Optimal Control and the Calculus of Variations (Revised)

Edition: 1st
Format: Paperback
Pub. Date: 1995-10-19
Publisher(s): Oxford
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Optimal control is a modern development of the calculus of variations and classical optimization theory. For that reason, this introduction to the theory of optimal control starts by considering the problem of minimizing a function of many variables. It moves through an exposition of the calculus of variations, to the optimal control of systems governed by ordinary differential equations. This approach should enable students to see the essential unity of important areas of mathematics, and also allow optimal control and the Pontryagin maximum principle to be placed in a proper context. A good knowledge of analysis, algebra, and methods is assumed. All the theorems are carefully proved, and there are many worked examples and exercises. Although this book is written for the advanced undergraduate mathematician, engineers and scientists who regularly rely on mathematics will also find it a useful text.

Table of Contents

The maxima and minima of functions
The calculus of variations
Optimal control
Optimization in
Functions of one variable
Critical points, end-points, and points of discontinuity
Functions of several variables
Minimization with constraints
A geometrical interpretation
Distinguishing maxima from minima
The calculus of variations
Problems in which the end-points are not fixed
Finding minimizing curves
Isoperimetric problems
Sufficiency conditions
Fields of extremals
Hilbert's invariant integral
Semi-fields and the Jacobi condition
Optimal Control I: Theory
Control of a simple first-order system
Systems governed by ordinary differential equations
The optimal control problem
The Pontryagin maximum principle
Optimal control to target curves
Optimal Control II: Applications
Time-optimal control of linear systems
Optimal control to target curves
Singular controls
Fuel-optimal controls
Problems where the cost depends on X (t l)
Linear systems with quadratic cost
The steady-state Riccai equation
The calculus of variations revisited
Proof of the Maximum Principle of Pontryagin
Convex sets in
The linearized state equations
Behaviour of H on an optimal path
Sufficiency conditions for optimal control
Table of Contents provided by Publisher. All Rights Reserved.

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