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Optimal Control and Estimation (Dover Books on Advanced Mathematics)

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Optimal Control and Estimation (Dover Books on Advanced Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

"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.

Book News Annotation:

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

Synopsis:

Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems. "Invaluable as a reference for those already familiar with the subject." — Automatica.

Synopsis:

Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing the application of basic concepts to real problems. "An excellent intorduction to optimal control and estimation theory and its relationship with LQG design. . . . invaluable as a reference for those already familiar with the subject." — Automatica.

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 Algeb

Product Details

ISBN:
9780486682006
Author:
Stengel, Robert F.
Publisher:
Dover Publications
Author:
Stengel
Author:
Mathematics
Location:
New York :
Subject:
General
Subject:
Robotics
Subject:
Dynamics
Subject:
Probability
Subject:
Stochastic processes
Subject:
Control theory
Subject:
Mathematical optimization
Subject:
Mathematical optimatization.
Subject:
General Mathematics
Subject:
Advanced
Subject:
Artificial Intelligence-Robotics
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19940931
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
639
Dimensions:
8.25 x 5.63 in 1.67 lb

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Optimal Control and Estimation (Dover Books on Advanced Mathematics) New Trade Paper
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$28.95 In Stock
Product details 639 pages Dover Publications - English 9780486682006 Reviews:
"Synopsis" by ,
Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems. "Invaluable as a reference for those already familiar with the subject." — Automatica.

"Synopsis" by ,
Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing the application of basic concepts to real problems. "An excellent intorduction to optimal control and estimation theory and its relationship with LQG design. . . . invaluable as a reference for those already familiar with the subject." — Automatica.

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