Dynamics Analysis And Control Of Markovian Jump Stochastic Hybrid Systems

Markov jump system,as a typical random hybrid dynamic system,can well describe the dynamical behavior and system structure with either abrupt change or switched charac-teristic for a variety of physical and mechanical systems in reality,such as industrial process systems,robot systems,power system,traffic system and nervous system,while showing the distinguished properties of complex dynamic systems,including high nonlinearity,un-certainty,multi-scale,multi-structure,strong coupling and time-delay transmission.There-fore,Markov jump system has attracted a great deal of increasing interests in recent years from many scholars in different disciplines,such as mathematics,mechanics,control and so on,and so it has become one of the important frontier areas of dynamics and control of stochastic dynamic systems.Most of previous studies demonstrated that the transfer rates among modes is a crucial factor affecting dynamics behavior and characteristics of stochastic hybrid Markov jump systems.By aiming at the Markov jump system with uncertain or partial unknown trans-fer rates among modes,and taking the event-triggered control scheme as the fundamental techniques,in view of some important nonlinear factors,such as uncertainty,external dis-turbance,randomness and time delay,etc.,in combination with nonlinear system dynamics and modern control theory,this dissertation is devoted to study the modeling,analysis,de-sign of several typical Markov jump systems and its application.Specifically,the main work of the dissertation can be summarized as the following three aspects:1.Fault detection filtering for nonhomogeneous Markov jump systemsThe problem of fault detection filtering for a class of nonhomogeneous Markov jump systems with randomly occurring sensor saturations is considered.It is assumed that sensor saturation is randomly occur satisfying the Bernoulli distribution,and transition probabil-ities are time-varying in nonhomogeneous Markov chain.By employing the suitable Lya-punov function and linear matrix inequalities(LMIs),some sufficient criteria are derived to guarantee that the augmented system is stochastically stable with the level of H_?perfor-mance.It is demonstrated that a key of the developed fault detection filter is to transformed into the design problem of robust filter,and the control gains of filter can be convenient-ly obtained by solving the linear matrix inequalities.Finally,a representative example of industrial stirred tank reactor systems is presented to illustrate the theoretical results.2.Dynamic output feedback stabilization for Markovian jump systemsThe stabilization issue of uncertain Markovian jump systems with partly unknown transition rates is considered based on an event-triggered dynamic output feedback con-trol strategy.By means of a suitable Lyapunov-Krasovskii functional and inequality anal-ysis technique,some sufficient conditions are obtained to guarantee that the closed-loop controlled system is asymptotical stability in sense of mean square.It is shown that the proposed dynamic output feedback control strategy possess several potential advantages in-cluding fast response,high adaptability and good robustness,and thus it is convenient to realize the stabilization control of uncertain Markov jump systems.To this end,two typ-ical examples of inverted pendulum and three tank systems are presented to illustrate the effectiveness of the proposed methodology.3.Event-triggered stochastic consensus for networked Lagrange systemsAn event-triggered sampling control strategy is used to design the distributed s-tochastic consensus scheme of networked Lagrange systems for two cases with leader and leaderless.Two delay-dependent consensus criteria are derived in the sense of mean square by use of a suitable Lyapunov-Krasovskii functional and the stochastic delayed Halanay inequality,respectively.A key feature of the developed event-triggered consensus algorithm is to introduce a suitable adjustment parameter on consensus control gains characterizing the effect of both semi-Markov switching topology and communication delay.Finally,an example of four manipulators with two links is presented to illustrate the effectiveness of the developed event-triggered methodology.