Optimal Control

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Mathematics, Calculus
Cover of the book Optimal Control by Leonid T. Aschepkov, Taekyun Kim, Dmitriy V.  Dolgy, Ravi P.  Agarwal, Springer International Publishing
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Author: Leonid T. Aschepkov, Taekyun Kim, Dmitriy V. Dolgy, Ravi P. Agarwal ISBN: 9783319497815
Publisher: Springer International Publishing Publication: January 11, 2017
Imprint: Springer Language: English
Author: Leonid T. Aschepkov, Taekyun Kim, Dmitriy V. Dolgy, Ravi P. Agarwal
ISBN: 9783319497815
Publisher: Springer International Publishing
Publication: January 11, 2017
Imprint: Springer
Language: English

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.

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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.

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