Minimum entropy fault diagnosis and fault tolerant control for the non-Gaussian stochastic system

Abstract

In this paper, the fault diagnosis (FD) and fault tolerant control (FTC) problems are studied for stochastic systems with non-Gaussian disturbance and fault. Unlike classical FD algorithm, the minimum entropy fault diagnosis is adopted, which has led to a new design approach that either minimizes the residual entropy or controls the shape of the probability density function (PDF) of the residual signal. The diagnostic algorithm is developed which produces the estimate of the fault so that the observation error systems is locally and ultimately bounded in the mean-square sense. Since the entropy has been used to characterize the uncertainty of the tracking error for non-Gaussian stochastic systems, the minimum entropy fault tolerant control is applied to decrease the uncertainty of the tracking error. The PDF of the output tracking error is approximated by the square-root B-spline model. By minimising the performance function with regard to the entropy of the tracking error, the controller is obtained. An illustrative example is utilized to demonstrate the use of the FD and FTC algorithm, and satisfactory results have been obtained.