Disturbance rejection of multi-agent systems: A reinforcement learning differential game approach

Distributed tracking control of multi-agent linear systems in the presence of disturbances is considered in this paper. The given problem is first formulated into a multi-player zero-sum differential graphical game. It is shown that the solution to this problem requires solving the coupled Hamilton-Jacobi-Isaacs (HJI) equations. A multi-agent reinforcement learning algorithm is developed to find the solution to these coupled HJI equations. The convergence of this algorithm to the optimal solution is proven. It is also shown that the proposed method guarantees L₂-bounded synchronization errors in the presence of dynamical disturbances.