Fault diagnosis and fault tolerant tracking control for the non-Gaussian singular time-delayed stochastic distribution system with PDF approximation error

In this paper, fault diagnosis and fault tolerant tracking control algorithms are proposed for the non-Gaussian singular time-delayed stochastic distribution control system. The square root B-spline model is used to approximate the output probability density function (PDF), and the PDF approximation error is taken into consideration. A fault diagnosis approach based on the adaptive observer is constructed to diagnose the size of fault in the singular stochastic distribution control (SDC) system. When fault occurs, in order to track the expected PDF, a distribution tracking error dynamic system is established. The purpose of fault tolerant tracking control is transformed into making the distribution tracking error at each time instant satisfy a certain upper bound beyond a limited time. Then the fault tolerant controller is designed using the fault diagnosis information and other measurable information. A simulation example is included to illustrate the effectiveness of the proposed algorithms and encouraging results have been obtained.