This paper addresses the event-triggered feedback optimization problem for a class of nonlinear systems in strict-feedback form with dynamic uncertainties. The system has access to real-time gradients of the objective function along its output trajectory, which is a milder requirement than having access to the objective function's analytical form. By employing backstepping and gain assignment techniques, two event-triggered mechanisms and a feedback optimization protocol are developed that construct the closed-loop system as a feedback interconnection of multiple Input-to-State Stable (ISS) subsystems. The small-gain theorem is applied to guarantee closed-loop stability, ensuring that the proposed protocol drives the system output to the optimal solution while excluding Zeno behavior. We further relax the uncertain system dynamics to allow nonvanishing terms at the equilibrium point and bounds given by nonlinear functions involving unknown parameters. Unlike existing small-gain methods for event-triggered control, the proposed approach avoids constructing set-valued maps and incorporates the optimization objective into the small-gain analysis. The effectiveness of the approach is demonstrated through its application to a source-seeking problem.

This paper is concerned with the prescribed time consensus (PTC) problem of a class of multi-agent systems (MASs) under DoS attacks, where the communication network between agents is jammed when the attack occurs. We introduce a natural concept of the so-called "realistic" settling time to address the PTC problem of the case for MASs under DoS attacks and develop a corresponding novel PTC control protocol for the concerned MASs under DoS attacks. It is shown that in this case the "realistic" settling time, which consists of both the attack duration and an arbitrarily prescribed time, can be achieved. Finally, the effectiveness of the proposed consensus protocol is illustrated by a simulation example. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This paper investigates the resilient fixed-time cooperative output regulation problem of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs. First, a novel distributed resilient fixed-time observer is proposed by accounting for denial-of-service attacks and detail-balanced directed graphs. Then, a novel distributed resilient fixed-time controller based on the proposed observer is developed. It is shown that under the proposed distributed controller, the resilient fixed-time cooperative output regulation problem for heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs is solved. Specifically, it is shown that the regulated output converges to zero in fixed time, where the upper bound of the settling time does not depend on the initial conditions of the concerned multi-agent system and is explicitly given. Finally, a simulation example is given to demonstrate the effectiveness of the proposed controller. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This paper studies the robust stabilization of 2 × 2 linear hyperbolic partial differential equations (PDEs) with Markov-jumping parameters and boundary input delay. The main challenge arises from the simultaneous presence of stochastic parameter variations and input delay, which complicates both the stability analysis and controller design. To address this issue, a nominal delay-compensating backstepping controller is first designed for a fixed nominal system. Applying the nominal transformation to the stochastic system yields a target system with additional perturbation terms induced by parameter mismatch. A mode-independent Lyapunov functional is then constructed to establish a pathwise exponential estimate, which directly implies mean-square exponential stability under an explicit small-mismatch condition. The proposed analysis provides a direct robustness certificate for nominal delay compensation without using mode-dependent Lyapunov functionals. Finally, we present simulation results and discuss how the conservative small-mismatch condition should be interpreted for the numerical example.

This paper addresses the stabilization problem for Aw-Rascle-Zhang (ARZ) traffic model in the presence of an arbitrarily large input delay. The linearized ARZ model is a 2 × 2 hyperbolic partial differential equation (PDE) system with proximal reflection, which introduces significant analytical challenges when combined with input delays. To tackle this problem, we propose a backstepping-based boundary controller capable of stabilizing the linearized ARZ model under these conditions. The input delay is modeled as a transport PDE, which reformulates the entire system into a 3 × 3 hyperbolic PDE system. A backstepping transformation is designed to map the original system into a stable target system, enabling the design of a delay-compensated controller. A key technical contribution of this work is that for hyperbolic PDEs with delays, we develop a characteristic-region-wise construction for kernel functions subject to two boundary constraints and close the proof via successive approximation. Another contribution is that we utilize the small-gain theorem for input-to-state stability (ISS) of hyperbolic PDEs. Two simulations are provided to illustrate the effectiveness of the proposed delay-compensated controller: one compares it with a controller without compensation, and the other employs real traffic vehicle data to validate its effectiveness.

Manipulating Deformable Linear Objects (DLOs) in cluttered environments is challenging due to their high dimensionality and complex constraints. In this paper, we propose a Hierarchical Constraint-projected Diffusion (HCDiff) framework that decomposes the problem into global constraint-aware planning and local robust control through a coarse-to-fine generative process. At the high level, we propose a Latent Control Barrier Function (LCBF) projection that is integrated directly into the score-based denoising process of a diffusion planner. By projecting the gradient flow within the latent manifold learned by a Graph AutoEncoder (GAE), our method biases the generation of subgoals toward collision-free and physically feasible configurations. At the low level, we develop a Goal-conditioned Diffusion Policy (GDP) for DLO manipulation that is trained solely on unstructured, task-agnostic play data. By offloading local control to this task-agnostic policy, our high-level planner only requires a small scale of task-specific human demonstrations, thereby significantly reducing the overall dependency on expensive expert data. Furthermore, we employ a dual GDP control strategy to enhance control robustness. Comprehensive experiments in 2D and 3D demonstrate that HCDiff outperforms multiple baselines in terms of task success rate and planning efficiency. Crucially, the framework exhibits superior adaptability, successfully navigating environments with modified obstacle geometries beyond the training distribution.

