Optimal Control: An Introduction to the Theory with Applications

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Clarendon Press, 1991 - Mathematics - 254 pages
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Systems that evolve with time occur frequently in nature and modelling the behavior of such systems provides an important application of mathematics. These systems can be completely deterministic, but it may be possible too to control their behavior by intervention through "controls." The theory of optimal control is concerned with determining such controls which, at minimum cost, either direct the system along a given trajectory or enable it to reach a given point in its state space. This textbook is a straightforward introduction to the theory of optimal control with an emphasis on presenting many different applications. Professor Hocking has taken pains to ensure that the theory is developed to display the main themes of the arguments but without using sophisticated mathematical tools. Problems in this setting can arise across a wide range of subjects and there are illustrative examples of systems from fields as diverse as dynamics, economics, population control, and medicine. Throughout there are many worked examples, and numerous exercises (with solutions) are provided.
 

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Contents

OPTIMAL CONTROL PROBLEMS
1
SYSTEMS OF DIFFERENTIAL EQUATIONS
14
PART A TIMEOPTIMAL CONTROL OF LINEAR
29
TIMEOPTIMAL CONTROL
46
Exercises 4
64
Exercises 5
79
Exercises 6
97
Exercises 7
111
OUTLINE SOLUTIONS TO THE EXERCISES Exercises 1
217
Exercises 3
219
Exercises 4
222
Exercises 5
224
Exercises 6
226
Exercises 7
229
Exercises 8
233
Exercises 9
236

Exercises 8
130
PROOF OF THE PONTRYAGIN MAXIMUM
132
FURTHER APPLICATIONS
151
APPLICATIONS OF OPTIMAL CONTROL
173
NUMERICAL METHODS FOR OPTIMAL
199
BIBLIOGRAPHY
213
Exercises 10
237
Exercises 11
242
Exercises 12
247
INDEX
249
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About the author (1991)

Leslie M. Hocking is at University College, London.

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