Study On Control And Filtering Theory For Systems With Constraints

Restricted by many factors such as technology,safety concern,environment condition,etc.,the input/output or the dynamic performance of physical systems are frequently constrained.The corresponding controller often encounters imprecision when it is digitalized.With loss of ideal assumption,the existing control theory and technique may lose its power in real applications.Hence,it is of great theoretic significance and practical value to research into the control theory and technique for systems with constraints.In this dissertation,several kinds of constrained systems are considered,the dynamics of which are analyzed under different constrained conditions.The control and filtering technique and relative performance are discussed in detail.The main contents and results in this dissertation are summarized as follows:1.For constrained Markov jump system and Semi-Markov jump system with loss of mod-e information,the case of mismatched modes during the controller and filter design process is considered.Based on the asynchronous strategy,a non-homogenous Markov chain and a hidden Semi-Markov model are introduced respectively.The observable stochastic processes are used to carry the mode information of the original system.Sufficient conditions are obtained to ensure the stability of the system and the prescribed performance.The design schemes are presented in the end.Numerical examples are applied to illustrate the effectiveness and the superiority of the pro-posed methods.Thus the control and filtering theory for Markov jump system and Semi-Markov jump system is supplemented and perfected.2.For time-delayed Markov jump neural networks with sate constraints,the researchable set estimation problem is considered under the peak-bounded input.The definition of the researchable set in this stochastic case is presented.Preliminary results are obtained by using a novel summa-tion inequality and the reciprocally convex approach,which is then extended to incomplete mode transition information cases.3.For complex networks with state constraints,the way of sampled-data communication is considered,which limits the instant information exchanging.We adopted the pinning control technique and analyzed the global H? pining synchronization problem for this kind of complex networks with state constraints.Based on the existing results on the synchronization control of complex networks,a new criterion is constructed by using a Lyapunov-like functional.Then less conservative results are obtained by applying a tighter integral inequality.By numerical exam-ples,our results give better estimation of the maximum allowable sampling interval,verifying the superiority of the proposed methods.4.Considering the precision constraints for filters when digitalized during real implementa-tion,we take 2-D switched systems for example and investigate the non-fragile filtering problem.Unlike regular systems,2-D systems evolves in two dimensions,like time and space or two dimen-sions in space,resulting in more crucial fragility of corresponding controllers or filers.By using a more practical filter structure,we analyze the dissipative performance and obtained the non-fragile filter parameters.A verification example is given in the end to illustrate our theoretical results.