Fault Detection And Fault Tolerance Control Of Discrete-time Stochastic Systems

Random factors usually will have bad influence on the the stability of the system,which will reduce the stability of the system,lead to the collapse of the whole system and even huge economic losses,due to he huge scale and increasingly complex structure of modern industrial system.Therefore,in order to study the industrial system,we need to establish a stochastic model in line with the actual situation.After referring to the existing literatures,the problem of fault detection and fault-tolerant control for stochastic system are hot topics in the academic area.The main goal of fault detection is to timely detect the faults occurring in the systems when faults occur in the system,and reduce the bad effects caused by faults by taking necessarily effective measures.The problem of fault-tolerant control is to design an effective control strategy,by which the stability of the control system can be guaranteed when there exists failures in the systems.The problems of fault detection and fault-tolerant control are discussed for two different kinds of discrete-time stochastic systems.Based on the theories of stochastic system and the existing results of fault detection and fault-tolerant control,the proposed problems are discussed in detail,and some valuable research results are obtained as follows:The fault detection problem is considered for a class of discrete-time systems with fault signal happening randomly.First,the random occurrence of fault is described by a Markov approach,which is transformed into some matrices experiencing Markov switchings.By using a fault detection filter as a residual generator,the fault detection and isolation(FDI)problem is transformed into an H_?filtering problem.Moreover,a mode-dependent Lyapunov functional is exploited to make its analysis and synthesis and is also named to be a fault-dependent approach.Then,sufficient conditions on the existence of an FDI filter are all provided in terms of linear matrix inequalities,in which two general cases about transition probability matrix are included.Finally,a practical example is used to illustrate the effectiveness and potential application of the developed theoretical results.A kind of fault-tolerant controller is proposed to study the stabilization problem of discrete-time Markovian jump systems,whose operation modes are not only partially-available but also unmatched.Here,such general properties of controller are modeled to be a controller having polytopic forms and uncertainties simultaneously.Based on the proposed model,concise conditions for the existence of such a controller are proposed with linear matrix inequality(LMI)forms,which are extended to consider observer design problem too.Compared with the traditional methods,not only is the designed controller more general but also the established results are fault free and could be solved directly.Finally,numerical examples are used to demonstrate the effectiveness of the proposed methods.