Nash Equilibrium Seeking for General Linear Systems With Disturbance Rejection

This article 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 the internal model are proposed for the case with perfect and imperfect information, respectively. Different from the existing algorithms based on gradient dynamics, by introducing the integral of the gradient of cost functions on the basis of the passivity theory, the rules are proposed to force the strategies of all agents to evolve to the Nash equilibrium, regardless of the effect of disturbances. The convergence of the two strategy-updating rules is analyzed via the Lyapunov stability theory, passivity theory, and singular perturbation theory. Simulations are performed to illustrate the effectiveness of the proposed methods.