Fault detection and fuzzy tolerant control for complex stochastic multivariable nonlinear systems

Abstract

Abstract In this paper, the problem of fault-tolerant control (FTC) is investigated for a class of multivariable stochastic nonlinear systems in the strict-feedback form. The considered systems possess unknown nonlinear functions, unmeasured states, virtual control coefficients 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. The problem of “explosion of complexity” is solved by using dynamic surface control (DSC) method. Based on the combination of Nussbaum gain function with Lyapunov function stability theory, an adaptive NNs output feedback FTC method is developed in the frame of adaptive backstepping design technique. It is shown that all signals in the closed-loop system are proved to be bounded in probability, and the system output can follow the given reference signal well. The effectiveness of the proposed approach is verified by a simulation example.