Distributed Nash Equilibrium Seeking for a Class of Uncertain Nonlinear Systems subject to Bounded Disturbances

TL;DR

This paper develops a distributed control method for N-player games with uncertain nonlinear dynamics over switching networks, achieving Nash equilibrium seeking and disturbance rejection.

Contribution

It introduces a novel integration of consensus, distributed estimation, and adaptive control for uncertain nonlinear systems in a networked game setting.

Findings

Successful Nash equilibrium convergence under switching network conditions.

Effective disturbance rejection for bounded, unknown disturbances.

Extension to high-order integrator systems.

Abstract

In this paper, we study the problem of the distributed Nash equilibrium seeking of N-player games over jointly strongly connected switching networks. The action of each player is governed by a class of uncertain nonlinear systems. Our approach integrates the consensus algorithm, the distributed estimator over jointly strongly connected switching networks, and some adaptive control technique. Furthermore, we also consider the disturbance rejection problem for bounded disturbances with unknown bounds. A special case of our results gives the solution of the distributed Nash equilibrium seeking for high-order integrator systems.