Distributed Nash Equilibrium Seeking for Multi-Cluster Games of Second-Order Nonlinear Systems

In this paper, the multi-cluster game of the second-order nonlinear system with partial-decision information is studied, which is a unified framework for distributed optimization and noncooperative games. Therein, the agents inside each cluster need to satisfy the linear coupled equality constraint. In addition, the intra-cluster communication digraphs are weight-balanced and the inter-cluster communication digraph is weight-unbalanced. A new algorithm is developed based on the state feedback and leader-following consensus protocol. By virtue of the Lyapunov stability theory, it is proved that the algorithm can converge asymptotically to the Nash equilibrium of the multi-cluster game. Finally, the effectiveness of the algorithm is illustrated by numerical simulations.