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# Optimal Control and Estimation

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## Description

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## Product details

- Paperback | 639 pages
- 142.24 x 205.74 x 35.56mm | 680.39g
- 20 Sep 1994
- Dover Publications Inc.
- New York, United States
- English
- New edition
- New edition
- 0486682005
- 9780486682006
- 316,726

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## Back cover copy

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## Table of contents

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

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