Fault Diagnosis And Minimum Entropy Fault Tolerant Control For Non-gaussian Singular Stochastic Distribution System

In many practical complex control systems, the shape of the output probabilitydensity function (PDF) rather than the output of the system needs to be controlled.Such systems can be described by stochastic distribution control (SDC) systems.The existing research of fault diagnosis (FD) and fault-tolerant control (FTC) inthe SDC system is rarely involved with singular dynamic systems. At present, FTCfor the SDC system mostly focus on the case that the target PDF is known inadvance. When the target PDF is unknown, the traditional method of FTC is onlonger applicable.Effective fault diagnosis and fault tolerant control algorithms are presented fornon-Gaussian singular stochastic distribution control systems in this thesis. Adaptiveobservers are used to diagnose the faults of the singular stochastic distributionsystems. Furthermore, the gain of the observer and adaptive updated law can bedetermined by solving the corresponding linear matrix inequality (LMI).When theobjective PDF information of the non-Gaussian singular stochastic distributionsystem is not known in advance. The concept of entropy is introduced to faulttolerant control for singular stochastic distribution systems. Theoretically, theresearch area of fault diagnosis and fault tolerant control for stochastic distributionsystems will be broadened. The main contents of this thesis include the followingthree issues:①Different from general SDC systems, the difficulty increases in the FD andFTC design of the singular SDC system as the dynamic relationship between theweights and the control input is expressed by a singular state space model. Anadaptive observer is used to diagnose the fault of the singular stochastic distributionsystem. Furthermore, the gain of the observer and adaptive updated law can beformulated by solving the corresponding LMI. Based on the estimated faultinformation, the controller is reconfigured by minimizing the performance functionwith regard to the Shannon entropy subject to mean constraint. The reconfigured controller can make the output of the post-fault SDC system still have minimumuncertainty, leading to the minimum entropy FTC of the non-Gaussian singular SDCsystem.②Due to the limitations of linear B-spline appromation, the rationalsquare-root B-spline model is used to approximate the system output PDF. Anadaptive observer is used to diagnose the fault of the singular stochastic distributionsystem. Furthermore, the gain of the observer and adaptive updated law can beformulated by solving the corresponding linear matrix inequality. Entropy isintroduced to fault tolerant control when the target probability density function is notknown in advance. Based on the estimated fault information, the controller isreconfigured by minimizing the performance function with regard to the entropysubject to mean constraint. The reconfigured controller can make the output of thepost-fault SDC system still have minimum uncertainty, leading to the minimumentropy fault tolerant control.③An adaptive observer and LMI based fault diagnosis algorithm is proposedfor the continuous Non-Gaussian singular SDC system. Entropy is introduced to thedesign of fault tolerant control for the continuous Non-Gaussian singular SDCsystem. A new type of entropy which is called N-entropy is used to construct theperformance index function of the continuous SDC system. Based on the estimatedfault information, the minimum N-entropy controller is reconfigured by minimizingthe performance function of the continuous SDC system.