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Calculus of Variations and Optimal Control

About this Title

A. A. Milyutin, Russian Academy of Sciences, Moscow, Russia and N. P. Osmolovskii, Moscow State Civil Engineeering University, Moscow, Russia. Translated by Dmitrii Chibisov

Publication: Translations of Mathematical Monographs
Publication Year: 1998; Volume 180
ISBNs: 978-0-8218-0753-8 (print); 978-1-4704-4594-2 (online)
DOI: https://doi.org/10.1090/mmono/180
MathSciNet review: MR1641590
MSC: Primary 49-02; Secondary 49K15, 49L05, 93-02

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Table of Contents

Front/Back Matter

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Chapters

• Introduction

First order conditions

• Theory of a weak minimum for the problem on a fixed time interval
• Theory of the maximum principle
• Extremals and the Hamiltonian of a control system
• Hamilton-Jacobi equation and field theory
• Transformations of problems and invariance of extremals

Quadratic conditions

• Quadratic conditions and conjugate points for broken extremals
• Quadratic conditions for a Pontryagin minimum and sufficient conditions for a strong minimum: Proofs
• Quadratic conditions in the general problem of the calculus of variations and related optimal control problems
• Investigation of extremals by quadratic conditions: Examples

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