Optimal Control and Estimation

Optimal Control and Estimation

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Reprint of the respected Wiley edition originally published in 1986. Annotation copyright Book News, Inc. Portland, Or.show more

Product details

  • Paperback | 639 pages
  • 142.24 x 205.74 x 35.56mm | 680.39g
  • Dover Publications Inc.
  • New York, United States
  • English
  • New edition
  • New edition
  • 0486682005
  • 9780486682006
  • 266,278

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"An excellent introduction to optimal control and estimation theory and its relationship with LQG design. . . . invaluable as a reference for those already familiar with the subject."--"Automatica."This highly regarded graduate-level text provides a comprehensive introduction to optimal control theory for stochastic systems, emphasizing application of its basic concepts to real problems. The first two chapters introduce optimal control and review the mathematics of control and estimation. Chapter 3 addresses optimal control of systems that may be nonlinear and time-varying, but whose inputs and parameters are known without error.Chapter 4 of the book presents methods for estimating the dynamic states of a system that is driven by uncertain forces and is observed with random measurement error. Chapter 5 discusses the general problem of stochastic optimal control, and the concluding chapter covers linear time-invariant systems.Robert F. Stengel is Professor of Mechanical and Aerospace Engineering at Princeton University, where he directs the Topical Program on Robotics and Intelligent Systems and the Laboratory for Control and Automation. He was a principal designer of the Project Apollo Lunar Module control system."An excellent teaching book with many examples and worked problems which would be ideal for self-study or for use in the classroom. . . . The book also has a practical orientation and would be of considerable use to people applying these techniques in practice."--"Short Book Reviews, " Publication of the International Statistical Institute."An excellent book which guides the reader through most of the important concepts and techniques. . . . A useful book for students (and their teachers) and for those practicing engineers who require a comprehensive reference to the subject."--"Library Reviews, " The Royal Aeronautical Society.show more

Table of contents

1. INTRODUCTION   1.1 Framework for Optimal Control   1.2 Modeling Dynamic Systems   1.3 Optimal Control Objectives   1.4 Overview of the Book     Problems     References 2. THE MATHEMATICS OF CONTROL AND ESTIMATION   2.1 "Scalars, Vectors, and Matrices "       Scalars       Vectors       Matrices       Inner and Outer Products       "Vector Lengths, Norms, and Weighted Norms "       "Stationary, Minimum, and Maximum Points of a Scalar Variable (Ordinary Maxima and Minima) "       Constrained Minima and Lagrange Multipliers   2.2 Matrix Properties and Operations       Inverse Vector Relationship       Matrix Determinant       Adjoint Matrix       Matrix Inverse       Generalized Inverses       Transformations       Differentiation and Integration       Some Matrix Identities       Eigenvalues and Eigenvectors       Singular Value Decomposition       Some Determinant Identities   2.3 Dynamic System Models and Solutions       Nonlinear System Equations       Local Linearization       Numerical Integration of Nonlinear Equasions       Numerical Integration of Linear Equations       Representation of Data   2.4 "Random Variables, Sequences, and Processes "       Scalar Random Variables       Groups of Random Variables       Scalar Random Sequences and Processes       Correlation and Covariance Functions       Fourier Series and Integrals       Special Density Functions of Random Processes       Spectral Functions of Random Sequences       Multivariate Statistics   2.5 Properties of Dynamic Systems       Static and Quasistatic Equilibrium       Stability       "Modes of Motion for Linear, Time-Invariant Systems "       "Reachability, Controllability, and Stabilizability "       "Constructability, Observability, and Detectability "       Discrete-Time Systems   2.6 Frequency Domain Modeling and Analysis       Root Locus       Frequency-Response Function and Bode Plot       Nyquist Plot and Stability Criterion       Effects of Sampling     Problems     References 3. OPTIMAL TRAJECTORIES AND NEIGHBORING-OPTIMAL SOLUTIONS   3.1 Statement of the Problem   3.2 Cost Functions   3.3 Parametric Optimization   3.4 Conditions for Optimality       Necessary Conditions for Optimality       Sufficient Conditions for Optimality       The Minimum Principle       The Hamiltonn-Jacobi-Bellman Equation   3.5 Constraints and Singular Control       Terminal State Equality Constraints       Equality Constraints on the State and Control       Inequality Constraints on the State and Control       Singular Control   3.6 Numerical Optimization       Penalty Function Method       Dynamic Programming       Neighboring Extremal Method       Quasilinearization Method       Gradient Methods   3.7 Neighboring-Optimal Solutions       Continuous Neighboring-Optimal Control       Dynamic Programming Solution for Continuous Linear-Quadratic Control       Small Disturbances and Parameter Variations     Problems     References 4. OPTIMAL STATE ESTIMATION   4.1 Least-Squares Estimates of Constant Vectors       Least-Squares Estimator       Weighted Least-Squares Estimator       Recursive Least-Squares Estimator   4.2 Propagation of the State Estimate and Its Uncertainty       Discrete- Time Systems       Sampled-Data Representation of Continuous-Time Systems       Continuous-Time Systems       Simulating Cross-Correlated White Noise   4.3 Discrete-Time Optimal Filters and Predictors       Kalman Filter       Linear-Optimal Predictor       Alternative Forms of the Linear-Optimal filter   4.4 Correlated Disturbance Inputs and Measurement Noise       Cross-Correlation of Disturbance Input and Measurement Noise       Time-Correlated Measurement Noise   4.5 Continuous-Time Optimal Filters and Predictors       Kalman-Bucy Filter       Duality       Linear-Optimal Predictor       Alternative Forms of the Linear-Optimal Filter       Correlation in Disturbance Inputs and Measurement Noise   4.6 Optimal Nonlinear Estimation       Neighboring-Optimal Linear Estimator       Extended Kalman-Bucy Filter       Quasilinear Filter   4.7 Adaptive Filtering       Parameter-Adaptive Filtering       Noise-Adaptive Filtering       Multiple-Model Estimation     Problems     References 5. STOCHASTIC OPTIMAL CONTROL   5.1 Nonlinear Systems with Random Inputs and Perfect Measurements       Stochastic Principle of Optimality for Nonlinear Systems       Stochastic Principle of Optimality for Linear-Quadratic Problems       Neighboring-Optimal Control       Evaluation of the Variational Cost Function   5.2 Nonlinear Systems with Random Inputs and Imperfect Measurements       Stochastic Principle of Optimality       Dual Control       Neigbboring-Optimal Control   5.3 The Certainty-Equivalence Property of Linear-Quadratic-Gaussian Controllers       The Continuous-Time Case       The Discrete-Time Case       Additional Cases Exhibiting Certainty Equivalence   5.4 "Linear, Time-Invariant Systems with Random Inputs and Imperfect Measurements "       Asymptotic Stability of the Linear-Quadratic Regulator       Asymptotic Stability of the Kalman-Bucy Filter       Asymptotic Stability of the Stochastic Regulator       Steady-State Performance of the Stochastic Regulator       The Discrete-Time Case     Problems     References 6. LINEAR MULTIVARIABLE CONTROL   6.1 Solution of the Algebshow more

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