Nash Equilibrium Seeking for General Linear Systems with Disturbance Rejection

TL;DR

This paper develops distributed strategy-updating rules for general linear systems in aggregative games that effectively reject external disturbances and converge to Nash equilibrium, using passive and Lyapunov stability theories.

Contribution

It introduces novel disturbance-rejection strategy-updating rules based on internal models and passive theory, applicable to systems with perfect and imperfect information.

Findings

Strategies converge to Nash equilibrium despite disturbances

Proposed rules outperform gradient-based algorithms in disturbance rejection

Simulation results confirm theoretical stability and convergence

Abstract

This paper explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on internal model are proposed for the case with perfect and imperfect information, respectively. Different from existing algorithms based on gradient dynamics, by introducing the integral of gradient of cost functions on the basis of passive theory, the rules are proposed to force the strategies of all players to evolve to Nash equilibrium regardless the effect of disturbances. The convergence of the two strategy-updating rules is analyzed via Lyapunov stability theory, passive theory and singular perturbation theory. Simulations are presented to verify the obtained results.