Active Tolerant Control For Non-gaussian Singular Stochastic Distribution Systems

Nearly twenty years, stochastic distribution control (SDC) system has appearedas a new branch in the field of stochastic control studies, where the input is as adeterministic input and the output is the probability density function (PDF) of theoutput variable. System variables of the stochastic distribution system are no longerrestricted to be Gaussian variables. The assumption that variable of stochasticsystems obey Gaussian distribution can be eliminated. Fault diagnosis and faulttolerant control of stochastic distribution system is an important part of controltheory and applications.For stochastic distribution system, the current modeling, fault diagnosis andfault-tolerant control are based on general dynamic systems. Few literatures reportfault diagnosis and fault tolerant control of singular stochastic distribution system. Insingular stochastic distribution system, the dynamic model is expressed by a singularsystem, which not only contains the singular characteristic of the system, but alsocontains the characteristics of stochastic distribution systems. The singular stochasticdistribution system in actual grinding process engineering and other fields have awide range of applications, therefore, the research of fault diagnosis andfault-tolerant control for singular stochastic distribution systems, not only theoretical,but also has practical significance.In this thesis, when the objective PDF is known, deep research of faultdiagnosis and fault tolerant control has been carried out for non-Gaussian singularstochastic distribution control systems. The main contents are shown as follows:①For class of nonlinear singular stochastic distribution control system, inwhich the Lipschitz condition is satisfied, a new fault diagnosis and fault tolerantcontrol algorithm is proposed. Different from general stochastic distribution controlsystems, the relationship between the weights and the control input in singularstochastic distribution control systems is expressed by a singular state space model,which increases the difficulty in design of fault detection and diagnosis (FDD) and fault-tolerant method. A non-singular state transformation is made to transform thesingular dynamic system into a differential-algebraic system. An adaptive nonlinearobserver is designed to estimate the size of the fault occurring in system. Based onthe estimated fault information, by minizing the tracking performance index,fault-tolerant controller is designed, which can make the post-fault probabilitydensity function still track the given distribution.②For a class of nonlinear singular stochastic distribution control system basedon the Takagi-Sugeno fuzzy model, a new fault diagnosis and fault tolerant controlalgorithms is proposed. The main contribution of this method is that an integratedfault diagnosis and fault tolerant control scheme is given. Fault diagnosis is based onthe use of a fuzzy fault diagnosis observer, with which the fault can be diagnosedand the disturbance can be rejected simultaneously. The fault tolerant controller isimplemented as an augmented state feedback and a fault compensation term. Basedon the estimated fault and system state estimation information, the fault-tolerantcontroller makes the post-fault output PDF still tracking the given distribution.③For a class of non-Gaussian discrete singular stochastic distribution systems,the whole control process is divided into several batches based on iterative learningmechanism. In each batch, an adaptive observer is designed to carry out faultdiagnosis. The tracking performance index is minimized and the optimalfault-tolerant controller can be obtained to make the post-fault output PDF still trackthe given distribution. Between adjacent batches, the iterative learning controlstrategy is used to update the center and width of radial basis function (RBF) neuralnetwork. At the end of the last batch, the output probability density function of thesystem can track the given probability density function.