Optimal Control Engineering Matlab: - V-Publishers [PDF]

Zitiervorschau

Engineering Tools, Techniques and Tables

Optimal Control Engineering with

MATLAB

Rami A. Maher

#P@va •V-publishers New York

Contents

Preface

xi

Acknowledgments Chapter 1

xiii

Mathematical Background and

Optimal Problem Modeling

1.1. Introduction 1.2.

1

Optimal Control in Engineering

1.3. Controller Design

2

Concepts

3

1.4. Finite Dimensional 1.5.

Chapter 2

Optimization—A Mathematical Review Optimal Problem Modeling

4

9

Problems

30

References

32

Controller

35

Design Based on Parameter Optimization

2.1. Introduction

35 Indices

2.2.

Performance

2.3.

Preliminary Design Concept

35

2.4. Parameter

-

The Inward Approach Outward Approach

41

Optimization Design 2.5. Limitations ofParameter Optimization

44

2.6. Parameter

64

—

Optimization with Constraints

2.7. Control Vector Parameterization

2.8. Parameters

Optimization

via Genetic

List

55

70

Algorithms

Problems

Chapter 3

1

ofMATLAB Programs

75

79 84

References

94

Calculus of Variations

95

3.1. Introduction

95

3.2. Motivation

95

3.3. Standard Problem Statement

97

3.4.

Transverzality Conditions

107

3.5. Extreme Functional with Dynamic Constraints

113

Problems

118

References

124

viii

Contents

Chapter 4

Optimal Control Based on Calculus of Variations

125

4.1. Introduction

125

4.2. Optimal Criteria

125

4.3. Statement

of Optimal Control Problem

127

4.4.

Conditions

132

Necessary

of Optimality

4.5. Terminal Controllers and Regulators

145

4.6. Terminal Constraints and Variable Terminal Time

155

4.7.

164

Approximate

Optimal State-Feedback Control

4.8. Numerical Solution

Using MATLAB

TBVP Solver

Problems List

176

of MATLAB

183

Programs

189

References Chapter 5

Optimal

Control with

5.2.

Input Constraints Optimization

191

5.3.

Pontryagin's Principle Optimal Time Problem

193

197

Control-Effort Problems

211

5.6.

Singular Problem

230

5.7.

Inequality Constraint ofPure State Variable

242

Problems

250

List of MATLAB Programs

255

References

258

Dynamic Programming

259

6.1. Introduction

259

6.2.

259

Multi-Stage Decision Problem and Principle of Optimality

6.3. A

Control Problem in Discrete-Time

Simple

6.4. Continuous Form

Chapter 7

191

191

5.5. Minimum

6

Input and State Variable Constraints

5.1. Introduction

5.4.

Chapter

167

261

ofDynamic Programming 6.5. Parametric Expansion

269

6.6. Cross-Product Terms

289

6.7.

290

Differential Dynamic Programming DDP

280

Problems

300

List

306

of MATLAB Programs

References

313

Linear-Quadratic (LQ) Optimal Control

315

7.1. Introduction

315

7.2.

Types of Optimal Control Problems

315

7.3.

Optimal

316

Solution

7.4. Selection

ofthe

Q

of the State

Regulating Problem

and R Matrices

7.5.

323

Optimal Solution of the Output Regulating Problem 7.6. Optimal Solution of the Tracking Problem 7.7. Equivalent Quadratic Cost Functional

328

7.8. Solution Based on Hamiltonian Matrix for Invariant Systems

353

7.9 Discrete-Time

360

LQ Optimal Control

335 348

Contents

7. / 0. Iterative

ix

LQ for Nonlinear Systems

367

Problems

372

List

379

ofMATLAB Programs References Chapter 8

Optimal Solution Based

on

385 Genetic

Programming

387

5.7. Introduction

387

8.2. Genetic Programming Review

387

8.3. Enhanced Genetic Programming 8.4.

Synthesizing Input

Constraints

Optimal

391 Control Problem

404

Problems

416

References

417