Adaptive NNs Fault-Tolerant Control for Nonstrict-Feedback Nonlinear Systems

In this paper, the problem of fault-tolerant control (FTC) is investigated for a class of nonlinear single input and single output (SISO) systems in the non-strict feedback form. The considered system possess unknown nonlinear functions, unmeasured states, unknown time-varying delays, unknown control direction and actuator faults (bias and gain faults). Neural networks (NNs) are adopted to approximate the unknown nonlinear functions. Then, a state observer is constructed to solve the problem of unmeasured states. In the frame of adaptive backstepping design technique, by combining with Nussbaum gain function and Lyapunov-Krasobskii functional theory, an adaptive NNs output feedback FTC method is developed. It is shown that all signals in the closed-loop system are proved to be bounded, and the system output can follow the given reference signal well.