Distributed Nash Equilibrium Seeking for Multi-Cluster Game of Second-Order Nonlinear Systems With Partial Information

In this brief, the multi-cluster game of unknown second-order nonlinear systems with partial information is investigated. Therein, each cluster consisting of several collaborating agents selfishly minimizes its own cost function with each other. The agents within each cluster are constrained by coupled inequality constraints and the local cost functions depend on the global decisions of all game participants. With the help of the state feedback, a novel distributed algorithm is designed by a synthesis of the primal-dual dynamic and the leader-following consensus protocol. Moreover, the convergence analysis is conducted by the Lyapunov stability theory, and it is proved that the algorithm can converge to the Nash equilibrium (NE) of the multi-cluster game. Finally, the effectiveness of the algorithm is verified by numerical simulation.

I. Introduction

In recent years, distributed optimization [1], [2], [3], [4] and noncooperative game [5], [6] on multi-agent networks have received a lot of attention, because of their wide applications in wireless network [7] and machine learning [8].