This article investigates the distributed source seeking problem for uncertain networked Euler-Lagrange systems over unbalanced directed communication topologies. The objective is to drive all agents toward the source of aggregated multiple unknown scalar fields. To achieve this, a novel distributed control protocol is proposed, which consists of three components: a distributed estimator for estimating the left eigenvector of the Laplacian matrix associated with the zero eigenvalue, a distributed optimizer for generating a virtual reference trajectory toward the source, and a trajectory tracker for exponentially driving each agent toward the reference trajectory. By employing the exponential trajectory tracker, the stochastic extremum seeking technique can be effectively integrated into our optimizer tailored for unbalanced directed topologies. By applying stochastic averaging theory, the weakly exponential convergence of the control protocol can be achieved. Finally, the effectiveness of the proposed distributed control protocol is demonstrated through a numerical example.

The multiuser haptic-enabled robotic system (M-Hers) facilitates shared control among human operators through task-dependent authority allocation, where interaction relationships are typically dictated by task requirements. However, some of these relationships can be nonpassive, generating excess energy that violates passivity constraints and compromises system stability. To address this, we first introduce the interaction architecture (IA) to formalize how operators influence task execution. Based on this framework, we propose a tank-based two-layer task model that ensures system passivity despite nonpassive IAs. This model comprises a virtual object (VO) layer for task rendering and a virtual system (VS) layer that passively executes nonpassive IA behaviors. The VS layer uses a global energy tank to compensate for IA-induced energy violations and modify the VO model when tank energy is depleted. This structure decouples task rendering from low-level robotic control, enabling seamless integration of an arbitrary number of robots with heterogeneous dynamics and control modes. Simulation and experimental results validate the proposed method’s scalability, flexibility, and effectiveness in preserving passivity while accurately realizing diverse IAs. This approach paves the way for scalable and easy-to-deploy control framework that supports multiuser haptic interaction.

This study investigates the resilient synchronization problem for multi-agent systems (MASs) under the stochastic sampling-based triggering algorithm. First, to explicitly characterize the vulnerability of communication links, random link failures are modeled by Bernoulli-type link-availability variables and fault-induced perturbations. Second, to reduce redundant inter-agent communication, the stochastic sampling-based triggering algorithm is introduced by embedding random sampling intervals into the triggering mechanism. Then, based on the random link failures and the stochastic sampling-based triggering algorithm, a distributed leader-state observer and a Riccati-equation-based PID controller are developed to realize resilient adaptive synchronization. Furthermore, sufficient conditions are derived by using algebraic Riccati equations and a Lyapunov functional to guarantee the mean-square stability of the closed-loop system and the convergence of the synchronization error. Finally, simulation studies based on helicopter flight data demonstrate the effectiveness and robustness of the proposed strategy under the stochastic sampling-based triggering algorithm and random link failures.

This paper addresses the nonconvex distributed resource allocation problem for uncertain nonlinear multi-agent systems. The objective is to design distributed real-time gradient feedback protocols that steer the agents' outputs to the set of Karush-Kuhn-Tucker (KKT) points. Unlike conventional offline algorithms that require explicit analytical expressions of the gradients of local objective functions, the proposed protocols use only gradient values along agent trajectories. With the exchange of this local gradient information among neighbors, two classes of distributed real-time gradient feedback protocols are proposed. The first employs a constant feedback gain and guarantees convergence provided that the feedback gain is chosen below an explicit bound. The second adopts a vanishing time-varying feedback gain, requiring no prior knowledge of parameters associated with the agents, local objective functions, or communication graph, and enabling its fully distributed implementation. The results are further extended to jointly optimizing the agents' inputs and outputs when each open-loop system admits a desired input–output property. The effectiveness and advantages of the protocols are demonstrated through a numerical example on economic optimization of interconnected chemical reactors.

