Calculus of Variations and Optimal Control

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Brand new. We distribute directly for the publisher. The theory of a Pontryagin minimum is developed for problems in the calculus of variations. The application of the notion of ... a Pontryagin minimum to the calculus of variations is a distinctive feature of this book. A new theory of quadratic conditions for a Pontryagin minimum, which covers broken extremals, is developed, and corresponding sufficient conditions for a strong minimum are obtained. Some classical theorems of the calculus of variations are generalized. Read more Show Less

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Overview

The theory of a Pontryagin minimum is developed for problems in the calculus of variations. The application of the notion of a Pontryagin minimum to the calculus of variations is a distinctive feature of this book. A new theory of quadratic conditions for a Pontryagin minimum, which covers broken extremals, is developed, and corresponding sufficient conditions for a strong minimum are obtained. Some classical theorems of the calculus of variations are generalized.

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Editorial Reviews

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Written for graduate students and research mathematicians working in the calculus of variations and control theory and in applications to mechanics, physics, and engineering. The principal type of control variations considered here are spiky variations, which lead to the notion of a minimum that is stronger than a weak minimum, referred to as a Pontryagin minimum. A new theory of quadratic conditions for a Pontryagin minimum is developed, and corresponding sufficient conditions for a strong minimum are obtained. No index. Translated from the original Russian edition (no date cited). Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Preface
Introduction 1
Pt. 1 First Order Conditions 5
Ch. 1 Theory of a Weak Minimum for the Problem on a Fixed Time Interval 7
Ch. 2 Theory of the Maximum Principle 23
Ch. 3 Extremals and the Hamiltonian of a Control System 43
Ch. 4 Hamilton-Jacobi Equation and Field Theory 87
Ch. 5 Transformations of Problems and Invariance of Extremals 125
Pt. 2 Quadratic Conditions 153
Ch. 1 Quadratic Conditions and Conjugate Points for Broken Extremals 155
Ch. 2 Quadratic Conditions for a Pontryagin Minimum and Sufficient Conditions for a Strong Minimum: Proofs 211
Ch. 3 Quadratic Conditions in the General Problem of the Calculus of Variations and Related Optimal Control Problems 283
Ch. 4 Investigation of Extremals by Quadratic Conditions: Examples 325
Bibliography 371
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