Optimal distributed learning for disturbance rejection in networked non-linear games under unknown dynamics

Abstract

In this study, an online distributed optimal adaptive algorithm is introduced for continuous-time non-linear differential graphical games under unknown systems subject to external disturbances. The proposed algorithm learns online the approximate solution to the coupled Hamilton–Jacobi–Isaacs equations. Each of the players in the game uses an actor-critic network structure and an intelligent identifier to find the unknown parameters of the systems. The authors use recorded past observations concurrently with current data to speed up convergence by exploring the state space. The closed-loop stability and convergence of the policies to Nash equilibrium are ensured by using Lyapunov stability theory. Finally, a simulation example shows the efficiency of the proposed algorithm.