Distributed Nash Equilibrium Seeking for Noncooperative Games of High-Order Nonlinear Multi-Agent Systems Over Weight-Unbalanced Digraphs

In this paper, we investigate the noncooperative games of multi-agent systems. Different from existing noncooperative games, our formulation involves the high-order nonlinear dynamics of players, and the communication topologies among players are weight-unbalanced digraphs. Due to the high-order nonlinear dynamics and the weight-unbalanced digraphs, existing Nash equilibrium seeking algorithms cannot solve our problem. In order to seek the Nash equilibrium of the noncooperative games, we propose two distributed algorithms based on state feedback and output feedback, respectively. Moreover, we analyze the convergence of the two algorithms with the help of variational analysis and Lyapunov stability theory. By the two algorithms, the high-order nonlinear players exponentially converge to the Nash equilibrium. Finally, two simulation examples illustrate the effectiveness of the algorithms.