Zero-Sum Differential Game-Based Optimal Fault-Tolerant Control for Interconnected Systems With Actuator Faults

This article investigates the zero-sum game-based optimal fault-tolerant control problem for a series of strict-feedback nonlinear interconnected systems with both multiplicative and additive actuator failure. According to the command-filter-based backstepping theory, the feedforward controller is derived, and the optimal fault-tolerant tracking problem can be converted into an equivalent game problem for the affine tracking error system. Afterward, the adaptive dynamic programming algorithm is utilized to deal with the two-player zero-sum differential game problem, in which a critic and two actor networks are constructed to evaluate the value function, the optimal controller, and the worst-case lumped faults, respectively. It is shown that the obtained feedforward controller and the game-based optimal controller can ensure the boundedness of tracking errors while minimizing the value function. Finally, several comparison results are conducted to illustrate the reliability and effectiveness of the proposed control scheme from the aspects of network weight and optimality.