Distributed Nash Equilibrium Seeking with Adaptive Group Coordination: A Hierarchical Framework

This paper devises an upper-layer distributed game algorithm and a lower-layer distributed dynamic clustering consensus method for a multi-agent system with multiple leaders to tackle the cluster consensus issue upon the upper-layer leader reach the Nash equilibrium. For any initial directed graph with incomplete clustering and any initial state of leader and follower, the leader presents a distributed Nash equilibrium finding plan for a non-cooperative game through integrating the leader-follower consensus protocol and the gradient game. Leaders and followers have one-direction connections, and the follower’s state does not influence the leader’s state. In the absence of interconnection among clusters, a distributed dynamic clustering approach is used to couple each leader with at least one follower. The consensus is ensured by the distributed consensus control law, which discards some initially accessible edges by incorporating real-time local details regarding the states and connections, and then a unified discriminative technique resolves the problem, ultimately enabling all agents in the same cluster to achieve consensus with the leader without any disruption from other clusters. Numerical simulations confirm the efficacy of the proposed method.