Linear Stochastic Control Systems

Linear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered.Reviews of the modern probability and random processes theories and the It= stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.

PrefaceIntroductionFrom Deterministic to Stochastic Linear Control SystemsText Organization and Reading SuggestionMATHEMATICAL PRELIMINARIESProbability and Random ProcessesProbability, Measure, and IntegrationConvergence of Random SequencesRandom Vectors and Conditional ExpectationsSecond Order Processes and Calculus in Mean SquareExercisesReferencesItô Integrals and Stochastic Differential EquationsMarkov ProcessesOrthogonal Increments Processes and the Wiener-Lévy ProcessItô Integrals and Stochastic Differential EquationsExercisesReferencesLINEAR STOCHASTIC CONTROL SYSTEMS: THE DISCRETE-TIME CASEAnalysis of Discrete-Time Linear Stochastic Control SystemsAnalysis of Discrete-Time Causal LTI SystemsAnalysis of Causal LTI Stochastic Control SystemsAnalysis of the "State" Description of Controlled Markov ChainsState Space Systems and ARMA ModelsMathematical Modeling and ApplicationsExercisesReferencesOptimal Estimation for Discrete-Time Linear Stochastic SystemsOptimal State EstimationRecursive Optimal Estimation and Kalman FilteringModified Kalman Filtering AlgorithmsExercises ReferencesOptimal Control of Discrete-Time Linear Stochastic SystemsIntroductionDynamic Programming and LQC Control ProblemsLQC Optimal Control ProblemsAdaptive Stochastic ControlExercises ReferencesLINEAR STOCHASTIC CONTROL SYSTEMS: THE CONTINUOUS-TIME CASEContinuous-Time Linear Stochastic Control SystemsAnalysis of Continuous-Time Causal LTI SystemsFurther Discussion of Markov ProcessesDynamic Programming and LQ Control ProblemsExercises ReferencesOptimal Control of Continuous-Time Linear Stochastic SystemsThe Continuous-Time LQ Stochastic Control ProblemStochastic Dynamic ProgrammingInnovation Processes and the Kalman-Bucy FilterOptimal Prediction and SmoothingThe Separation PrincipleExercises ReferencesStability Analysis of Stochastic Differential EquationsStability of Deterministic SystemsStability of Stochastic SystemsStability of MomentsExercisesReferencesAppendixFundamental Real and Functional AnalysisFundamental Matrix Theory and Vector CalculationsMartingalesReferencesIndex

Chen\, Goong; Chen\, Guanrong; Hsu\, Shih-Hsun