Optimal Control Theory An Introduction

by Kirk, Donald E.

• ISBN13: 9780486434841
• ISBN10: 0486434842
• Format: Paperback
• Copyright: 2004-04-30
• Publisher: Dover Publications

Summary

Geared toward upper-level undergraduates, this text introduces three aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous problems, which introduce additional topics and illustrate basic concepts, appear throughout the text. Solution guide available upon request. 131 figures. 14 tables. 1970 edition.

Table of Contents

Describing the System and Evaluating Its Performance
Introduction	p. 3
Problem Formulation	p. 3
State Variable Representation of Systems	p. 16
Concluding Remarks	p. 22
References	p. 23
Problems	p. 23
The Performance Measure	p. 29
Performance Measures for Optimal Control Problems	p. 29
Selecting a Performance Measure	p. 34
Selection of a Performance Measure: The Carrier Landing of a Jet Aircraft	p. 42
References	p. 47
Problems	p. 47
Dynamic Programming
Dynamic Programming	p. 53
The Optimal Control Law	p. 53
The Principle of Optimality	p. 54
Application of the Principle of Optimality to Decision-Making	p. 55
Dynamic Programming Applied to a Routing Problem	p. 56
An Optimal Control System	p. 58
Interpolation	p. 64
A Recurrence Relation of Dynamic Programming	p. 67
Computational Procedure for Solving Control Problems	p. 70
Characteristics of Dynamic Programming Solution	p. 75
Analytical Results--Discrete Linear Regulator Problems	p. 78
The Hamilton-Jacobi-Bellman Equation	p. 86
Continuous Linear Regulator Problems	p. 90
The Hamilton-Jacobi-Bellman Equation--Some Observations	p. 93
Summary	p. 94
References	p. 95
Problems	p. 96
The Calculus of Variations and Pontryagin's Minimum Principle
The Calculus of Variations	p. 107
Fundamental Concepts	p. 108
Functionals of a Single Function	p. 123
Functionals Involving Several Independent Functions	p. 143
Piecewise-Smooth Extremals	p. 154
Constrained Extrema	p. 161
Summary	p. 177
References	p. 178
Problems	p. 178
The Variational Approach to Optimal Control Problems	p. 184
Necessary Conditions for Optimal Control	p. 184
Linear Regulator Problems	p. 209
Pontryagin's Minimum Principle and State Inequality Constraints	p. 227
Minimum-Time Problems	p. 240
Minimum Control-Effort Problems	p. 259
Singular Intervals in Optimal Control Problems	p. 291
Summary and Conclusions	p. 308
References	p. 309
Problems	p. 310
Iterative Numerical Techniques for Finding Optimal Controls and Trajectories
Numerical Determination of Optimal Trajectories	p. 329
Two-Point Boundary-Value Problems	p. 330
The Method of Steepest Descent	p. 331
Variation of Extremals	p. 343
Quasilinearization	p. 357
Summary of Iterative Techniques for Solving Two-Point Boundary-Value Problems	p. 371
Gradient Projection	p. 373
References	p. 408
Problems	p. 409
Conclusion
Summation	p. 417
The Relationship Between Dynamic Programming and the Minimum Principle	p. 417
Summary	p. 423
Controller Design	p. 425
Conclusion	p. 427
References	p. 427
Appendices	p. 429
Useful Matrix Properties and Definitions	p. 429
Difference Equation Representation of Linear Sampled-Data Systems	p. 432
Special Types of Euler Equations	p. 434
Answers to Selected Problems	p. 437
Index	p. 443
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