Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, **Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions,** considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: * Block-pulse functions and shifted Legendre polynomials * State estimation of linear time-invariant systems * Linear optimal control systems incorporating observers * Optimal control of systems described by integro-differential equations * Linear-quadratic-Gaussian control * Optimal control of singular systems * Optimal control of time-delay systems with and without reverse time terms * Optimal control of second-order nonlinear systems * Hierarchical control of linear time-invariant and time-varying systems IntroductionOptimal Control ProblemHistorical PerspectiveOrganization of the BookOrthogonal Functions and Their PropertiesIntroductionBlock-Pulse Functions (BPFs)Legendre Polynomials (LPs)Shifted Legendre Polynomials (SLPs)Nonlinear Operational MatrixRationale for Choosing BPFs and SLPsState EstimationIntroductionInherent Filtering Property of OFsState EstimationIllustrative ExamplesConclusionLinear Optimal Control Systems Incorporating ObserversIntroductionAnalysis of Linear Optimal Control Systems Incorporating ObserversIllustrative ExampleConclusionOptimal Control of Systems Described by Integro-Differential EquationsIntroductionOptimal Control of LTI Systems Described by Integro-Differential EquationsIllustrative ExampleConclusionLinear-Quadratic-Gaussian ControlIntroductionLQG Control ProblemUnified ApproachIllustrative ExampleRecursive AlgorithmsConclusionOptimal Control of Singular SystemsIntroductionRecursive AlgorithmsUnified ApproachIllustrative ExamplesConclusionOptimal Control of Time-Delay SystemsIntroductionOptimal Control of Multi-Delay SystemsOptimal Control of Delay Systems with Reverse Time TermsConclusionOptimal Control of Nonlinear SystemsIntroductionComputation of the Optimal Control LawIllustrative ExamplesConclusionHierarchical Control of Linear SystemsIntroductionHierarchical Control of LTI Systems with Quadratic Cost FunctionsSolution of Hierarchical Control Problem via BPFsExtension to Linear Time-Varying SystemsComputational AlgorithmIllustrative ExamplesConclusion "This book presents the developments in problems of state estimation and optimal control of continuous-time dynamical systems using orthogonal functions since 1975. It deals with both full and reduced-order state estimation and problems of linear time-invariant systems. It also addresses optimal control problems of varieties of continuous-time systems such as linear and nonlinear systems, time-invariant and time-varying systems, as well as delay-free and time-delay systems. Content focuses on development of recursive algorithms for studying state estimation and optimal control problems"-- Provided by publisher.
