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＜電子ブック＞
Optimal Control / by Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
本文言語	英語
大きさ	XV, 209 p. 55 illus : online resource
著者標目	*Aschepkov, Leonid T author Dolgy, Dmitriy V author Kim, Taekyun author Agarwal, Ravi P author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:System theory LCSH:Control theory FREE:Calculus of Variations and Optimization FREE:Systems Theory, Control
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-49781-5

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