
Abstract: Given an autonomous exosystem, generating a reference output, we consider the problem of designing a distributed data-driven control law for a family of discrete time heterogeneous LTI agents, connected through a directed graph, in order to synchronize the agents’ outputs to the reference one. Agents split into two categories: leaders, with direct access to the exosystem output, and followers, that only receive information from their neighbors. All agents aim to achieve output synchronization by means of a state feedback that makes use of their own states as well as of an estimate of the exogenous system state, provided by an internal state observer. Such an observer has a different structure for leaders and followers. Necessary and sufficient conditions for the existence of a solution are first derived in the model-based set-up and then in a data-driven context.

Keywords: Feedback linearization, Data driven control, Predictive control for nonlinear systems
Abstract: This article contributes a theoretical framework for data-driven feedback linearization of nonlinear control-affine systems. We unify the traditional geometric perspective on feedback linearization with an operator-theoretic perspective involving the Koopman operator. We first show that if the distribution of the control vector field and its repeated Lie brackets with the drift vector field is involutive, then there exists an output and a feedback control law for which the Koopman generator is finite-dimensional and locally nilpotent. We use this connection to propose a data-driven algorithm ‘Koopman generator-based feedback linearization (KGFL)’ for feedback linearization of single-input systems. Particularly, we use experimental data to identify the state transformation and control feedback from a dictionary of functions for which feedback linearization is achieved in a least-squares sense. We also propose a single-step data-driven formula which can be used to compute the linearizing transformations. When the system is feedback linearizable and the chosen dictionary is complete, our data-driven algorithm provides the same solution as model-based feedback linearization. Finally, we provide numerical examples for the data-driven algorithm and compare it with model-based feedback linearization. We also numerically study the effect of the richness of the dictionary and the size of the dataset on the effectiveness of feedback linearization.

Keywords: Compartmental and Positive systems, Data driven control, Networked control systems
Abstract: This paper proposes a localized data-driven distributed controller design method for positive stabilization of network systems. In particular, we consider a network system consisting of multiple unknown agents, each of which has a local controller to be designed. In addition, we assume that each agent has access to the local time-series data and communicates with neighboring agents. In this situation, we address the problem of finding a protocol in which each agent autonomously updates its local controller such that the entire network system is positive and stable. In this paper, we provide a solution to the problem based on the projected consensus algorithm.

Keywords: Autonomous robots, Constrained control, Output regulation
Abstract: We consider nonconvex obstacle avoidance where a robot described by nonlinear dynamics and a nonconvex shape has to avoid potentially nonconvex obstacles. Obstacle avoidance is a fundamental problem in robotics and well studied in control. However, existing solutions are computationally expensive (e.g., model predictive controllers), neglect nonlinear dynamics (e.g., graph-based planners), use diffeomorphisms to obtain convex problems (e.g., for star shapes), or are conservative as convex overapproximations are used. We instead provide an efficient yet non-conservative solution for general nonconvex obstacles.Our approach is based on efficient computation of the distance between the robot and obstacles via sampling-based distance functions. We quantify the sampling error and show that, for certain systems, sampling-based distance functions are valid nonsmooth control barrier functions. We also study how to deal with disturbances on the robot dynamics in our setting. Finally, we illustrate our method on a robot navigation task involving an omnidirectional robot and nonconvex obstacles. We also analyze performance and computational efficiency of our controller as a function of the number of samples.

Keywords: Learning, Optimization, Agents-based systems
Abstract: We address distributed learning problems over undirected networks. Specifically, we focus on designing a novel ADMM-based algorithm that is jointly computation- and communication-efficient. Our design guarantees computational efficiency by allowing agents to use stochastic gradients during local training. Moreover, communication efficiency is achieved as follows: i) the agents perform multiple training epochs between communication rounds, and ii) compressed transmissions are used. We prove exact linear convergence of the algorithm in the strongly convex setting. We corroborate our theoretical results by numerical comparisons with state of the art techniques on a classification task.

Keywords: Distributed control, Cooperative control, Networked control systems
Abstract: The advancements in resilient consensus research have largely relied on the assumption of a timeinvariant agent set, limiting their applicability in dynamic environments. This paper extends the resilient consensus problem to a more dynamic setting by incorporating agent arrivals and departures, modeling an open multi-agent system. To ensure resilient consensus in such systems, we propose a novel algorithm that separately designs update schemes for cooperative remaining agents and newly joining agents. Furthermore, we establish and analyze the sufficient condition for resilient consensus under malicious attacks in open multi-agent systems. Numerical examples are provided to validate the effectiveness of our theoretical findings.

