Estimation And Tracking Control For Markov Jump Systems

The research of control theories and applications of stochastic hybrid systems is a hot topic in the field of control. The stochastic hybrid systems combine time-driven with event-driven dynamics. These systems typically contain variables or signals that take values from an Euclidean vector space (R~n) and also variables that take values from a discrete finite state space (e.g., the set of symbols S = {1, 2, …,N}). These continuous or discrete-valued variables or signals depend on independent variables such as time, which may also be continuous or discrete. some of the variables may also be discrete-event driven in an asynchronous manner. The occurrence and the development of stochastic hybrid systems are both the demand of theory and practice, and the inevitable outcome of the development of control theory, system theory, mathematics and computer technology.The special class of stochastic systems considered here is hybrid systems with Marko-vian jumping parameters-Markov jump systems (or jump systems briefly), in which the transitions between the different regimes have to be considered as random; in other words, randomicity enters the plant primarily through its discrete component, and the natural model for the parameter process is given by a Markov jump process. Due to the complicated stochastic hybrid information structure, we can not substitute the traditional control theories of the continuous systems driven by time or the discrete events systems for the control theories of jump systems simply. Thus, the investigation of the control theories of Markov jump systems is a new and challenging task.In this dissertation, the problems of estimation and tracking control for Markov jump systems have been investigated, which include: the improvement of sub-optimal filtering algorithm, robust Kalman filtering, optimal tracking control, guaranteed control performance robust tracking, robust tracking and model following, and adaptive tracking control for non-linear Markov jump systems. The main contributes of the dissertation are as follows:·The basic conceptions of Markov jump systems are presented firstly, then our topic's internal and overseas research situations, theoretical and practical significance are classified and summarized in detail, and the research objects and contents of this dissertation are introduced.·With the sub-optimal algorithm of the Markov jump systems-traditional IMM algorithm, the precision of the system modes probabilities which are updated based on the thought of "soft switching" , will decrease along with time growth, and the estimation error of the systems states will increase at the same time. To improve the estimation...