Geodesic
Optimal control of impulsive systems with nonlocal boundary conditions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 75-84.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study an optimal control problem, where states of a control system are described by impulsive differential equations with nonlocal boundary conditions. With the help of the contraction principle we prove the existence and uniqueness of a solution to the corresponding boundary value problem with fixed admissible controls. We calculate the first and second variations of the functional. Using the variation of controls, we establish various necessary optimality conditions of the second order.
Keywords: nonlocal boundary conditions, optimal control, impulsive systems, existence and uniqueness of solutions. 
@article{IVM_2013_2_a7,
     author = {Ya. A. Sharifov},
     title = {Optimal control of impulsive systems with nonlocal boundary conditions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {75--84},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_2_a7/}
}
TY  - JOUR
AU  - Ya. A. Sharifov
TI  - Optimal control of impulsive systems with nonlocal boundary conditions
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 75
EP  - 84
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_2_a7/
LA  - ru
ID  - IVM_2013_2_a7
ER  - 
%0 Journal Article
%A Ya. A. Sharifov
%T Optimal control of impulsive systems with nonlocal boundary conditions
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 75-84
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_2_a7/
%G ru
%F IVM_2013_2_a7
Ya. A. Sharifov. Optimal control of impulsive systems with nonlocal boundary conditions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 75-84. http://geodesic.mathdoc.fr/item/IVM_2013_2_a7/

[1] Samoilenko A. M., Perestyuk N. A., Differentsialnye uravneniya s impulsnym vozdeistviem, Vischa Shkola, Kiev, 1987

[2] Khalanai A., Veksler D., Kachestvennaya teoriya impulsnykh sistem, Mir, M., 1971 | MR

[3] Lakshmikantham V., Bainov D. D., Simeonov P. S., Theory of impulsive differential equations, World Scientific, Singapore, 1989 | MR | Zbl

[4] Benchohra M., Henderson J., Ntouyas S. K., Impulsive differential equations and inclusions, v. 2, Contemporary mathematics and its application, Hindawi Publishing Corporation, N.-Y., 2006 | MR

[5] Selvaraj B., Arjunan M., Kavitha V., “Existence of solutions for impulsive nonlinear differential equations with nonlocal conditions”, J. KSIAM, 13:3 (2009), 203–215 | MR

[6] Anguraj A., Arjunan M., “Existence and uniqueness of mild and classical solutions of impulsive evolution equations”, Elect. J. Differ. Equ., 111 (2005), 1–8 | MR

[7] Ji Sh., Wen Sh., “Nonlocal Cauchy problem for impulsive differential equations in Banach Spaces”, Int. J. Nonlinear Sci., 10:1 (2010), 88–95 | MR | Zbl

[8] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[9] Vasileva O. O., Mizukami K., “Optimalnoe upravlenie kraevoi zadachei”, Izv. vuzov. Matem., 1994, no. 12, 33–41 | MR | Zbl

[10] Vasileva O. O., Mizukami K., “Dinamicheskie protsessy, opisyvaemye kraevoi zadachei: neobkhodimye usloviya optimalnosti i metody resheniya”, Izv. RAN. Teoriya i sistemy upravleniya, 2000, no. 1, 95–100 | MR

[11] Vasilieva O., Mizukami K., “Optimality criterion for singular controllers: linear boundary conditions”, J. Math. Anal. Appl., 213 (1997), 620–641 | DOI | MR | Zbl

[12] Sharifov Y. A., “Necessary optimality conditions of first and second order for systems with boundary conditions”, Transactions of NAS of Azerbaijan issue mathematics and mechanics series of physical-technical and mathematical science, 28:1 (2008), 189–198 | MR | Zbl

[13] Sharifov Y. A., “Necessary conditions for optimality of singular controls with nonlocal boundary conditions”, International Conference “Differential Equations and Topology” Dedicated to the Centennial Anniversary of Lev Semenovich Pontryagin, Abstracts (Moscow, June 17–22, 2008)

[14] Mekhtiev M. F., Dzhabrailov Sh. I., Sharifov Ya. A., “Neobkhodimye usloviya optimalnosti vtorogo poryadka v klassicheskom smysle v zadachakh optimalnogo upravleniya trekhtochechnymi usloviyami”, Problemy upr. i teor. inform., 2010, no. 2, 64–73

[15] Sardarova R. A., Sharifov Ya. A., “O neobkhodimykh usloviyakh optimalnosti dlya sistem s mnogotochechnymi usloviyami”, Izv. NANA. Teoriya i sistemy upravleniya, 2004, no. 2, 66–70

[16] Gabbasov R., Kirillova F. M., Osobye optimalnye upravleniya, Nauka, M., 1973 | MR

[17] Mansimov K. B., Osobye upravleniya v sistemakh s zapazdyvaniem, ELM, Baku, 1999