Distributed nash equilibrium seeking for heterogeneous second-order nonlinear noncooperative games with communication delays

Abstract

Abstract This paper investigates the noncooperative game problems over weight-balanced digraphs with communication delays. Compared with existing noncooperative games, a class of noncooperative games that are more aligned with practical systems is discussed, where all agents have uncertain heterogeneous second-order nonlinear dynamics. Then, considering two different types of communication delays, respectively slowly-varying communication delays and fast-varying communication delays, the distributed algorithm is designed to seek the Nash equilibrium (NE). By designing appropriate Lyapunov functions and constructing linear matrix inequalities, the designed algorithm has been proven to be effective, even though second-order nonlinear dynamics and communication delays increase the challenges of system convergence analysis. Furthermore, simulation cases are given to illustrate the validity of the designed algorithm.

Keywords

• Second-order nonlinear dynamics
• Nash equilibrium
• Communication delays
• Noncooperative games