Counterexamples in optimal control theory / S. Ya. Serovaiskii.

Format:

Book

Author/Creator:

Serovaĭskiĭ, S. I︠A︡.

Series:

Inverse and Ill-Posed Problems Series

Inverse and ill-posed problems series, 1381-4524

Language:

English

Subjects (All):

Control theory.

Mathematical optimization.

Physical Description:

1 online resource (184 p.)

Edition:

Reprint 2011

Place of Publication:

Utrecht ; Boston : VSP, 2004.

Language Note:

English

Summary:

This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations. A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect. The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems.

Contents:

Frontmatter

Contents

Preface

Introduction

Example 1. Insufficiency of the optimality conditions

Example 2. The singular control

Example 3. Nonexistence of optimal controls

Example 4. Nonexistence of optimal controls (Part 2)

Example 5. Ill-posedness in the sense of Tikhonov

Example 6. Ill-posedness in the sense of Hadamard

Example 7. Insufficiency of the optimality conditions (Part 2)

Example 8. The Chafee-Infante problem

Comments

Conclusion

Bibliography

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [169]-175).

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9783110915532

3110915537

OCLC:

979946720