This article investigates the distributed Nash equilibrium (NE) seeking problem of uncertain multiagent systems in unreliable communication networks. In this problem, the action of each agent is subject to a class of nonlinear systems with uncertain dynamics, and the communication network among agents will be affected by the nonperiodic denial of service (DoS) attacks. Note that, in this insecure network environment, the existence of DoS attacks will directly destroy the connectivity of the network, which leads to performance degradation or even failure of the most existing distributed NE seeking algorithms. To address this problem, we propose a two-stage distributed NE seeking strategy, including the attack-resilient distributed NE estimator and the neuroadaptive tracking controller. The estimator based on the projection subgradient method and the consensus protocol can converge exponentially to virtual NE against DoS attacks. Then, the neuroadaptive tracking controller is designed for uncertain multiagent systems with the output of the estimator as the reference signal such that the actual action of all agents can reach NE. Based on the Lyapunov stability theory and improved average dwell time automaton, the stability of the estimator and the controller is proven, and all signals in the closed-loop system are uniformly bounded. Numerical examples are presented to verify the effectiveness of the proposed strategy.

This article investigates noncooperative formation control in the presence of malicious agents who disseminate negative information to their neighbors, resulting in misbehavior. A local cost function for agents is introduced to transform the formation control problem into a noncooperative game problem such that the Nash equilibrium solution corresponds to the agents' decisions in the desired formation. The resilient game strategy is proposed, comprising an event-triggered game algorithm and a threshold-based malicious agents detection algorithm, enabling each agent to determine the malice of their neighbors at each trigger moment and selectively interact with them, which guarantees that all normal agents can achieve Nash equilibrium, and the stability is analyzed by Lyapunov theory. Finally, the effectiveness of the algorithms is verified through a multi-unmanned aerial vehicles formation control experiment.

In this article, we investigate the problem of seeking Nash equilibrium (NE) in multiagent systems within cooperation–competition networks. Each agent aims to optimize a total cost function that accounts for its own interests as well as those of its cooperators, considering both cooperative and noncooperative interactions with other agents. It is worth noting that, unlike in existing N-coalition games, the agents in this study only have knowledge of whether they are cooperative or noncooperative with their neighboring agents; they do not have information about non-neighboring agents who might be cooperators. As a result, due to potential disconnections in the communication topology within the cluster, it is not possible to consider the entire cluster as a virtual player to optimize its objective functions. To address this issue, we developed an algorithm using the singular perturbation technique, which divides the system into two distinct timescales. We propose a novel estimation algorithm to estimate the total cost function of disconnected subnetworks within the fast system. In the slow system, the search for NE is based on a gradient algorithm, while the Lyapunov stability theory is utilized to analyze the convergence of the algorithms. Furthermore, we extend the problem to accommodate scenarios where multiple subnetworks exist within the network. Numerical simulations are conducted to demonstrate their capability for resolving the noncooperative game problem in cooperation–competition networks.

In this paper, we investigate the distributed optimization problem in the presence of unreliable agents who transmit unfavorable state information to their neighbors, resulting in misbehavior among cooperative agents. This gives rise to untrustworthy interactive information between agents. To overcome this challenge, we propose observer-based and sample-and-hold-based event-triggered resilient optimization strategies, complemented by threshold-based detection and isolation strategies. These strategies enhance the system's robustness against unreliable agents and enable cooperative agents to identify and disregard interaction information from unreliable neighbors. The system exhibits right-discontinuity due to intermittently changing communication networks and event-triggered time sequences. To analyze the convergence of nonsmooth systems, we integrate Filippov's differential inclusions with Lyapunov stability theory. Finally, we validate the efficacy of the proposed algorithms through comprehensive simulation results.

This article investigates the time-varying formation control problem (TVFCP) of multiagent systems (MAS) across two networks, wherein agents from distinct networks amalgamate to form a fully connected network through mixed interactions. Notably, each network is internally disconnected, resulting in unknown member identities within each network, and unobservable relative positions among agents. A game-based formation control (GBFC) strategy is proposed, incorporating private costs to delineate formation tasks, and a novel information exchange mechanism to realize the reconstruction of disconnected network characteristics, ensuring rapid convergence of all agents to the desired formation within their respective networks. Importantly, this strategy does not rely on inter-agent position or formation vector information exchange. Experimental and simulation results validate the effectiveness of the proposed algorithm.