Despite extensive investigations into the multi-user haptic-enabled robotic system (M-Hers), achieving scalable control design in the presence of non-passive human operators remains a key challenge. This is primarily due to the increasing complexity of stability conditions and interaction coupling as the number of operators grows. In this study, we address this challenge in two steps. First, we introduce the individual interaction environment (IIE) to isolate the passivity violations, which facilitates the independent control design for each human-robot subsystem, thereby enhancing the scalability with respect to the number of subsystems. Second, within the IIE framework, we identify passivity-violating components caused by partners' active behaviors and propose a novel augmented tank-based controller (ATBC) to guarantee passive IIE while maintaining high rendering accuracy. Specifically, the ATBC employs an energy-related power regulation strategy to enhance interaction safety and a time-varying control gain to mitigate the negative effects of power regulation on rendering fidelity. We validated the proposed method through collaborative haptic tasks on a customized M-Hers composed of three robots in four different scenarios. Comparative studies demonstrate that our approach effectively ensures IIE passivity in the presence of active human behaviors, while ensuring high reproducibility and achieving a favorable balance between passivity and rendering accuracy.

This paper addresses the problem of fixed-time cooperative output regulation for linear multi-agent systems over directed graphs under denial-of-service attacks. A novel distributed resilient fixed-time controller is developed that comprises a distributed resilient fixed-time observer taking general directed graphs into consideration, and a distributed resilient fixed-time control law for each agent. The proposed controller neither depends on Laplacian symmetry nor requires strong connectivity and detail-balanced condition, in contrast to existing distributed resilient fixed-time controllers. Under the proposed controller, the regulated outputs converge to zero in a fixed time with its upper bound independent of the initial states of the multi-agent system. Ultimately, the efficacy of the proposed controller is demonstrated via a simulation example.

This paper addresses the distributed optimal coordination problem for a class of heterogeneous uncertain nonlinear multiagent systems. Instead of relying on the analytical forms of gradient functions, we use the measured gradient values depending on agents' real-time outputs and propose a novel adaptive distributed control scheme. This scheme integrates event-triggered optimal coordinators, high-order filters, and tracking controllers. To handle the interaction between optimal coordinators and filters, we incorporate a new compensation term into the updating law for the coupling weight of each edge. Moreover, we design a novel adaptive distributed dynamic event-triggering mechanism that ensures that the inter-event times of each agent are lower bounded by a positive constant. Asymptotic convergence of agents' outputs to the optimal point is proved by constructing a composite Lyapunov function. The proposed control scheme does not depend on global topology information. A numerical example is given to demonstrate the effectiveness of the proposed control scheme. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This paper addresses the moving target enclosing control problem for nonholonomic multi-agent systems with guaranteed network connectivity and collision avoidance. We propose a novel control scheme to handle distance constraints imposed by the agents' limited interaction ranges and collision-free thresholds. By leveraging a Henneberg construction method, we innovatively formulate the target enclosing requirements within an isostatic distance-based formation framework, facilitating the integration of distance constraints. Compared with existing results, our approach ensures the positive definiteness of the underlying rigidity matrix and does not require controlling the target's motion. To eliminate the occurrences of control singularities caused by nonholonomic constraints, we propose a fixed-time angular control law using barrier Lyapunov functions. Additionally, we develop a linear velocity control law using the prescribed performance control approach and transformed error constraints. We rigorously prove that our control laws enable the multi-agent system to asymptotically achieve the desired angular formation pattern around a moving target while satisfying the established distance constraints. Finally, a simulation example is provided to validate the effectiveness of the proposed method.

Achieving desired cooperative tracking under limited onboard resources is an interesting yet challenging issue. This article proposes a fully distributed adaptive double event-triggered framework to solve the time-critical cooperative tracking problem of multiagent systems with unknown disturbances. We first design a neighborhood-weighted event-triggered communication function to create a pathway to achieve fixed-time convergence without any global network information. By developing an integral sliding manifold, we manage to separate the design of event-triggered communication and adaptive event-triggered control for disturbance rejection. This approach provides a feasible design tool that not only extends single or double event-triggered strategies to adaptive double event-triggered strategies but also handles unknown external disturbances. Besides, we rigorously derive sufficient conditions for guaranteeing the feasibility of the proposed algorithm and exclude Zeno behavior. Extensive simulations and experiments on multiple quadrotors are conducted.

This paper investigates two-player zero-sum games for discrete-time linear systems. The associated game algebraic Riccati equation (GARE) can be solved using existing policy-iteration algorithms. However, the convergence of these algorithms depends heavily on the choice of the initial gain pair. To overcome this limitation, a generalized policy-iteration algorithm is proposed, where an admissible initial gain pair is determined by solving a linear matrix inequality (LMI). The proposed algorithm is proved to converge to the saddle point of the two-player zero-sum game. Compared with existing policy-iteration algorithms, the proposed algorithm provides an easily implementable initialization while ensuring convergence. Finally, numerical examples are provided to illustrate the effectiveness of the proposed algorithm.

