Optimal Control / by Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal.

Format:

Book

Author/Creator:

Aschepkov, Leonid T., Author.

Dolgy, Dmitriy V., Author.

Kim, Taekyun, Author.

Agarwal, Ravi P., Author.

Language:

English

Subjects (All):

Calculus of variations.

System theory.

Calculus of Variations and Optimal Control; Optimization.

Systems Theory, Control.

Local Subjects:

Calculus of Variations and Optimal Control; Optimization.

Systems Theory, Control.

Physical Description:

1 online resource (XV, 209 p. 55 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Further exercises and a large number of additional tasks are provided for use as practical training in order for the reader to consolidate the theoretical material.

Contents:

NOTATIONS

PREFACE

INTRODUCTION

1. Subject of optimal control

2. Mathematical model of controlled object

3. Reachability set

4. Controllability of linear systems

5. Minimum time problem

6. Synthesis of optimal system performance

7. The observability problem

8. Identification problem

9. Types of optimal control problems

10. Small increments of a trajectory

11. The simplest problem of optimal control

12. General optimal control problem

13. Sufficient optimality conditions

CONCLUSION

APPENDIX

EXAMPLES OF TASKS AND SOLUTIONS

LITERATURE.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-49781-2

OCLC:

988794464