Optimal adaptive fuzzy FTC design for strict-feedback nonlinear uncertain systems with actuator faults

In this paper, the optimal fault-tolerant control (FTC) design problem is investigated for strict-feedback nonlinear systems. The considered nonlinear systems contain actuator faults, which are bias fault and gain fault. The problem of actuator faults is solved by utilizing the adaptive compensation technique. Applying the backstepping design technique, a main fault-tolerant controller is established. Via the designed main fault-tolerant control strategy, the controlled nonlinear system can be converted to an equivalent nonlinear system in affine form. Subsequently, a fuzzy logic system (FLS) is introduced to approximate the unknown cost function, and an adaptive fuzzy feedback optimal controller is developed. The whole adaptive fuzzy fault-tolerant optimal control scheme consists of a main controller and a feedback optimal controller. Based on the Lyapunov theory, it is proved that all the signals in the closed-loop system are bounded, the system output can track a bounded reference signal. In addition, the proposed control method can guarantee the cost function is the smallest. Simulation results are provided to illustrate the effectiveness of the proposed fault-tolerant optimal control scheme.