Fault Estimation And Fault-tolerant Control For Markovian Jump Systems

With the continuous development of control technology and the increasing complexity of control systems,various factors including environmental disturbances,component faults,and changes in subsystem connection usually cause random jumps or switching of system parameters and structures during the operation of the actual control system.In response to such system problems,Markovian jump systems possess accurate modeling capabilities.The systems are driven by two mechanisms,event and time,and includes modal variables and state variables in the mathematical description.Due to the special structure of Markovian jump systems,the research method for this kind of systems is different from the traditional single-event-driven or single-time-driven control systems.In recent years,the research on this kind of system has received extensive attention from researchers in the control field.In the application of the Markovian jump systems,there are always non-ideal conditions that affect the normal system operation,such as actuator faults,sensor faults,time delays,external disturbances and nonlinearities.The non-ideal conditions may degrade the system performances,or even result in serious operation accidents.In view of this,this thesis will focus on the actuator faults,sensor faults,external disturbances and nonlinear problems in Markovian jump systems,specifically in combination with sliding mode control theory,stochastic control theory,adaptive control theory,fuzzy logic system,observer design and other technical methods to conduct systematic research on fault estimation and fault-tolerant control methods based on Markovian jump systems.The main research contents of the paper are as follows:Chapter 2 focuses on the problem that the existing sliding mode observer methods cannot be directly used in the Markovian jump systems with actuator faults and sensor faults for fault estimation,a reduced-order linear observer is designed to simultaneously realize the purposes of state estimation and sensor fault estimation for Markovian jump systems.By introducing an augmented vector composed of state vectors and sensor fault vectors,the proposed fault and state estimation method employs decoupling technology to realize sensor fault estimation and state estimation of Markovian jump system with actuator faults,sensor faults and external disturbances.In this design scheme,the sliding mode observer method is not employed,thus the problem of sliding mode switching is effectively avoided.Chapter 3 studies the problems of actuator fault estimation,sensor fault estimation and state estimation of linear Markovian jump systems,and proposes an adaptive observer-based fault estimation method.First,the coordinate transformation method is used to decompose the original system into two subsystems,so that actuator faults and sensor faults exist in different subsystems.Then,corresponding adaptive observers are proposed for each subsystem,and the two adaptive observers are used to realize state estimation,sensor fault and actuator fault estimation.This method can avoid the problem of high dimensions of the observer.Chapter 4 focuses on linear Markovian jump systems which the system parameters of actuator faults and inputs are different.The state estimation,actuator fault estimation and sensor fault estimation are studied and a reduced-ordered sliding mode observer-based fault estimation method is proposed.Using coordinate transformation,the original system is decomposed into two reduced-order subsystems and then a descriptor augmentation strategy is developed for the second reduced-order system.By designing a descriptor reduced-order sliding mode observer,state estimation,actuator fault estimation and sensor fault estimation are simultaneously achieved.In this method,since the actuator fault vector has been assembled into the extended state vector of the new augmented descriptor system,the actuator faults can be estimated directly without introducing the equivalent output error in the traditional sliding mode observer method to perform actuator fault reconstruction.Therefore,this method can also effectively solve the technical problems in Chapter 2.Chapter 5 proposes a fuzzy logic system-based adaptive fault-tolerant compensation control method for nonlinear Markovian jump systems with simultaneous additive and multiplicative actuator faults.First,fuzzy logic systems are used to approximate the model-dependent smooth nonlinear functions.Then,using adaptive backstepping technology,an adaptive fault-tolerant compensation controller based on fuzzy logic system is designed.This controller can completely compensate for the adverse effects caused by additive actuator faults,multiplicative actuator faults and model-dependent nonlinearities.The proposed adaptive controller based on fuzzy logic system can guarantee the stability of the closed-loop system.Chapter 6 discusses the stability of nonlinear Markovian jump systems with output disturbances,actuator faults,and sensor faults.A sliding mode observer design method based on augmented system is proposed,and a controller based on the sliding modeobserver is designed.With the proposed sliding mode observer and the sliding mode observer based controller,the effects caused by actuator faults,sensor faults and disturbances can be eliminated.Considering the reachability of the model-dependent sliding mode surfaces,the extended fault vectors can be estimated.The fault-tolerant control method proposed in this chapter can ensure the stability of the entire closed-loop system,that is,this method can simultaneously stabilize the state estimation system and the error estimation system.