Geodesic
Asymptotics of the solution to a liner-quadratic periodic problem with a singular matrix perturbation in the performance index
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 603-616 
G. A. Kurina; S. S. Shchekunskikh. Asymptotics of the solution to a liner-quadratic periodic problem with a singular matrix perturbation in the performance index. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 603-616. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A liner-quadratic periodic optimal control problem with a singular matrix perturbation in the performance index is considered. An asymptotic expansion of its solution in nonnegative integer powers of is constructed by applying a direct scheme. The proximity of the exact solution to the approximate one is estimated for the control, trajectory, and functional. It is shown that the functional minimized does not increase when a higher order asymptotic approximation to the optimal control is used.

[1] Muradova H. D., “Singulyarnye vozmuscheniya v lineino-kvadratichnoi periodicheskoi zadache optimalnogo upravleniya”, Izv. AN TurkmSSR. Ser. fiz.-tekhn., khimich. i geologich. nauk, 1983, no. 1, 10–14 | MR

[2] Dmitriev M. G., Kurina G. A., Ovezov Kh. A., “Ispolzovanie pryamoi skhemy dlya resheniya lineino-kvadratichnoi zadachi optimalnogo upravleniya s singulyarnym vozmuscheniem”, Izv. RAN. Teoriya i sistemy upravleniya, 1996, no. 4, 62–68 | Zbl

[3] Kurina G. A., Shabanova S. S., “Formalnaya asimptotika resheniya lineino-kvadratichnoi periodicheskoi zadachi optimalnogo upravleniya s matrichnym singulyarnym vozmuscheniem v kriterii kachestva”, Materialy konf. po funkts. analizu i matem. fiz., posvyaschennoi 80-ti letiyu Kreina Selima Grigorevicha (Voronezh, 1997), 55–59 | MR | Zbl

[4] Zharikova E. H., Singulyarno vozmuschennye periodicheskie zadachi upravleniya, Avtoref. dis. ...kand. fiz.-matem. nauk, Samara, 1995, 16 pp.

[5] Kurina G. A., “Dostatochnye usloviya optimalnosti upravleniya dlya lineinykh periodicheskikh sistem, ne razreshennykh otnositelno proizvodnoi”, Ukr. matem. zhurnal, 39:6 (1987), 783–786 | MR

[6] Kurina G. A., Martynenko G. V., “O privodimosti neotritsatelno gamiltonovoi periodicheskoi operator-funktsii, deistvuyuschei v veschestvennom gilbertovom prostranstve, k blochno-diagonalnoi forme”, Differents. ur-niya, 37:2 (2001), 212–217 | MR | Zbl

[7] Azizov T. Ya., Kiriakidi V. K., Kurina G. A., “Indefinitnyi podkhod k zadache o privodimosti neotritsatelno gamiltonovoi operator-funktsii k blochno-diagonalnoi forme”, Funkts. analiz i ego prilozh., 35:3 (2001), 73–75 | MR | Zbl

[8] Hatto L., Levinson N., “Periodic solution of singularly perturbed systems”, J. Ration. Mech. Analysis, 4 (1955), 943–950 | MR