Optimal Control of Singular Stationary Systems with Phase Constraints and State Variation
Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 761-766.

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

An optimal control problem for a system described by a singular nonlinear equation of elliptic type with an inclusion phase constraint is considered. Necessary optimality conditions are obtained by varying system states.
Keywords: optimal control, singular nonlinear control system with an inclusion phase constraint, variational method.
@article{MZM_2015_97_5_a9,
     author = {S. Ya. Serovaǐskiǐ},
     title = {Optimal {Control} of {Singular} {Stationary} {Systems} with {Phase} {Constraints} and {State} {Variation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {761--766},
     publisher = {mathdoc},
     volume = {97},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_5_a9/}
}
TY  - JOUR
AU  - S. Ya. Serovaǐskiǐ
TI  - Optimal Control of Singular Stationary Systems with Phase Constraints and State Variation
JO  - Matematičeskie zametki
PY  - 2015
SP  - 761
EP  - 766
VL  - 97
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_97_5_a9/
LA  - ru
ID  - MZM_2015_97_5_a9
ER  - 
%0 Journal Article
%A S. Ya. Serovaǐskiǐ
%T Optimal Control of Singular Stationary Systems with Phase Constraints and State Variation
%J Matematičeskie zametki
%D 2015
%P 761-766
%V 97
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_97_5_a9/
%G ru
%F MZM_2015_97_5_a9
S. Ya. Serovaǐskiǐ. Optimal Control of Singular Stationary Systems with Phase Constraints and State Variation. Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 761-766. http://geodesic.mathdoc.fr/item/MZM_2015_97_5_a9/

[1] A. V. Fursikov, Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Universitetskaya seriya, 5, Nauchnaya kniga, Novosibirsk, 1999 | Zbl

[2] Zh.-L. Lions, Upravlenie singulyarnymi raspredelennymi sistemami, Nauka, M., 1987 | MR | Zbl

[3] A. S. Matveev, V. A. Yakubovich, Abstraktnaya teoriya optimalnogo upravleniya, Izd. S.-Peterb. un-ta, SPb., 1994 | MR | Zbl

[4] P. Neittaanmäki, D. Tiba, Optimal Control of Nonlinear Parabolic Systems. Theory, Algorithms, and Applications, Monogr. Textbooks Pure Appl. Math., 179, Marcel Dekker, New York, 1994 | MR | Zbl

[5] B. S. Mordukhovich, J.-P. Raymond, “Neumann boundary control of hyperbolic equations with pointwise state constraints”, SIAM J. Control Optim., 43:4 (2005), 1354–1372 | DOI | MR | Zbl

[6] A. Rösch, F. Tröltzsch, “On regularity of solutions and Lagrange multipliers of optimal control problems for semilinear equations with mixed pointwise control-state constraints”, SIAM J. Control Optim., 46:3 (2007), 1098–1115 | MR | Zbl

[7] L. Wang, “State-constrained optimal control governed by elliptic differential equations in unbounded domains”, J. Optim. Theory Appl., 141:2 (2009), 411–427 | DOI | MR | Zbl

[8] J. Bonnans, E. Casas, “Optimal control of semilinear multistate systems with state constraints”, SIAM J. Control Optim., 27:2 (1989), 446–455 | DOI | MR | Zbl

[9] S. Ya. Serovaiskii, “Metod approksimatsionnogo shtrafa v zadache optimalnogo upravleniya negladkimi singulyarnymi sistemami”, Matem. zametki, 76:6 (2004), 893–904 | DOI | MR | Zbl

[10] S. Ya. Serovaiskii, “Metod shtrafa v singulyarnykh nelineinykh upravlyaemykh sistemakh s potochechnymi fazovymi ogranicheniyami”, Tr. IVMiMG SO RAN. Ser. Informatika, 10 (2011), 184–190

[11] S. Ya. Serovaiskii, “Zadacha optimalnogo upravleniya dlya nelineinogo ellipticheskogo uravneniya s fazovym ogranicheniem i variatsiya sostoyaniya sistemy”, Izv. vuzov. Matem., 2013, no. 9, 81–86 | Zbl

[12] Zh.-L. Lions, Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR | Zbl

[13] I. Ekland, R. Temam, Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979 | MR | Zbl

[14] Funktsionalnyi analiz, ed. S. G. Krein, Nauka, M., 1972 | MR | Zbl

[15] R. Glovinski, Zh.-L. Lions, R. Tremoler, Chislennoe issledovanie variatsionnykh neravenstv, Mir, M., 1979 | MR | Zbl