Zero-sum games-based optimal fault tolerant control for control-constrained multiplayer systems with external disturbances via adaptive dynamic programming

Abstract

In this paper, the optimal fault tolerant control problem is investigated for constrained multiplayer systems with external disturbances and completely unknown dynamics. According to games theory, each control player along with its corresponding fault player and disturbance player can be regarded as a two-player zero-sum game, respectively. To release the restriction on the system dynamics, a neural network-based system identification technique is employed to reconstruct the completely unknown system models. A new nonquadratic function is constructed to incorporate the control constraints into the optimization, and the corresponding constrained Hamilton–Jacobi-Isaacs equations (HJIEs) are derived. Then, the constrained HJIEs are solved by adopting a single critic neural network, where an experience replay technique is utilized to exclude the persistence of excitation condition. Furthermore, all signals of the close-loop system are proven to be uniformly ultimately bounded based on the Lyapunov stability theory. Finally, two examples are presented to verify the effectiveness of the developed optimal zero-sum games scheme.