This paper investigates distributed online optimization for multi-agent dynamical systems with constrained inputs and time-varying cost functions. While online convex optimization offers a principal framework for sequential decision-making, existing online learning and optimization algorithms typically require accurate system models, limiting their applicability in practical settings. To overcome this challenge, we propose a distributed bandit online feedback optimization algorithm that relies solely on real-time input-output data. The algorithm employs a smoothing zeroth-order one-point estimator to construct local gradient approximations directly from cost evaluations. Additionally, to enforce input constraints effectively, we integrate a projection-free conditional gradient update, making the algorithm well-suited for online and large-scale settings. Furthermore, we establish a sublinear dynamic regret bound that depends on a temporal variation measure of system non-stationarity. Finally, numerical simulations demonstrate the effectiveness of the proposed algorithm.

This paper investigates the problem of resilient global practical fixed-time cooperative output regulation of uncertain nonlinear multi-agent systems subject to denial-of-service attacks. A novel distributed resilient adaptive fixed-time control strategy is proposed, which consists of a novel distributed resilient fixed-time observer with a chain of nonlinear filters and a novel distributed resilient adaptive fixed-time controller. It is shown that the problem of resilient global practical fixed-time cooperative output regulation can be solved by the proposed control strategy. More specifically, the proposed distributed control strategy ensures the global boundedness of all the signals in the resulting closed-loop system and the global convergence of the regulated outputs to a tunable residual set in a fixed time. A simulation example is finally provided to illustrate the efficacy of the proposed control strategy.

This article investigates the cooperative target enclosing control problem of multi-agent systems under uncertain target motion using event-triggered communication. A novel event-triggered adaptive internal-model-based observer is proposed to estimate the target’s position and velocity asymptotically without requiring exact knowledge of target dynamics and continuous monitoring among neighboring agents. A new event-triggering mechanism (ETM) with a strictly positive minimum inter-event time (MIET) is developed by incorporating three non-increasing resettable timer variables based on the observer states. The proposed observer design not only compensates for the sampling errors, but also associates the existence of the positive MIET with the boundedness of the system states. In addition, a new distributed formation control law that only uses the event-triggered neighboring information is designed. Simulations show that the MAS tracks the target’s position and velocity asymptotically while achieving the prescribed formation pattern.

Shape control of deformable linear objects (DLOs) is a major challenge in robotics due to their high-dimensional, nonlinear dynamics and sensitivity to boundary conditions. Existing data-driven and physics-based models either require large datasets or suffer from excessive computational cost for real-time control. This paper presents a Cosserat-based Physics-Informed Neural Network (C-PINN) framework for efficient, real-time DLO modeling and automatic shape control. By embedding Cosserat rod theory directly into the PINN loss, C-PINN achieves accurate, physically consistent predictions of the DLO while dramatically reducing the requirement for large-scale training data and is robust to unseen scenarios. To enhance generalization and training stability, we introduce a curriculum learning strategy and propose an online sim-to-real residual adaptation module to bridge the gap between simulation and real-world deployment. The learned surrogate model is integrated into a gradient-based model predictive controller (MPC), enabling real-time, closed-loop shape control. Extensive experiments demonstrate that our approach generalizes well to various DLO materials and configurations in both 2D and 3D scenarios, and adapts robustly to interactive, human-in-the-loop manipulation. Both simulation and real-world experiments show that our method consistently attains significantly lower RMSE, as confirmed by comprehensive comparisons with various baselines. These results highlight the effectiveness and versatility of C-PINN for practical, high-precision DLO manipulation in diverse robotic scenarios. Compared to traditional analytical solvers, C-PINN achieves up to a 228-fold improvement in computational speed. Note to Practitioners-This work is motivated by the need for fast and accurate shape control of flexible objects such as cables, wires, and ropes, which is a common challenge in fields like electronics assembly, robotics, and medical devices. Existing solutions based on physics simulation are often too computationally intensive for real-time use, while purely data-driven methods require large datasets and may struggle with new or changing conditions. Our approach integrates physical modeling directly into a neural network, allowing for quick and reliable prediction and control of deformable linear objects using much less training data. In practice, this means engineers can achieve high-precision manipulation and adapt to different object types or tasks without the need for massive data collection or extensive parameter tuning. Our framework also supports real-time feedback and online adaptation to real-world conditions, making it robust to variations in material properties and external disturbances. We also show how the physics-embedded model can be effectively integrated with model predictive control. A key limitation is that our method currently assumes slow or quasi-static motion and does not account for rapid dynamics or complex environmental contacts, which may affect accuracy in certain scenarios. Future work will focus on handling dynamic effects and environmental interactions. This approach could also be extended to other flexible material handling tasks, such as textile automation or surgical tool positioning.