Geodesic
Tracking of solution to parabolic equation with memory for general class of controls
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 53-64.

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

We consider a control problem for parabolic equation with memory. It consists in constructing an algorithm for finding a feedback control such that a solution to a given equation should track a solution to another equation generated by an unknown right-hand side. We propose two noise-resistant solution algorithms for this problem which are based on the method of extremal shift. The first algorithm is applicable in the case of continuous measurements of phase states, whereas the second one presumes discrete measurements.
Keywords: systems with distributed parameters, retarded systems, control. 
@article{IVM_2016_10_a6,
     author = {P. G. Surkov},
     title = {Tracking of solution to parabolic equation with memory for general class of controls},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {53--64},
     publisher = {mathdoc},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_10_a6/}
}
TY  - JOUR
AU  - P. G. Surkov
TI  - Tracking of solution to parabolic equation with memory for general class of controls
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2016
SP  - 53
EP  - 64
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2016_10_a6/
LA  - ru
ID  - IVM_2016_10_a6
ER  - 
%0 Journal Article
%A P. G. Surkov
%T Tracking of solution to parabolic equation with memory for general class of controls
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2016
%P 53-64
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2016_10_a6/
%G ru
%F IVM_2016_10_a6
P. G. Surkov. Tracking of solution to parabolic equation with memory for general class of controls. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 53-64. http://geodesic.mathdoc.fr/item/IVM_2016_10_a6/

[1] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[2] Vasileva E. V., Maksimov V. I., “O dinamicheskoi rekonstruktsii upravlenii v differentsialnom uravnenii s pamyatyu”, Differents. uravneniya, 35:6 (1999), 813–821 | MR | Zbl

[3] Grimmer R. C., Pritchard A. J., “Analytic resolvent operators for integral equations in Banach space”, J. Differ. Equat., 50:2 (1983), 234–259 | DOI | MR | Zbl

[4] Oka H., “Abstract quasilinear Volterra integrodifferential equations”, Nonlinear Anal., 28 (1997), 1019–1045 | DOI | MR | Zbl

[5] Coleman B. D., Gurtin M. E., “Equipresence and constitutive equations for rigid head conductors”, Z. Angew. Math. Phys., 18 (1967), 199–208 | DOI | MR

[6] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR

[7] Kryazhimskii A. V., Osipov Yu. S., “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Tekhnich. kibernetika, 1975, no. 2, 51–68 | MR

[8] Maksimov V. I., “Ob otslezhivanii resheniya parabolicheskogo uravneniya”, Izv. vuzov. Matem., 2012, no. 1, 40–48 | MR | Zbl

[9] Vrabie I. I., Compactness methods for nonlinear evolutions, Longman Scientific Technical, Harlow, 1987 | MR | Zbl

[10] Barbashin E. A., Vvedenie v teoriyu ustoichivosti, Nauka, M., 1967

[11] Barbu V., Optimal control of variational inequalities, Pitman Advanced Publishing Program, London, 1984 | MR | Zbl

[12] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, Izd-vo UrO RAN, Ekaterinburg, 2000

[13] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR