Ensuring robust privacy protection and efficient data transmission is critical for collaborative learning in the Internet of Vehicles (IoV). Although decentralized federated learning (DFL) allows for privacy-preserving model training, existing approaches remain vulnerable to inference attacks from honest-but-curious clients who can recover private data during model aggregation. Furthermore, current DFL frameworks typically require symmetric vehicle-to-vehicle communications, limiting their practical deployment in IoV scenarios with heterogeneous communication capabilities. To address these limitations, we propose a novel privacy-preserving DFL algorithm based on the alternating direction method of multipliers (ADMM-DFL). This algorithm incorporates an average consensus mechanism that accommodates asymmetric networks while providing theoretical privacy guarantees against honest-but-curious clients. Under mild assumptions of convex objectives, we prove that ADMM-DFL achieves an O(1/k) convergence rate. Extensive experiments on traffic sign recognition datasets demonstrate that the proposed approach achieves comparable accuracy to the nonprivate federated averaging method while effectively defending against state-of-the-art inference attacks.

This paper investigates the formation tracking problem for open multiple autonomous surface vessel (multi-ASV) systems subject to external disturbances and unmodeled dynamics. Unlike conventional multi-ASV systems with a fixed number of ASVs, an open multi-ASV system allows ASVs to leave or join the formation freely, which naturally leads to a dynamically evolving communication topology. These structural variations directly affect the information exchange and the control execution, introducing significant challenges to the achievement of formation tracking. To address these issues, a hierarchical control protocol is developed. First, a distributed observer is designed to estimate the formation tracking error and the velocity of the leader. Then, a virtual controller is constructed to generate reference velocity signals for each ASV. Based on the reference signal, a controller is subsequently designed to regulate the motion of each ASV. To compensate for unmodeled dynamics, a neural network-based estimator is incorporated into the control loop. Furthermore, an analytical method is proposed to characterize the evolution of the error system when an ASV leaves or joins the formation. By constructing appropriate inequalities and employing Lyapunov based techniques, the formation tracking problem of open multi ASV systems with external disturbances and unmodeled dynamics is effectively addressed using the proposed control protocol. The effectiveness of the theoretical results is validated through a simulation example.

Open multi-agent systems (OMASs), characterized by the dynamic joining and leaving of agents, possess distinct attributes such as agent-level autonomy, time-varying network topologies, and environmental openness. These characteristics make them highly applicable to dynamic scenarios like robotic swarms, smart grids, and vehicular networks. However, such dynamism introduces core challenges in maintaining system stability, achieving efficient collaboration, and guaranteeing decision robustness. This paper presents a brief overview of recent advances in distributed control and decision-making algorithms for OMASs. First, the fundamental concepts and control strategies of OMASs are systematically reviewed. Second, distributed decision-making mechanisms encompassing distributed consensus optimization, separable resource allocation, and Nash equilibrium (NE) seeking in non-cooperative games are discussed, highlighting key technologies and typical methods. Finally, an outlook on future perspectives in the field is presented.

This article addresses the distributed aggregative optimization challenge in uncertain multiple Euler-Lagrange (EL) systems, where each EL agent's local objective function depends on its own position and the aggregation of all EL agents' positions. The goal is to control all EL agents to reach their optimal positions as defined by the aggregative optimization problem. Two distributed aggregative optimization algorithms are proposed for uncertain EL systems, which are based on distinct optimization-control strategies, namely, the open-loop optimization-control strategy and the closed-loop optimization-control strategy. To address the model uncertainty in EL systems, an auxiliary second-order system is introduced, integrating with adaptive compensation and tracking techniques to mitigate the uncertainty. Given the unique structure of the aggregative optimization problem, two distributed estimation protocols are developed for handling the aggregation terms in the optimization problem. Specifically, in the open-loop optimization-control strategy, the optimization gradient is derived from the position information of the auxiliary system; whereas, in the closed-loop optimization-control strategy, the optimization gradient relies on the real-time position of the EL system. The convergence of both algorithms is rigorously proved. Unlike existing studies that mainly concentrate on distributed optimization algorithms based on either open-loop or closed-loop strategies, this article is dedicated to conducting a comprehensive comparative analysis of open-loop and closed-loop optimization-control strategies, with a special emphasis on the robustness of the closed-loop strategy in counteracting external disturbances and variations. Finally, the proposed distributed aggregative optimization algorithms are applied to the optimal localization problem of networked marine vehicles with parameter uncertainties. Comprehensive simulation comparisons are conducted to verify the theoretical results.

