Analysis And Synthesis Of Hidden Semi-markov Jump Systems Based On Semi-markov Kernel

The abrupt changes of working environment,failures of sensors or actuators,and working points of nonlinear systems can be regarded as the phenomena of stochastic switching,which can be widely found in aerospace engineering,chemical process,com-munication,and other various practical systems.Based on the advantages of describing the stochastic switching phenomena,stochastic switching systems have attracted increas-ing attention and been widely studied in the past few decades.In addition,since system modes of semi-Markov jump systems are not always accessible in practice,hidden semi-Markov chain,which is widely applied in the field of statistics and machine learning,is introduced into the control system field for describing the practical stochastic switching phenomena.In recent years,most of the remarkable results on such stochastic process mainly focus on the machine learning field,rather than the field of control systems.Thus,there are still a lot of issues to be found,proposed,and solved in analysis and synthesis of the hidden semi-Markov jump systems.Moreover,as the system performance require-ment which actual production needed is higher and higher,and the operating conditions of the control systems are more and more complex,the switching systems only considering simple subsystem dynamic usually can not well reflect many practical dynamic process-es,and thus the existing results are difficult to be utilized to real stochastic systems with complex dynamics,including packet dropouts,uncertain stochastic parameters,limited sojourn-time information,etc.Therefore,it is of great practical significance to further systematically and profoundly carry out the modeling,analysis,and synthesis of hidden semi-Markov jump systems with complex subsystem dynamics.Based on the existing related work,this thesis aims to deal with analysis and synthe-sis issues of hidden semi-Markov jump systems,and further proposes some new models,new problems,and new methods.In addition,the thesis also introduces some new con-cepts,e.g.,observed-mode and elapsed-time-dependent controller and estimator,time-varying Lyapunov function method,?-error mean square stable,etc.Some unrealis-tic assumptions are abandoned,and further the conservatism of the developed result-s is reduced.The design methods of time-varying controller and state estimator for semi-Markov jump systems with hidden modes are proposed,and the issues of model-ing,stability analysis,and controller design of hidden semi-Markov jump systems are solved.Furthermore,aiming at the problems of uncertain measurement loss rate,time-inhomogeneous process,and partly known sojourn-time information of linear and non-linear stochastic switching systems in the networked environment,new stability concept and design approaches of such switching systems are proposed for analysis and synthesis of hidden semi-Markov jump systems in the above cases.Finally,theoretical results have been successfully applied to the cart pendulum system,single-link robotic arm system,and suspension system,which not only proves the effectiveness of the proposed theoreti-cal methods but also provides the necessary theoretical reference and basis for engineering practices.The main contents and research results are as follows:The idea of hidden Markov jump systems dealing with hidden modes is introduced to abandon the ideal assumption in the existing work that the modes of semi-Markov stochastic jump systems are completely known.A model of hidden semi-Markov jump system based on semi-Markov kernel and emission probability is proposed in the thesis,which can describe a class of stochastic jump systems with hidden modes and any types of distribution of sojourn-time probability density function.Furthermore,the stability conditions of the jump systems satisfying admissible error and the existence conditions of the proposed controller and estimator are given.In contrast to the existing research on mode transition probability,this thesis avoids the complex calculation process of solving the upper bound or approximates the value of transition probability by using the semi-Markov kernel.Furthermore,the proposed time-varying and mode-dependent Lyapunov function method can reduce the conservatism of the theoretical results.A novel design method on observed-mode and elapsed-time-dependent controller and estimator is also proposed,which weakens the negative effect of mode mismatch on the performance of the system.The stability analysis,stabilization,and state estimation issues of fuzzy hidden semi-Markov jump systems with parameter uncertainties and unknown missing rate of mea-surement are studied.Unlike the existing modeling methods for stochastic uncertain pa-rameters,the fuzzy system with uncertain parameters is modeled as a more general fuzzy hidden semi-Markov stochastic jump system.Moreover,the conditions of H? stability under the definition of ?-error mean square stability are given,and a design method of fuzzy time-varying state estimator is proposed in this thesis.In addition,as for the fuzzy stochastic systems with unknown missing rate of measurements,the non-convex con-ditions containing uncertain and non-linear parameters are transformed into the criteria which can be solved via linear matrix inequalities by introducing external variables and matrix processing techniques.Furthermore,a novel design method of H? fuzzy time-varying state estimators is proposed,and further the influence of the emission probability on the performance of control systems is revealed.The effectiveness of the proposed method is verified by comparing with a time-invariant fuzzy estimation approach,and further the advantages of the proposed methods are verified by practical examples of cart pendulum system and single-link robotic arm system.The stability and stabilization problems of non-homogeneous hidden semi-Markov jump systems with limited sojourn-time information are also studied.The correspond-ing upper and lower bounds as well as nominal values are given for jump parameters in non-homogeneous stochastic jump systems,including time-varying transition probability and time-varying semi-Markov kernel,which makes it possible to analyze and synthe-size non-homogeneous hidden semi-Markov jump linear systems.Based on the above re-search,the stability of hidden semi-Markov stochastic jump systems with partly unknown sojourn-time probability density function is analyzed.By introducing external variables,the problem of matrix power introduced by matrix product is successfully solved,and further the design method of time-varying state-feedback controller is given.The relevant simulations are carried out in the control problems of the vehicle suspension system.