LEADER 03871nam 22005655 450 001 9910254084903321 005 20200704173712.0 010 $a3-319-49781-2 024 7 $a10.1007/978-3-319-49781-5 035 $a(CKB)3710000001041189 035 $a(DE-He213)978-3-319-49781-5 035 $a(MiAaPQ)EBC6314074 035 $a(MiAaPQ)EBC5576378 035 $a(Au-PeEL)EBL5576378 035 $a(OCoLC)988794464 035 $a(PPN)198342330 035 $a(EXLCZ)993710000001041189 100 $a20170111d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOptimal Control /$fby Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XV, 209 p. 55 illus.) 311 $a3-319-49780-4 327 $aNOTATIONS -- 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. 330 $aThis 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. 606 $aCalculus of variations 606 $aSystem theory 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 615 0$aCalculus of variations. 615 0$aSystem theory. 615 14$aCalculus of Variations and Optimal Control; Optimization. 615 24$aSystems Theory, Control. 676 $a629.8312 700 $aAschepkov$b Leonid T$4aut$4http://id.loc.gov/vocabulary/relators/aut$0934995 702 $aDolgy$b Dmitriy V$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKim$b Taekyun$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aAgarwal$b Ravi P$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254084903321 996 $aOptimal Control$92105561 997 $aUNINA