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@article{IIMI_2002_24_1_a0, author = {A. G. Ivanov}, title = {Elements of the mathematical apparatus in the almost periodic optimization {problems.~I}}, journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta}, pages = {3--100}, publisher = {mathdoc}, volume = {24}, number = {1}, year = {2002}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/IIMI_2002_24_1_a0/} }
TY - JOUR AU - A. G. Ivanov TI - Elements of the mathematical apparatus in the almost periodic optimization problems.~I JO - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta PY - 2002 SP - 3 EP - 100 VL - 24 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IIMI_2002_24_1_a0/ LA - ru ID - IIMI_2002_24_1_a0 ER -
%0 Journal Article %A A. G. Ivanov %T Elements of the mathematical apparatus in the almost periodic optimization problems.~I %J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta %D 2002 %P 3-100 %V 24 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/IIMI_2002_24_1_a0/ %G ru %F IIMI_2002_24_1_a0
A. G. Ivanov. Elements of the mathematical apparatus in the almost periodic optimization problems.~I. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 24 (2002) no. 1, pp. 3-100. http://geodesic.mathdoc.fr/item/IIMI_2002_24_1_a0/
[1] Tonkov E. L., “Optimalnye periodicheskie dvizheniya upravlyaemoi sistemy”, Matematicheskaya fizika, 1977, no. 21, 45–59
[2] Halanay A., “Optimal control of periodic solution”, Rev. Roumaine de mat. Pures et appl., 19:1 (1974), 3–16 | MR | Zbl
[3] Panasyuk A. I., Panasyuk V. I., Asimptoticheskaya magistralnaya optimizatsiya upravlyaemykh sistem, Nauka i tekhnika, Minsk, 1986, 296 pp.
[4] Panasyuk A. I., Panasyuk V. I., “Optimalnoe upravlenie s usrednennym vdol traektorii funktsionalom”, PMM, 49:4 (1985), 525–536
[5] Belousov L. A., Tonkov E. L., “Nekotorye matematicheskie zadachi, svyazannye s odnoi modelyu khimicheskogo kataliza”, Izv. In-ta matem. i inform., 1997, no. 1(9), 3–62
[6] Gaitsgori V. G., Upravlenie sistemami s bystrymi i medlennymi dvizheniyami, Nauka, M., 1991, 224 pp.
[7] Zubov V. I., Teoriya kolebanii, Vyssh. shkola, M., 1979, 400 pp.
[8] Horn J., Lin R. C., “Periodic Processes: A Variational Approach”, Eng. Chem. Process Desing and Development, 6:1 (1967), 21–30 | DOI
[9] Belousov L. A., Tonkov E. L., “Ob optimalnom upravlenii periodicheskimi kolebaniyami nekotorykh protsessov khimicheskogo kataliza”, Nestatsionarnye protsessy v katalize, Tr. konf. (Novosibirsk, 1987), 212–225
[10] Dukelskii M. S., Tsirlin A. M., “Usloviya nestatsionarnosti ustanovivshegosya rezhima upravlyaemogo ob'ekta”, Avtomatika i telemekhanika, 1977, no. 8, 5–12
[11] Petrova V. V., Tonkov E. L., “Dopustimost periodicheskikh protsessov i teoremy suschestvovaniya periodicheskikh reshenii”, Izv. vuzov. Matematika, 1996, no. 11, 65–71
[12] Perov A. I., Tananika A. A., “Ob odnom geometricheskom rezultate v voprosakh periodicheskoi optimizatsii”, Differents. uravneniya, 26:4 (1990), 718–721 | MR | Zbl
[13] Perov A. I., Belousova E. P., Ob odnoi nelineinoi zadache periodicheskoi optimizatsii, Dep. v VINITI 09.08.95, No 2409-95, Voronezh. un-t, Voronezh, 1995, 23 pp.
[14] Tonkov E. L., “Optimalnye periodicheskie dvizheniya upravlyaemoi sistemy”, Matematicheskaya fizika, 1977, no. 22, 54–64
[15] Tonkov E. L., “Lineinaya zadacha optimalnogo upravleniya periodicheskimi resheniyami”, Differents. uravneniya, 12:6 (1976), 1007–1011 | MR | Zbl
[16] Tonkova V. S., “Voprosy effektivnogo rasshireniya zadach matematicheskogo programmirovaniya”, Metody vychislitelnogo eksperimenta v inzhenernoi praktike, 1, IMM, Izhevsk, 1991, 90–99 | MR
[17] Troitskii V. A., Optimalnye protsessy kolebanii mekhanicheskikh sistem, Mashinostroenie, L., 1976, 248 pp.
[18] Tsirlin A. M., Balakirev V. S., Dudnikov E. G., Variatsionnye metody optimizatsii upravlyaemykh ob'ektov, Energiya, M., 1976, 448 pp.
[19] Fedorenko R. P., Priblizhennoe reshenie zadach optimalnogo upravleniya, Nauka, M., 1978, 488 pp.
[20] Chernousko F. L., Akulenko L. D., Sokolov B. N., Upravlenie kolebaniyami, Nauka, M., 1978, 348 pp.
