Distributed-Observer-Based Nash Equilibrium Seeking Algorithm for Quadratic Games With Nonlinear Dynamics

Abstract

In this article, a class of distributed quadratic games is considered over an undirected graph. The issue on the communication topology restriction is introduced and the players’ dynamics are with nonlinear dynamics and unknown time-varying perturbation. A distributed Nash equilibrium seeking algorithm is proposed based on a high-gain observer method, and the convergence is analyzed by the Lyapunov stability theory. It is shown that each player estimates the rival players’ states, and the errors between the players’ states and the Nash equilibrium are ultimately bounded by a small bound. Moreover, the presented algorithm is free of chattering phenomena because it is designed using the hyperbolic tangent function instead of the signum function to dominant the perturbation. The effectiveness of the proposed algorithm is validated via a simulation of the oligopoly game in which five firms produce the same products in a duopoly market structure.