This paper investigates the distributed leader escort control problem for multiple autonomous surface vessels (ASVs) with cooperative and competitive interactions. A signed graph is employed to model the complex communication relationships among the vessels, where positive and negative edge weights represent cooperation and competition, respectively. A distributed sliding mode controller is developed to achieve time-varying formation and symmetric escort control under structurally balanced signed graphs. To address the challenges of unknown dynamics and external disturbances, a double-layer adaptive neural network is introduced to approximate the system uncertainties, and a pseudo-ideal weight matrix is designed to suppress parameter drift and reduce steady-state fitting errors. Theoretical analysis demonstrates that the proposed control scheme ensures asymptotic stability of the formation system. Numerical simulations are provided to verify the effectiveness and robustness of the proposed approach.

This paper studies two types of finite-time robust distributed optimization problems for second-order multi-agent systems with disturbances. The first type of optimization problem focuses on handling consensus constraints, while the second type emphasizes solving supply-demand balance constraints. To address the adverse effects of external disturbances on the optimization process, this paper proposes a two-stage optimization framework. The first stage employs an integral sliding mode control strategy integrated with super-twisting algorithm to reject unbounded disturbances, relaxing the restrictive assumption of bounded disturbances. The second stage implements two types of distributed finite-time controllers designed for two distinct optimization problems, respectively. One is designed for consensus optimization, employing homogeneous control and finite-time estimator-based techniques to achieve state consensus while collaboratively minimizing the global cost function; the other is developed for supply-demand balance optimization, utilizing backstepping method to address supply-demand balance constraint. Through rigorous theoretical analysis, it is proved that the proposed control strategies can effectively suppress external disturbances and enable the second-order multi-agent system to converge to the optimal solutions of the optimization problems in finite time while ensuring stability. The proposed control strategies are validated through numerical simulations.

Focusing on two-layer multi-agent systems affected by malicious network attacks that trigger topology switching, this work investigates the problem of distributed node-to-node consensus control. Unlike the majority of existing research that presumes a static communication topology for the follower layer, this work examines a more demanding scenario in which the follower-layer topology changes over time and might temporarily lose connectivity due to cyberattacks. A new distributed control protocol is put forward, and on this basis, adequate criteria for realizing practical node-to-node consensus are deduced, a result that guarantees consensus tracking errors will be confined to a bounded range. A set of multiple Lyapunov functions are established to assess system stability during both regular operation and attack time slots. Moreover, specific limits on the attack duration within each cycle are presented. To validate the performance of the proposed control protocol, a simulation case is implemented in the final section.

This paper proposes a predictive control approach for discrete-time multi-agent systems (MASs) under limited data rates and denial-of-service (DoS) attacks. By integrating dynamic quantization with distributed model predictive control (DMPC), a resilient quantized predictive control approach is developed. The predictive control approach not only proactively mitigates DoS-induced consensus performance degradation but also reduces the conservatism of the dynamic quantization scheme in preventing quantizer saturation during attacks. Finally, effectiveness of the theoretical results is demonstrated through comparative numerical simulations.

This paper addresses the problem of distributed online generalized Nash equilibrium (GNE) learning for multi-cluster games with delayed function feedback. Specifically, each agent in the game is assumed to be informed of a sequence of local cost functions and constraint functions, which are known to the agent with time-varying delays subsequent to decision-making at each round. The objective of each agent within a cluster is to collaboratively optimize the cluster's cost function, subject to time-varying coupled inequality constraints and local constraint sets over time. Additionally, it is assumed that each agent is required to estimate the decisions of all other agents through interactions with its neighbors, rather than directly accessing the decisions of all agents, i.e., each agent needs to make decisions under partial-decision information. To solve such a challenging problem, a novel distributed online delay-tolerant GNE learning algorithm is developed based upon the primal-dual algorithm with an aggregation gradient mechanism. The system-wise regret and the constraint violation are formulated to measure the performance of the algorithm, demonstrating sublinear growth with respect to the time horizon ${\boldsymbol} T$ under certain conditions. Finally, numerical results are presented to verify the effectiveness of the proposed algorithm.

This paper presents a comprehensive overview of distributed Nash equilibrium (NE) seeking algorithms in non-cooperative games for multi-agent systems (MASs), with a distinct emphasis on the dynamic control perspective. It specifically focuses on the research addressing distributed NE seeking problems in which agents are governed by heterogeneous dynamics. The paper begins by introducing fundamental concepts of general non-cooperative games and the NE, along with definitions of specific game structures such as aggregative games and multi-cluster games. It then systematically reviews existing studies on distributed NE seeking for various classes of MASs from the viewpoint of agent dynamics, including first-order, second-order, high-order, linear, and Euler-Lagrange (EL) systems. Furthermore, the paper highlights practical applications of these theoretical advances in cooperative control scenarios involving autonomous systems with complex dynamics, such as autonomous surface vessels, autonomous aerial vehicles, and other autonomous vehicles. Finally, the paper outlines several promising directions for future research.

