Optimal Fault-tolerant Control for A Class of Nonlinear Systems by Using Zero-sum Differential Game

In this paper, an optimal fault-tolerant control (FTC) method using zero-sum differential game is proposed for a class of nonlinear systems with actuator faults. Firstly, it is reveals that the FTC problem is equivalent to a zero-sum differential game problem, in which the controller and the fault are regarded as two opposite players. Secondly, the Nash-equilibrium is established by minimax principle, and the coupling Hamilton-Jacobi-Isaacs (HJI) equation is further solved by adaptive dynamic programming (ADP) method. Besides, a FTC learning law of the weight is proposed, which only uses a critic network. Finally, an example is given to illustrate the efficiency and applicability of the obtained theoretical results.