Analysis And Synthesis Of Markov Jump Systems With Partial Unknown Transition Probabilities

In the actual control system,some physical parameter changes will affect the structure of the control system,such as failure or repair of components,drift of parameters,and changes in the inter-connection of subsystems.Systems with these characteristics typically have many working models,and each model can be described by a set of state-space equations.Markov jump system can describe such system.As a special type of hybrid dynamic system,Markov jump system has been widely used in aerospace,mechanical arm,traffic and other fields.Although Markov jump system has been involved in many control fields and has achieved remarkable results,there exists an ideal condition that all elements in the universal transition rate matrix are known while Markov jump system is used to establish the computational model for practical problems.However,in practical control systems,the information of the transition rate is difficult to measure via sensor or there is an error during the measurement.The incompleteness and error of information of the transition rate are likely to cause the designed controllers that are unable to stabilize the dynamic system.Therefore,in real production and life,it is often impossible to assume that the elements of the transition rate are completely known.For example,a typical example can be found in a networked control system where packet loss and communication delay are established by Markov chain model,and it is assumed that,in the literature,all transition probabilities are fully measurable.But almost all types of communication networks,during the operation of different networks,the change of communication delay or packet loss may be ambiguous and random.That is to say,the element information in the transition rate matrix is difficult to obtain completely or measure at a great cost.Therefore,what we should do is to establish a mathematical model with Markov chain that is more consistent with the real situation and to provide effective control methods for such system.Therefore,it is of great practical sense and theoretical value to study the analysis and control problems of Markov jump systems with available transition probabilities.In this paper,under the unified framework of Markov jump systems,the problems of stochastic stability analysis,robust control and filtering of Markov jump systems subject to partial unknown transition probabilities are mainly studied by utilizing H-infinity filter,adaptive control and sliding mode control approaches.The paper studies the control and filtering of continuous and discrete-time Markov jump systems with partially undetectable transition probabilities.The main research work of the thesis can be summarized as follows:The first chapter introduces the research background,significance and research status of the Markov jump systems firstly.Secondly,the advantages and wide application prospects of the Markov jump systems are introduced.In addition,the stability conditions for continuous-time and discrete-time Markov jump systems are introduced.In the second chapter,the robust H-infinity filtering problem of Markov jump systems with unknown transition probabilities and mode-dependent output quantization is studied.Since the measured output is affected by external disturbances,the system state is disturbed by noises and uncertainties,the transition rate is difficult to obtain and the communication is constrained,by designing the H-infinity filter,the closed-loop system is guaranteed to be stochastically stable and has H-infinity performance index.Finally,two examples to verify the serviceability of the proposed methodology are given.In Chapter 3,the adaptive sliding mode controller design for Markov jump systems with partial unknown transition probabilities and actuator failures is discussed.In an actual control system,nonlinearities,external disturbances,and actuator failures are inevitably existed.It is really difficult to measure the whole information of the transition rates by sensor.The incompleteness and the error of information of the transition rates are likely to result in the controller being unable to stabilize the actual system under the assumption that the elements of transition rate matrix are completely accurate.Therefore,the case where the transition rate is completely known is unrealistic,that is,the transition probability of the system is partially known.The adaptive sliding mode controller designed in this condition is used to adjust the unknown constants in the actuator faults,nonlinearities,and external disturbances of the closed-loop system online such that the stability results obtained are less conservative.Finally,the effectiveness of the proposed method is proved by numerical simulation.In the fourth chapter,we discuss the adaptive sliding mode control problem for time-delay Markov jump systems with unknown transition probabilities.For the unmeasured system state,a sliding mode observer is designed to measure the system state variables.It is difficult for all the information of the transition rate to be measured by sensor.Such information incompleteness and error are likely to cause the constructed sliding mode controller to be unable to stabilize the actual system under the assumption that the transition probability matrix elements are completely accurate.Therefore,the case where the transition rate is completely known is often untenable,which means that the transition probability of the system is partially known.Therefore,aiming at the above problems,this chapter designs the corresponding switching surface function and the adaptive sliding mode controller to ensure the stability of the state-delayed Markov jump systems with unknown transition probabilities.Finally,numerical examples are used to verify the effectiveness of the proposed theoretical method.Chapter 5 solves the problem of adaptive sliding mode control for discrete-time uncertain Markov jump systems with unknown transition probabilities.By constructing an appropriate stable sliding surface and a novel adaptive sliding mode controller,the stability and reachability of the overall closed-loop system are ensured.The adaptive sliding mode controller designed can effectively weaken the chattering problem.Finally,the proposed method is verified by a practical example.Chapter 6 solves the sliding mode control problem of Markov jump systems with partial unknown transition probabilities,unmeasured states and random sensor delays.In the presence of sensor delays and unknown transition probabilities,based on the sliding mode observer,the constructed sliding mode controller can guarantee the stability of the closed-loop system consisting of the original system and the error dynamic system.Finally,the effectiveness of the proposed method is proved by numerical simulation.