Keywords: Robotics, Autonomous systems, Optimal control
Abstract: This work proposes a novel multi-robot task allocation framework for robots that can switch between multiple modes, e.g., flying, driving, or walking. We first provide a method to encode the multi-mode property of robots as a graph, where the mode of each robot is represented by a node. Next, we formulate a constrained optimization problem to decide both the task to be allocated to each robot as well as the mode in which the latter should execute the task. The robot modes are optimized based on the state of the robot and the environment, as well as the energy required to execute the allocated task. Moreover, the proposed framework is able to encompass kinematic and dynamic models of robots alike. Furthermore, we provide sufficient conditions for the convergence of task execution and allocation for both robot models.

Keywords: Autonomous systems, Autonomous robots, Cooperative control
Abstract: We conduct research on a distributed task assignment algorithm, which is one of the distributed decision-making methods in multi-agent system. We consider a mission in which multi-agents transport multiple packages. In particular, we deal with a problem in which one agent can carry multiple packages depending on its loading capacity, and there are heavy packages which require multiple agents to transport. To achieve the goal, we combine two methods. The first is Grouping, a method of calculating the groups of packages that one agent can carry at a time. The second one is two types of lists which record task start time of agents. In consequence, we decrease the task start time and agents’ moving distance. We also consider transportation control, by using consensus based control to second-order system.

Keywords: Nonlinear output feedback
Abstract: Control barrier functions (CBFs) offer a powerful tool for enforcing safety specifications in control synthesis. This paper deals with the problem of constructing valid CBFs. Given a second-order system and any desired safety set with linear boundaries in the position space, we construct a provably control-invariant subset of this desired safety set. The constructed subset does not sacrifice any positions allowed by the desired safety set, which can be nonconvex. We show how our construction can also meet safety specification on the velocity. We then demonstrate that if the system satisfies standard Euler- Lagrange systems properties then our construction can also handle constraints on the allowable control inputs. We finally show the efficacy of the proposed method in a numerical example of keeping a 2D robot arm safe from collision.

Keywords: Constrained control
Abstract: This letter shows how to design control barrier functions for underactuated and fully-actuated Euler-Lagrange systems subject to state and input constraints. The proposed method uses passivity-based considerations to limit the total energy available to the system and ensure constraint satisfaction. The approach can handle multiple state and input constraints regardless of relative degree.

Keywords: Neural networks, Uncertain systems, Stochastic systems
Abstract: Ensuring the safety of neural networks under input uncertainty is a fundamental challenge in safety-critical applications. This paper presents a risk-aware variant of Fazlyab’s neural network safety verification, which certifies robustness to input uncertainties using quadratic constraints and semidefinite programming. The proposed approach integrates the Worst-Case Conditional Value-at-Risk to explicitly account for tail risk. This not only expands the freedom of the input uncertainty geometry but also the applicability of Fazlyab’s approach to scenarios where tail-risk is crucial, such as automotive systems and medical applications. Applications of the proposed approach to closed-loop reachability analysis of control systems, dynamical system analysis, and classification are demonstrated through numerical experiments.

Keywords: Variable-structure/sliding-mode control
Abstract: In this letter, we construct an output feedback control scheme tailored to a class of linear time-varying (LTV) systems with a single output and single matched non-vanishing perturbation. The control is shown to be capable of stabilizing the origin of the system in finite-time, or even more, in fixed-time. The result is obtained by constructing a nonlinear homogeneous in the bi-limit controller and observer. For a particular choice of parameters and gains, a high-order sliding mode (HOSM) controller is obtained, capable of global convergence when the system perturbation is bounded. The closed-loop stability of the system is demonstrated by means of a bl-homogeneous Lyapunov function, which allows us to conclude a principle of separation between the observer and controller design. The effectiveness of the proposal is illustrated by an academic example.

Keywords: Learning, Stability of nonlinear systems, Neural networks
Abstract: State space models (SSMs) have emerged as a powerful architecture in machine learning and control, fea- turing stacked layers where each consists of a linear time- invariant (LTI) discrete-time system followed by a nonlinearity. While SSMs offer computational efficiency and excel in long- sequence predictions, their widespread adoption in applications like system identification and optimal control is hindered by the challenge of ensuring their stability and robustness properties. We introduce L2RU, a novel parametrization of SSMs that guarantees input-output stability and robustness by enforcing a prescribed L2-bound for all parameter values. This design elim- inates the need for complex constraints, allowing unconstrained optimization over L2RUs by using standard methods such as gradient descent. Leveraging tools from system theory and con- vex optimization, we derive a non-conservative parametrization of square discrete-time LTI systems with a specified L2-bound, forming the foundation of the L2RU architecture. Additionally, we enhance its performance with a bespoke initialization strategy optimized for long input sequences. Through a system identification task, we validate L2RU’s superior performance, showcasing its potential in learning and control applications.

