Study On Disturbance-observer-based-control Of Markov Jump Systems With Partly Unknown Transition Probabilities

With the development of automatic control technologies,the structures of controlled plants become more complex and huger.The requirements for control system are also improved.Random abrupt changes frequently happen in practical control systems due to random failures,changing subsystem interconnections,sudden environmental disturbances and so on.As a special class of hybrid systems,Markov jumping systems with the characteristics of continuous time and discrete state can tackle random problems.The jumps among different modes are governed by Markov process.Transition probability,as a critical factor,affects the stabilization of Markov jumping systems.However,the exact information about the transition probabilities is often insufficient or even unknown in practice.Therefore,the study of the Markov jumping systems with unknown transition probability has become a hot topic in recent years.On the other hand,there widely exist control systems with external disturbance uncertainty in the practical production process.Disturbance attenuation,compensation and rejection have been a hot topic in the control field,and many effective anti-disturbance control methods are emerging.However,because of the uncertainty of the disturbance in the practical engineering,the disturbance estimation technique is introduced into the control process named disturbance-observer-based-control(DOBC)through which the disturbance is compensated through the feed-forward channel and thus the disturbance is effectively rejected.In the actual control system,time-delay and actuator saturation phenomenon occurs frequently making the structure of the system more complex and increases the difficulty of control.Aiming at the above problem,there exist some excellent research achievements,but there remains a great potential for research in this area.This dissertation further studies the problems of observer and controller design for Markov jumping systems with partly unknown transition probabilities.The main contents of this dissertation are as follows:(1)The problem of disturbance-observer-based control for Markov jumping system subject to actuator saturation is investigated.First,the disturbance observer is constructed to estimate the disturbance generated by an exogenous system.Then this paper constructs the control scheme by integrating the output of the disturbance observer with the state feedback control law such that the corresponding closed-loop system can be guaranteed to be stochastically stable.By using Lyapunov function,sufficient conditions for stochastic stability of the closed-loop system are proposed.And then the obtained results can be converted into a set of linear matrix inequalities.Thus,the optimal gain matrices of the observer and controller are solved with LMI toolbox.Finally,the estimation of attractive region is obtained through the iterative optimization algorithm.(2)The problem of disturbance-observer-based control for Markov jumping system with time-delay is studied.The random stability of Markov jumping system with external disturbance uncertainties is discussed divided into two cases i.e.time-delay and time-varying delay.For time-varying delay,by constructing the proper mode-dependent Lyapunov-Krasovskii functional and introducing the free-connection weighting matrices,the stochastic stability criterion of the closed-loop system is obtained.Compared with the stable conditions of mode-independent,it reduces the conservative of the results.The gain matrices solving of controller and observer are transformed into a feasible problem of linear matrix inequalities.In addition,the simulation results demonstrate the effectiveness of the theoretical results.(3)The stochastic stability analysis and controller design of the time-delay Markov jump system with disturbance and actuator saturation are proposed.The stochastic stability problem of the closed-loop system with disturbance estimation error is analyzed.Two conditions of time-delay and time-varying delay are considered respectively.By constructing the appropriate mode-dependent Lyapunov-Krasovskii functions and introducing the free-connection weighting matrices,the random stability criterions of the closed-loop system are given.By transforming it into a feasible problem with linear matrix inequalities,the gain matrices are acquired.And the estimation of maximized attractive domain is obtained by an iterative optimization algorithm.Finally,the simulation results show the effectiveness of the results.(4)Considering that there may exist other kinds of disturbances in the actual system,the multi-disturbances compound control system is constructed for the time-delay Markov jump system with multi-disturbances subject to the actuator saturation.The compound control method combines the DOBC control method with the H? control to reject and attenuate the disturbance of the external system with perturbation and the norm-bounded disturbance.On the basis of the resulting composite close-loop system stochastic stable conditions,the observer and state feedback controller are solved with H? performance.And the estimation of the maximized attractive region is computed with the iterative optimization algorithm.Finally,the results of the dissertation are summarized and further research topics are proposed.