Interval optimal control problem in a Hilbert space
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 4, pp. 531-537 Cet article a éte moissonné depuis la source Math-Net.Ru

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An optimal control problem for a system involving an interval parameter is considered. The concepts of a universal optimal state and a universal optimal control are introduced. The existence and uniqueness of a universal solution to the interval optimal control problem is proved, and an algorithm for its determination is presented. The interval optimal control problem for a system described by the boundary value problem for a second-order ordinary differential equation is solved as an example.
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Victoria Olegovna O. Interval optimal control problem in a Hilbert space. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 4, pp. 531-537. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_4_a3/

[1] Aschepkov L. T., Davydov D. V., Universalnye resheniya intervalnykh zadach optimizatsii i upravleniya, Nauka, M., 2006

[2] Aschepkov L. T., Dolgy D. V., “The universal soltion of interval systems of linaer algebraical equations”, Intern. J. Software Eng. and Knowledge Eng., 3:4 (1993), 477–485 | DOI

[3] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[4] Aschepkov L. T., Kosogorova I. B., “Minimizatsiya kvadratichnoi funktsii s intervalnymi koeffitsientami”, Zh. vychisl. matem. i matem. fiz., 42:5 (2002), 653–664 | MR

[5] Aschepkov L. T., Davydov D. V., “Stabilizatsiya nablyudaemoi lineinoi sistemy upravleniya s postoyannymi intervalnymi koeffitsientami”, Izv. vyssh. uchebn. zavedenii. Matematika, 2002, no. 2(477), 11–17

[6] Zakharov A. V., Shokin Yu. I., “Sintez sistem upravleniya priintervalnoi neopredelennosti parametrov i ikh matematicheskikh modelei”, Dokl. AN SSSR, 299:2 (1988), 292–295 | Zbl

[7] Lakeev A. V., Noskov S. I., “O mnozhestve reshenii lineinogo uravneniya s intervalno zadannym operatorom i pravoi chastyu”, Sibirsk. matem. zh., 35:5 (1994), 1074–1084 | MR | Zbl

[8] Shashikhin V. N., “Optimizatsiya intervalnykh sistem”, Avtomatika i telemekhanika, 2000, no. 11, 94–103 | MR | Zbl

[9] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972 | MR

[10] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Fizmatlit, M., 2005