Distributed Nash equilibrium seeking for aggregative games with second-order nonlinear players

The aggregative games of multi-agent systems are studied in this paper, where the players have second-order nonlinear dynamics with uncertain parameters and the communication networks among the players are weight-balanced digraphs. In order to control these heterogeneous second-order nonlinear players to autonomously seek the Nash equilibrium of aggregative games, two distributed algorithms are developed. Moreover, the convergence of the two algorithms is analyzed via Lyapunov theorems and variational analysis. By the two algorithms, the players globally exponentially converge to the Nash equilibrium, although the second-order nonlinear dynamics contain uncertain parameters. Finally, the effectiveness of the two algorithms are verified by a numerical example. (c) 2021 Elsevier Ltd. All rights reserved.