Geodesic
Solvability of mixed-type optimal control problems for distributed systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 37-47.

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

In this paper we consider optimal control problems for distributed systems which are not solved with respect to the time derivative, where performance functionals have a quadratic form. We concurrently use the distributed and starting controls.
Keywords: optimal control
Mots-clés : Sobolev-type equations. 
@article{IVM_2011_7_a4,
     author = {M. V. Plekhanova and A. F. Islamova},
     title = {Solvability of mixed-type optimal control problems for distributed systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {37--47},
     publisher = {mathdoc},
     number = {7},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_7_a4/}
}
TY  - JOUR
AU  - M. V. Plekhanova
AU  - A. F. Islamova
TI  - Solvability of mixed-type optimal control problems for distributed systems
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 37
EP  - 47
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_7_a4/
LA  - ru
ID  - IVM_2011_7_a4
ER  - 
%0 Journal Article
%A M. V. Plekhanova
%A A. F. Islamova
%T Solvability of mixed-type optimal control problems for distributed systems
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 37-47
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2011_7_a4/
%G ru
%F IVM_2011_7_a4
M. V. Plekhanova; A. F. Islamova. Solvability of mixed-type optimal control problems for distributed systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 37-47. http://geodesic.mathdoc.fr/item/IVM_2011_7_a4/

[1] Showalter R. E., “Nonlinear degenerate evolution equations and partial differential equations of mixed type”, SIAM J. Math. Anal., 6:1 (1975), 25–42 | DOI | MR | Zbl

[2] Fedorov V. E., Plekhanova M. V., “Optimalnoe upravlenie lineinymi uravneniyami sobolevskogo tipa”, Differents. uravneniya, 40:1 (2004), 1548–1556 | MR | Zbl

[3] Plekhanova M. V., Fedorov V. E., “Zadacha optimalnogo upravleniya dlya odnogo klassa vyrozhdennykh uravnenii”, Izv. RAN. Teoriya i sistemy upravleniya, 2004, no. 5, 40–44 | MR

[4] Fedorov V. E., Plekhanova M. V., “Issledovanie odnoi zadachi optimalnogo upravleniya”, Vestn. Chelyabinsk. gos. ped. un-ta. Ser. 4. Estestv. nauki, 2005, no. 6, 23–31

[5] Müller P. C., “Linear control design of linear descriptor systems”, 14th Triennial World Congress, Beijing, P. R. China, 1999, 31–36

[6] Chistyakov V. F., Scheglova A. A., Izbrannye glavy teorii algebro-differentsialnykh sistem, Nauka, Novosibirsk, 2003 | MR | Zbl

[7] Sviridyuk G. F., Efremov A. A., “Optimalnoe upravlenie lineinymi uravneniyami tipa Soboleva s otnositelno $p$-sektorialnymi operatorami”, Differents. uravneniya, 31:11 (1995), 1912–1919 | MR | Zbl

[8] Sviridyuk G. F., Efremov A. A., “Zadacha optimalnogo upravleniya dlya lineinykh uravnenii tipa Soboleva”, Izv. vuzov. Matem., 1996, no. 12, 75–83 | MR | Zbl

[9] Sviridyuk G. F., Efremov A. A., “Optimalnoe upravlenie odnim klassom lineinykh vyrozhdennykh uravnenii”, Dokl. RAN, 364:3 (1999), 323–325 | MR | Zbl

[10] Fedorov V. E., Plekhanova M. V., “Slabye resheniya i problema kvadraticheskogo regulyatora dlya vyrozhdennogo differentsialnogo uravneniya v gilbertovom prostranstve”, Vychisl. tekhnologii, 9:2 (2004), 92–102 | Zbl

[11] Fursikov A. V., Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999 | Zbl

[12] Plekhanova M. V., Fedorov V. E., “Kriterii optimalnosti v zadache upravleniya dlya lineinogo uravneniya sobolevskogo tipa”, Izv. RAN. Teoriya i sistemy upravleniya, 2007, no. 2, 37–44 | MR

[13] Plekhanova M. V., Fedorov V. E., “Zadachi startovogo upravleniya dlya lineinykh uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. Fiz. Khimiya, 2005, no. 6, 43–49

[14] Cviridyuk G. A., Fedorov V. E., “O edinitsakh analiticheskikh polugrupp operatorov s yadrami”, Sib. matem. zhurn., 39:3 (1998), 604–616 | MR | Zbl

[15] Sviridyuk G. A., Fedorov V. E., Linear Sobolev type equations and degenerate semigroups of operators. Inverse and ill-posed problems, VSP, Utrecht, 2003 | MR | Zbl

[16] Sveshnikov A. G., Alshin A. B., Korpusov M. O., Pletner Yu. D., Lineinye i nelineinye uravneniya sobolevskogo tipa, Fizmatlit, M., 2007 | Zbl