Optimal Control and Estimation

by Robert F. Stengel

Overview

"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.

Product Details

ISBN-13:	9780486134819
Publisher:	Dover Publications
Publication date:	09/18/2012
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	672
File size:	40 MB
Note:	This product may take a few minutes to download.

About the Author

Robert F. Stengel

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.

Editorial Reviews

Reprint of the respected Wiley edition originally published in 1986. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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