Event-Triggered Robust Control for Fully Cooperative Games of Uncertain Nonlinear Multi-player Systems

This paper develops an adaptive dynamic programming-based event-triggered robust control method for fully cooperative games of nonlinear multi-player systems with uncertainties. By designing a modified value function, the robust control problem is transformed into a fully cooperative (FC) game of the nominal system. Then, a critic neural network is constructed to solve the Hamilton-Jacobi-Bellman equation of the FC game, and the optimal control laws of all players are obtained. Under the event-triggered mechanism, the designed event-triggering condition is employed to determine whether the control laws should be updated or not. The developed method saves computation and communication resources, since both the updating frequency of control laws and the communication between controllers and actuators are reduced. Furthermore, the closed-loop system is proven to be uniformly ultimately bounded thanks to the Lyapunov’s direct method. A numerical example is employed to verify the effectiveness of the developed method.

I. Introduction

For practical applications, complex systems such as aerospace systems, communication systems and micro-grid systems are always controlled by multiple controllers which can be regarded as players trying to minimize their individual performance index functions. Game theory has been widely applied to make decisions for multi-players. According to the roles of players, the multi-player games can be divided into several categories, i.e., fully cooperative (FC) games, zero-sum games and non-zero-sum games [1]. In the FC game, all players cooperatively fulfill proper tasks based on the same value function. As it is well known, it is difficult to solve the Hamilton-Jacobi-Bellman (HJB) equation whose analytic solution is difficult or impossible to obtain for nonlinear systems [2], [3].