Robust Kalman Filtering And Nonlinear Control Of Markovian Jump Systems

The research of hybrid systems is now a hot theme in the field of modern control.These systems namely combine time-driven factors with event-driven factors,in which time and event effects and affects each other so that the states evolve . As a result of both theoretics and practice, hybrid systems are inevitable outcomes of the development of control theory,system theory,mathematics and computer science.The special class of hybrid systems considered here is the so-called Markovian jump systems(or jump systems briefly), in which the transitions between the different regimes are random and are further supposed as a Markov process. Due to the complicated structure, the research of jump systems can not be treated as simple combination of traditional control theories for the continuous systems or discrete events systems, respectively. Thus,the investigation of Markovian jump systems is a new and challenging task.In this dissertation, robust Kalman filtering and nonlinear control for Markovian jump systems are investigated,and our work includes: stochastic differential equations and Lasalle theory for Markovian jump systems,robust Kalman filtering and robust JLQG regulator for Markovian jump linear systems with uncertain noise,robust adaptive controller design for Markovian jump nonlinear systems under unknown Wiener noise , robust adaptive controller design for Markovian jump nonlinear systems with uncertainties. The dissertation is organized as follows:The basic conceptions and the practical models of jump systems are presented firstly, secondly we go over the overall research situations in the area,then comes the motivation of our research, finally the research contents and innovations of this dissertation are introduced.The models of both Markovian jump linear and nonlinear systems are introduced. Moveover,the stochastic differential equations for jump systems with Wiener noise are also educed. Then we define the the stochastic stabilities of the jump systems and as an important theory of system stability, the Lasalle theory for jump systems are considered and an integrated proof is given. Thus the sufficient conditions for the systems to be stable with probability 1 are given.Robust Kalman filtering problems for a class of discrete-time Markovian jump systems with unknown bounded noises were investigated. The upper bound of the disturbance to the noise covariance matrix was given based on the estimation error performance, and an optimal state estimator was therefore adopted under the worst situation .Not only can this method minimize the worst performance function of the uncertainty, but the...