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9780198596820

Optimal Control An Introduction to the Theory with Applications

by
  • ISBN13:

    9780198596820

  • ISBN10:

    0198596820

  • Format: Paperback
  • Copyright: 1991-03-28
  • Publisher: Clarendon Press

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Summary

Systems that evolve with time occur frequently in nature and modelling the behaviour of such systems provides an important application of mathematics. These systems can be completely deterministic, but it may be possible too to control their behaviour by intervention through 'controls'. Thetheory 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 sophisticatedmathematical tools. Problems in this setting can arise across a wide range of subjects and there are illustrative examples of systems from as diverse fields as dynamics, economics, population control, and medicine. Throughout there are many worked examples, and numerous exercises (with solutions) are provided.

Table of Contents

Optimal control problems; Systems of differential equations, matrices, and sets
Time-Optimal Control of Linear Systems: Controllability
Time-optimal control
Further examples
The Pontryagin Maximum Principle: The basic Pontryagin Maximum Principle (PMP)
Extensions to the PMP
Linear state equations with quadratic costs
Proof of the Pontryagin Maximum Principle
Further applications and extensions
Applications of Optimal Control Theory: Some applied optimal control problems
Numerical methods for optimal control problems
Bibliography
Outline solutions to the exercises
Index
Table of Contents provided by Publisher. All Rights Reserved.

Supplemental Materials

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