Keywords: Predictive control for linear systems, Machine learning, Learning
Abstract: Model Predictive Control (MPC) is a powerful strategy for constrained multivariable systems but faces computational challenges in real-time deployment due to its online optimization requirements. While explicit MPC and neural network approximations mitigate this burden, they suffer from scalability issues or lack interpretability, limiting their applicability in safety-critical systems. This work introduces a data-driven framework that directly learns the Linear MPC control law from sampled state-action pairs using Oblique Decision Trees with Linear Predictions (ODT-LP), achieving both computational efficiency and interpretability. By leveraging the piecewise affine structure of Linear MPC, we prove that the Linear MPC control law can be replicated by finite-depth ODT-LP models. We develop a gradient-based training algorithm using smooth approximations of tree routing functions to learn this structure from grid-sampled Linear MPC solutions, enabling end-to-end optimization. Input-to-state stability is established under bounded approximation errors, with explicit error decomposition into learning inaccuracies and sampling errors to inform model design. Numerical experiments demonstrate that ODT-LP controllers match MPC's closed-loop performance while reducing online evaluation time by orders of magnitude compared to MPC, explicit MPC, neural network, and random forest counterparts. The transparent tree structure enables formal verification of control logic, bridging the gap between computational efficiency and certifiable reliability for safety-critical systems.

Keywords: Formal Verification/Synthesis, Robust control, Machine learning
Abstract: Even though neural networks are being increasingly deployed in safety-critical control applications, it remains difficult to enforce constraints on their output, meaning that it is hard to guarantee safety in such settings. While many existing methods seek to verify a neural network's satisfaction of safety constraints, few address how to correct an unsafe network. The handful of works that extract a training signal from verification cannot handle non-convex sets, and are either conservative or slow. To begin addressing these challenges, this work proposes a neural network training method that can encourage the exact image of a non-convex input set for a neural network with rectified linear unit (ReLU) nonlinearities to avoid a non-convex unsafe region. This is accomplished by reachability analysis with scaled hybrid zonotopes, a modification of the existing hybrid zonotope set representation that enables parameterized scaling of non-convex polytopic sets with a differentiable collision check via mixed-integer linear programs (MILPs). The proposed method was shown to be effective and fast for networks with up to 240 neurons, with the computational complexity dominated by inverse operations on matrices that scale linearly in size with the number of neurons and complexity of input and unsafe sets. We demonstrate the practicality of our method by training a forward-invariant neural network controller for an affine dynamical system with a non-convex input set, as well as generating safe reach-avoid plans for a black-box dynamical system.

Keywords: Constrained control, Neural networks, Flight control
Abstract: In this paper, we present a novel theoretical framework for online adaptation of Control Barrier Function (CBF) parameters, i.e., of the class K functions included in the CBF condition, under input constraints. We introduce the concept of locally validated CBF parameters, which are adapted online to guarantee finite-horizon safety, based on conditions derived from Nagumo’s theorem and tangent cone analysis. To identify these parameters online, we integrate a learning-based approach with an uncertainty-aware verification process that account for both epistemic and aleatoric uncertainties inherent in neural network predictions. Our method is demonstrated on a VTOL quadplane model during challenging transition and landing maneuvers, showcasing enhanced performance while maintaining safety.

Keywords: Estimation, Time-varying systems, Differential-algebraic systems
Abstract: In this paper, we apply the recently developed generalized parameter estimation-based observer design technique for state-affine systems to the practically important case of linear time-varying differential-algebraic equations (DAE) systems with uncertain parameters. We proceed from the general description of the system given by the Standard Canonical Form and try to develop a comprehensive theory for the design of adaptive observers for these systems.

Keywords: Cooperative control, Agents-based systems, Distributed control
Abstract: In this paper, a consensus algorithm is proposed for interacting multi-agents, which can be modeled as simple Mechanical Control Systems (MCS) evolving on a general Lie group. The standard Laplacian flow consensus algorithm for double integrator systems evolving on Euclidean spaces is extended to a general Lie group. A tracking error function is defined on a general smooth manifold for measuring the error between the configurations of two interacting agents. The stability of the desired consensus equilibrium is proved using a generalized version of Lyapunov theory and LaSalle's invariance principle applicable for systems evolving on a smooth manifold. The proposed consensus control input requires only the configuration information of the neighboring agents and does not require their velocities and inertia tensors. The design of tracking error function and consensus control inputs are demonstrated through an application of attitude consensus problem for multiple communicating rigid bodies. The consensus algorithm is numerically validated by demonstrating the attitude consensus problem.

Keywords: Cooperative control, Distributed control, Network analysis and control
Abstract: In a paper by Nishikawa and Motter, a quantity called the normalized spread of the Laplacian eigenvalues is used to measure the synchronizability of certain network dynamics. Through simulations, and without theoretical validation, it is conjectured that among all simple directed graphs with a fixed number of vertices and arcs, the optimal value of this quantity is achieved if the Laplacian spectrum satisfies a specific pattern. This paper proves that the conjectured Laplacian spectrum is always achievable by a class of almost regular directed graphs. For a few special cases, it is also shown that the corresponding value of the quantity is indeed optimal.

