Satisfactory Control And Filtering For A Class Of Nonlinear Stochastic Systems

This thesis is concerned with the satisfactory control and filtering problems for a class of nonlinear stochastic systems. In each chapter, for such a kind of nonlinear stochastic systems, the stability, robustness and the pre-specified system performance indices, such as system covariance (or variance) index, H∞performance index, H2 per-formance index, are firstly analyzed, and then, sufficient conditions of robust asymp-totically stochastic stability or robust exponentially stochastic stability are derived for the closed-loop systems with the parameter uncertainty, external and internal non-linear disturbances. Then, the controller (or filter) synthesis problems are considered, and sufficient conditions for the existence of the desired controller (or filter) with which all the required pre-specified system performance indices can be satisfied are given in terms of feasibility of a set of linear matrix inequalities (LMIs). The compendious frame and description of the thesis are given as follows:●In Chapter 1, the research background and motivation are discussed, the outline and contribution of the thesis are introduced, and the research problems to be addressed in each individual chapters are also outlined.●In Chapter 2, a robust H∞variance-constrained controller has been designed for a class of uncertain discrete-time nonlinear stochastic systems. A unified framework has been established to solve the controller design problem which requires the exponential stability, H∞performance index and individual variance constraints satisfied simultaneously. Two types of optimization problems have been proposed either optimizing H∞performance or the system state variances.●Chapter 3 is concerned with the robust filtering problem for a class of nonlinear stochastic systems with missing measurements and parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. A sufficient condition for the exponential mean-square stability of the filtering error system is first derived and an upper bound of the state estimation error variance is then obtained, and afterwards the explicit expression of the desired filters has been parameterized. ●Chapter 4 deals with robust fault-tolerant controller design problem with vari-ance constraints for a class of nonlinear stochastic systems with both norm-bounded parameter uncertainties and possible sensor failures. The actuator fail-ure model adopted here is more practical than the conventional outage case.●Chapter 5 deals with the variance-constrained control problem for a class of stochastic nonlinear systems with multiple missing measurements. The purpose of the problem is to design a state feedback controller as well as an state esti-mator such that, for all possible measurements missing, the closed-loop system is exponentially mean square stable and strictly dissipative, while the individual steady state variance satisfies the pre-specified upper bound constraints.●In Chapter 6, the robust H∞control problem for a class of uncertain nonlinear discrete time-varying stochastic systems has been considered. An output feed-back controller has been designed by means of recursive linear matrix inequalities (RLMIs), satisfying the H∞disturbance rejection attenuation level in the finite horizon.●Chapter 7 is concerned with robust SMC design for uncertain nonlinear discrete-time stochastic systems with H2 performance constraint has been studied. The nonlinearities considered in this chapter are containing both matched and un-matched form. An improved form of discrete switching function is also proposed, with which several typical classes of stochastic nonlinearities can be dealt with via SMC method.●In Chapter 8, the robust control problem for a class of uncertain nonlinear dis-crete systems with stochastic communication delays has been considered via slid-ing mode conception (SMC). A discrete-time SMC controller has been synthe-sized to guarantee the discrete-time sliding mode reaching condition with the specified sliding surface.