Fault diagnosis and fault-tolerant control for non-Gaussian non-linear stochastic systems using a rational square-root approximation model

The purpose of the fault detection and diagnosis of stochastic distribution control systems is to use the measured input and the system output probability density functions (PDFs) to obtain the fault information of the system. In this paper, the rational square-root B-spline model is used to represent the dynamics between the output PDF and the input. This is then followed by the novel design of a non-linear neural network observer-based fault diagnosis (FD) algorithm so as to diagnose the fault in the dynamic part of such systems. Convergency analysis is performed for the error dynamic system raised from the fault detection and diagnosis phase using the Lyapunov stability theorem. Finally, based on the FD information, a new fault-tolerant control based on proportional integral tracking control scheme is designed to make the post-fault PDF still track the given distribution. A simulated example is given to illustrate the efficiency of the proposed algorithms.