Fuzzy Based Optimal Fault Tolerant Control and Adaptive Critic Design for Strict Feedback Systems

In this paper, the optimal fault tolerant control (OFTC) problem is solved for a class of uncertain nonlinear strict feedback discrete-time systems based on the adaptive critic design (ACD). By introducing an auxiliary signal, the influence of the actuator fault on the control performance can be compensated. According to the gradient descent scheme, the updating law for the auxiliary signal is developed based on a quadratic cost function. Since the matched condition is not satisfied, it will lead to additional difficulty such as the causal problem. On the basis of the diffeomorphism theory, the considered system is transformed into a novel model, which is suitable to deal with the problem. In the design of OFTC, fuzzy logic systems (FLSs) are exploited to approximate the unknown functions. By combining the backsteppping technique with the reinforcement learning (RL) scheme, the OFTC can not only maintain the stability of the systems, but also obtain an optimal performance as well. Finally, the feasibility simulation is studied to further give the evidence of the present control approach.