This paper addresses the challenge of distributed optimization for multiple Euler-Lagrange (EL) systems subject to local inequality constraints. We develop a distributed nonlinear control algorithm featuring an inner-outer loop architecture. The outer loop embeds a constraint-handling mechanism that handles local inequality constraints while solving the optimization problem, whereas the inner loop tracks reference trajectories. Theoretical analysis using Lyapunov methods proves that all closed-loop signals remain bounded, with agents’ positions converging exponentially to the optimal solution under standard assumptions. Comprehensive numerical simulations on multi-robotic manipulator coordination validate the algorithm’s effectiveness in achieving constraint satisfaction and solution optimality.

This paper explores a class of distributed optimal coordination problems with coupled objectives, incorporating features of distributed optimization and non-cooperative game. In this context, the local objective functions of agents depend on their own decisions as well as the decisions made by other agents. The objective of the agents is to achieve optimal coordination by minimizing the team objective function, which represents the average of all agents' local objective functions. The main challenge lies in obtaining the partial derivatives of the team objective function, which are aggregations of all local objective functions' partial derivatives and cannot be directly obtained by the agents. To tackle this problem, distributed optimal coordination control laws based on fixed-time estimation are developed. These control laws utilize distributed fixed-time estimators that enable agents to estimate the team decision and partial derivatives of the team objective function within a fixed time. The proposed distributed optimal coordination control laws guarantee the exponential convergence of the agents to the optimal states when the constraint sets are independent. Under the condition of a common constraint set, the proposed laws further ensure fixed-time optimal coordination. A numerical example involving coordinated dynamic positioning of a multi-agent system is presented to demonstrate the effectiveness of the proposed algorithms. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This paper addresses the challenges of formation tracking control and distributed node-to-node monitoring for multi-autonomous surface vessels (ASVs) in the presence of unknown nonlinear dynamics. To facilitate real-time monitoring of remote ASVs, a virtual-node-mapping-based monitoring architecture is proposed. Within this architecture, a virtual node corresponding to each real ASV is established on the remote monitoring platform. Based on this framework, a two-layer cooperative control strategy is developed. Specifically, in the real ASV layer, an adaptive neural network (NN) controller is designed to utilize local and neighboring information for com-pensating unknown nonlinear dynamics and achieving precise formation tracking. In the virtual node layer, virtual node control inputs are formulated by leveraging sparse state information of ASVs (e.g., position and velocity), enabling the monitoring platform to reconstruct the full system formation state and accomplish distributed node-to-node monitoring. The asymptotic stability of both the closed-loop multi-ASV system and the virtual monitoring system is rigorously proven using Lyapunov stability theory. Simulation results demonstrate that the proposed method achieves formation tracking and distributed node-to-node monitoring even under constraints of partial information transmission.

This paper considers the fully distributed formation control problem of autonomous surface vessels (ASVs) with multiple conflicting tasks using a non-cooperative game approach. In the present problem, each ASV is assigned a global formation task while simultaneously having an individual task to approach a specified target with a local desired displacement. Due to the conflicting relationship between the individual task and the global task, this paper proposes the construction of a local cost function for each ASV. This formulation aims to transform the formation control problem, considering task conflicts, into a non-cooperative game problem. To achieve a balance between the global task and the individual task, a formation control law based on non-cooperative game theory is proposed. The control law aims to enable the ASVs to distributively search for the Nash equilibrium of the non-cooperative game. Specifically, the proposed formation control law is fully distributed, with control gains being designed to be adaptive. Theoretical analysis demonstrates that the designed controllers can drive all ASVs' states to converge to the Nash equilibrium without relying on any global information, even in the context of external disturbances. Finally, numerical simulations are performed to verify the validity of the theoretical results.

This article addresses the distributed leader escort control problem for multiple autonomous surface vessels (multi-ASVs) by adopting a signed graph-based modeling approach to represent interaction relationships among the ASVs. Within this framework, the ASVs are classified into two groups, with the control objective of forming time-varying formations on either side of the dynamic leader while maintaining consistent distances. One challenge in addressing this issue is that only a subset of the following ASVs has access to the escort information and the motion data of the leader. Focusing on scenarios with only external disturbances, we introduce a predefined-time escort control scheme that confines error systems within a designated manifold using two auxiliary time-varying functions. It is proven that the predefined-time leader escort can be achieved under the present control scheme with appropriate gain parameters. To address the leader escort control problem in the presence of internal model uncertainties and external disturbances, we develop a fully distributed robust adaptive leader escort controller that guarantees the asymptotic convergence of escort errors. Specifically, neural networks and nonsmooth feedback are employed to approximate model uncertainties and to compensate for unknown bounded disturbances, respectively. Notably, the control gains are adaptively adjusted without reliance on any global information. The efficacy of the proposed escort controllers is verified through comprehensive simulation and experimental studies.