Keywords: Agents-based systems, Cooperative control
Abstract: This paper investigates the effect of constant time delay in weakly connected multi-agent systems modeled by double integrator dynamics. A novel analytical approach is proposed to establish an upper bound on the permissible time delay that ensures stability and consensus convergence. The analysis employs the Lambert W function method in higher-dimensional systems to derive explicit conditions under which consensus is achieved. The theoretical results are rigorously proven and provide insight into the allowable delay margins. The analysis applies to general leaderless undirected network topologies. The framework also accounts for complex and realistic delays, including non-commensurate communication delays. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Keywords: Network analysis and control, Agents-based systems
Abstract: The paper addresses the synchronization of multi-agent systems with continuous-time dynamics interacting through a very general class of monotonic continuous signal functions that covers estimation biases, approximation of discrete quantization, or state-dependent estimation. Our analysis reveals that, in the setup under consideration, synchronization equilibria are exactly the fixed points of the signal function. We also derive intuitive stability conditions based on whether the signal underestimates or overestimates the state of the agents around these fixed points. Moreover, we show that network topology plays a crucial role in asymptotic synchronization. These results provide interesting insights into the interplay between communication nonlinearity and network connectivity, paving the way for advanced coordination strategies in complex systems.

Keywords: Stability of nonlinear systems, Network analysis and control, Biological systems
Abstract: In recent years, there has been an increasing interest towards the theory and applications of decision-making in multi-agent systems, where the interactions among multiple groups of individuals exhibit complex behaviors. However, a large body of works considers only a single homogeneous population, limiting the applications in real settings. To this end, we develop a general framework for collective decision-making on a networked multi-population. We study this problem in populations with a large number of agents, where each agent has to choose one of two available options, or remain uncommitted. The contribution of this paper is threefold. First, we develop a framework for collective decision-making on a networked multi-population where the transition rates depend on the neighboring populations. Second, we characterize the equilibria and find the conditions for local asymptotic stability. Finally, we study globally stability for the equilibrium where all players are committed to neither option.

Keywords: Network analysis and control, Control of networks
Abstract: Connectivity is a critical aspect of a multi-agent system (MAS), as it determines the system's ability to successfully accomplish cooperative tasks. Consequently, it is essential to develop algorithms that design networks or graphs that not only ensure nominal connectivity but also provide guarantees of connectivity despite node failures. This characteristic of maintaining connectivity even in the face of node failures is referred to as biconnectivity. In this paper, we utilize the concept of graph resistance to ensure connectivity in the presence of emph{articulation nodes/sets} when node failures occur. First, an algorithm is presented to identify articulation nodes/sets within the graph. Subsequently, we introduce a connectivity index to quantify the extent of connectivity loss when nodes fail. Additionally, we propose a method for designing a network that preserves connectivity against node failures with addition of a minimal number of edges.

Keywords: Discrete event systems
Abstract: Dynamical Tropical systems are described by means of Tropical Algebra (for instance, Min- or Max-plus ones), which is a kind of idempotent semifield. For such systems, we are interested in the study of general algebraic properties ensuring optimal balancing through feedback control. By balancing, we mean that all events, or transitions, occur at the same rate, meaning that there is no sub-product accumulation inside the system. In this context, after formulating the problem for Tropical Semifields, the first result is the development, thanks to Residuation Theory, of the expression of the maximum feedback matrix expressed in terms of a vector parameter, ensuring that the closed-loop matrix has a desired eigenvalue. Under the assumption of controllability and boundedness of the controllability matrix, we develop a method to properly choose this maximum feedback matrix. In order to illustrate the method, we present a solution for the problem of balancing two unconnected networks by means of feedback control.

Keywords: Mean field games, Reinforcement learning, Markov processes
Abstract: We study the inverse reinforcement learning problem for discrete-time, infinite-horizon mean-field games with an average-reward criterion. Unlike the forward setting, where the reward function is known, IRL assumes access only to expert demonstrations that are optimal under some unknown reward function. The objective is to recover the reward structure that explains these expert behaviors. Our approach is based on the maximum causal entropy principle, which selects the least biased policy among those consistent with the observed demonstrations. We show that the resulting non-convex formulation is equivalently reformulated as a convex optimization problem over occupation measures. Furthermore, we establish that the dual objective is smooth and strongly convex over compact sets and derive a variational representation using a log-partition formulation. Finally, we propose a first-order algorithm for solving the dual problem and recovering an entropy-maximizing equilibrium policy.