Geodesic
Control of a family of nonlinear dynamic systems under measurements with bounded disturbances
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 178-186 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a control synthesis problem for nonlinear dynamic systems under parametric uncertainty and bounded measurement noises. Because of bounded disturbances in measurements of the state vector and the nonlinearity in the control object, the initially formulated control synthesis problem for a family of nonlinear systems as a generalized Zubov problem is transformed into a symbiosis of generalized Zubov–Bulgakov problems. The main result of the paper is the analytic solution of a minimax synthesis problem, which yields a constructive method for finding an invariant set.
Keywords: control, uncertainty, Lyapunov functions, bounded disturbances, robust stability
Mots-clés : invariant sets. 
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V. M. Kuntsevich. Control of a family of nonlinear dynamic systems under measurements with bounded disturbances. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 178-186. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a15/

[1] Kurzhanskii A. B., Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977, 390 pp. | MR | Zbl

[2] Izbrannye trudy A. B. Kurzhanskogo, Izd-vo Mosk. un-ta, M., 2009, 756 pp.

[3] Zubov V. I., Lektsii po teorii upravleniya, Nauka, M., 1975, 494 pp. | MR | Zbl

[4] Kuntsevich V. M., Lychak M. M., Sintez sistem avtomaticheskogo upravleniya s pomoschyu funktsii Lyapunova, Nauka, M., 1977, 399 pp. | MR | Zbl

[5] Kuntsevich A. V., Kuntsevich V. M., “Ustoichivost v oblasti nelineinykh raznostnykh vklyuchenii”, Kibernetika i sistemnyi analiz, 2010, no. 5, 51–59

[6] Kuntsevich V. M., Kurzhanskii A. B., “Oblasti dostizhimosti lineinykh i nekotorykh klassov nelineinykh diskretnykh sistem i upravleniya imi”, Problemy upravleniya i informatiki, 2010, no. 1, 5–21 | MR

[7] Kuntsevich V. M., Kuntsevich A. V., “Invariantnye mnozhestva semeistv lineinykh i nelineinykh diskretnykh sistem s ogranichennymi vozmuscheniyami”, Avtomatika i telemekhanika, 2012, no. 1, 92–106 | MR

[8] Lure A. I., Postnikov V. N., “K teorii ustoichivosti reguliruemykh sistem”, Prikladnaya matematika i mekhanika, 8:3 (1944), 246–248 | Zbl

[9] Aizerman M. A., Gantmakher F. R., Absolyutnaya ustoichivost reguliruemykh sistem, Izd-vo AN SSSR, M., 1963, 261 pp.

[10] Bulgakov B. V., “O nakoplenii vozmuschenii v lineinykh kolebatelnykh sistemakh s postoyannymi parametrami”, Dokl. AN SSSR, 51:5 (1946), 7–15 | MR