This paper investigates the problem of non-cooperative game-based formation tracking control for unmanned surface vessels (USVs) under Markovian switching topologies. In contrast to previous works on collaborative tracking control with fixed communication topologies, the USVs considered in this paper exhibit non-cooperative relationships, and the communication topology is subject to Markovian switching. To address these challenges, a game-theoretic approach is employed to balance the conflicting tasks of the USVs. Specifically, a distributed estimate protocol is designed to enable the USVs to estimate information about non-neighboring USVs through Markovian switching topologies. Based on this distributed estimate protocol, a distributed control law is developed to guide the USVs towards the Nash equilibrium of the non-cooperative game. The effectiveness of the proposed control law is validated through numerical simulations.

This paper investigates the problem of Nash equilibrium (NE) seeking in noncooperative games involving multiple uncertain Euler-Lagrange (EL) systems. In the considered noncooperative game, each EL agent aims to minimize its local objective function, which depends on its own position and the positions of other EL agents. The objective is to control all EL agents to reach the NE positions defined by the noncooperative game. Different from existing decoupled decision-control methods, this paper proposes a closed-loop decision-control approach for addressing the noncooperative game problem of uncertain EL systems. In this approach, the decision-making process for game purposes and the control process of the EL agents are coupled with each other and form a closed loop. By utilizing adaptive techniques, the strong monotonicity requirement for the pseudo-gradient in noncooperative game is eliminated. The global asymptotic convergence of the proposed algorithm is established. Finally, numerical simulations are conducted to validate the theoretical results.

This paper aims to investigate the fully distributed Nash equilibrium (NE) seeking problem in networked games under Denial of Service (DoS) attacks. A fully distributed NE seeking algorithm is proposed, specifically designed to be resilient against DoS attacks. In an environment where DoS attacks can impair network connectivity, existing NE algorithms may experience degraded performance or even failure. To seek NE in a distributed manner without relying on any global information, adaptive control gains are introduced and a topology-dependent adaptive protocol for switching topologies is designed. Moreover, an estimation-feedback-based distributed NE seeking algorithm is proposed. The exponential convergence to NE of the proposed algorithm is established under specific conditions regarding the duration of the DoS attacks. Finally, the effectiveness of the algorithm is validated by numerical simulations.

In this article, a target protection problem of multiunmanned surface vessels (multiUSVs) with conflicting individual and group goals is formulated and investigated. In the present problem, the group goal of the USVs is to cooperatively protect a given moving global target by maintaining it at the center of the formation formed by the USVs, whereas each USV has an individual goal of tracking its designated target. Striking a balance between inherently conflicting goals poses a significant challenge, especially in the face of the unknown aggregated information about the center of the formation. This article aims to determine trajectories for USVs to achieve a balance between conflicting individual and group goals. To fulfill this objective, the target protection problem is first transformed into a time-varying aggregative game. Then, a distributed multiround prediction-correction algorithm (DMPCA) is designed to track the unique Nash equilibrium trajectory (NET) of the time-varying aggregative game. It is theoretically proved that the trajectory generated by DMPCA could linearly converge to a bounded domain of NET if the underlying undirected communication graph among the USVs is connected and the algorithm parameters are appropriately selected. Finally, experimental studies are performed to verify the effectiveness of the algorithm.

Distributed aggregative optimization (DAO) is a special class of optimization problems of networking agents where the local objective function of each agent relies on the aggregation of other agents’ decisions as well as its own. It is widely known that convergence rate is one of the most important evaluation indexes for practical applications of DAO algorithms. However, it is challenging to achieve fast convergence rate for DAO algorithms over a directed graph, owing to the fact that the underlying interaction graph may be unbalanced, and the local objective functions of individual agent depend upon the decisions of other ones. To efficiently solve the DAO problem over directed graphs, a kind of accelerated distributed optimization algorithm with Nesterov momentum and constant step-size is designed and analyzed. To handle the effect of unbalanced property of the directed networks on solving the DAO problem, a consensus iteration law is embedded into the optimization algorithm to estimate the left Perron eigenvector of the weight matrix. Furthermore, a kind of distributed aggregative gradient tracking technology associated with the Nesterov momentum coefficient is developed and employed to construct the accelerated distributed aggregative algorithm. It is theoretically shown that the proposed optimization algorithm could yield a favorable linear convergence rate after limited iterative steps when the global objective function is $\mu$ -strongly convex and $L_{1}$ -smooth. At last, numerical experiments are provided to confirm the findings.