[21] Guardabassi G., Locatelli A., Rinaldi S., “The status of periodic optimization of dynamic systems”, J. Optimization Theory and Appl., 14:1 (1974), 1–20 | DOI | MR | Zbl
[22] Gilbert E. G., “Optimal Periodic Control: a General Theory of Necessary Conditions”, SIAM J. Contr. Optimisation, 15:5 (1977), 717–746 | DOI | MR | Zbl
[23] Bittanti S., Locatelli A., Guardabassi G., “Periodic control: A frequency domain approach”, IEEE Trans. Automat. Control, 18:1 (1973), 33–34 | DOI | MR
[24] Bittanti S., Locatelli A., Maffezoni C., “Second-variation mehhods in periodic optimisation”, J. Optim. Theory and Appl., 14:14 (1974), 31–49 | DOI | MR | Zbl
[25] Markus L., “Optimal control of limit cycles or what control theory can do to cure a heart attack or to cause one”, Lect. Notes Math., 312, 1973, 108–134 | DOI | MR | Zbl
[26] Chang K. S., “Necessary and sufficient conditions for optimality”, Periodic optimization, Springer-Verlag, New York, 1972, 183–217
[27] Ivanov A. G., Tonkov E. L., “Zadacha optimalnogo upravleniya periodicheskimi protsessami i ee rasshireniya”, Funkts. differents. uravneniya, Perm, 1992, 35–49
[28] Panasjuk A., Panasjuk V., “Die wichtigsten Leitsatze der magistralen asymptotischen Theorie der optimalen Steuerung”, 27 Intern. Wiss. Kolloq., H. 5 (Ilmenau, 1982), v. B1, B2, Ilmenau, s. a., 99–104
[29] Ivanov A. G., “O suschestvovanii pochti periodicheskogo resheniya lineinoi sistemy s kvadratichnym funktsionalom kachestva”, Differents. uravneniya, 37:2 (2001), 203–211
[30] Demidovich B. P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967, 472 pp.
[31] Levitan B. M., Pochti-periodicheskie funktsii, Gostekhizdat, M., 1953, 396 pp.
[32] Levitan B. M., Zhikov V. V., Pochti periodicheskie funktsii i differentsialnye uravneniya, Izd-vo Mosk. un-ta, M., 1978, 205 pp.
[33] Ivanov A. G., “Optimalnoe upravlenie pochti periodicheskimi dvizheniyami pri nalichii ogranichenii na srednie”, Dokl. RAN, 343:6 (1995), 51–53
[34] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1976, 392 pp.
[35] Blagodatskikh V. I., Filippov A. F., “Differentsialnye vklyucheniya i optimalnoe upravlenie”, Tr. MIAN SSSR, 169, 1985, 194–252 | MR | Zbl
[36] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 623 pp.
[37] Gamkrelidze R. V., Osnovy optimalnogo upravleniya, Izd-vo Tbil. un-ta, Tbilisi, 1975, 230 pp.
[38] Dmitruk A. V., “Printsip maksimuma dlya obschei zadachi optimalnogo upravleniya s fazovymi i regulyarnymi smeshannymi ogranicheniyami”, Optimalnost upravlyaemykh dinamicheskikh sistem, 14, VNIISI, M., 1990, 26–42 | Zbl
[39] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 518 pp.
[40] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 287 pp.
[41] Chentsov A. G., Prilozheniya teorii mery k zadacham upravleniya, Sredn.-Ural. kn. izd-vo, Sverdlovsk, 1985, 128 pp.
[42] Chentsov A. G., Konechno-additivnye mery i relaksatsii ekstremalnykh zadach, Nauka, Ekaterinburg, 1993, 232 pp.
[43] Ivanov A. G., Meroznachnye pochti periodicheskie funktsii, Preprint, Sverdlovsk, 1990, 53 pp.
[44] Ivanov A. G., Meroznachnye pochti periodicheskie funktsii, II, Dep. v VINITI 24.04.91, No 1721-B91, UdGU, Izhevsk, 1991, 62 pp.
[45] Ivanov A. G., “Ob optimalnom upravlenii pochti periodicheskimi dvizheniyami pri nalichii ogranichenii na srednie tipa ravenstv i neravenstv, I”, Differents. uravneniya, 33:2 (1997), 167–176
[46] Ivanov A. G., “Ob optimalnom upravlenii pochti periodicheskimi dvizheniyami pri nalichii ogranichenii na srednie tipa ravenstv i neravenstv, II”, Differents. uravneniya, 33:3 (1997), 316–323 | MR | Zbl
[47] Ivanov A. G., “Ob optimalnom upravlenii pochti periodicheskimi dvizheniyami pri nalichii ogranichenii na srednie tipa ravenstv i neravenstv, III”, Differents. uravneniya, 33:4 (1997), 478–485 | MR | Zbl
[48] Ivanov A. G., “O pochti-periodicheskoi lyapunovskoi zadache”, PMM, 55:5 (1991), 718–724 | MR | Zbl
[49] Ivanov A. G., “Ob optimalnom upravlenii pochti periodicheskimi dvizheniyami”, PMM, 56:5 (1992), 745–753
[50] Ivanov A. G., “Ob ekvivalentnosti differentsialnykh vklyuchenii upravlyaemykh pochti periodicheskikh sistem”, Differents. uravneniya, 33:7 (1997), 876–884 | MR | Zbl
[51] A. G. Ivanov, “O nepreryvnoi differentsiruemosti po parametru pochti periodicheskogo resheniya”, Differents. uravneniya, 37:5 (2001), 601–608
[52] Ivanov A. G., “O nepreryvnoi zavisimosti pochti periodicheskogo resheniya ot meroznachnogo upravleniya”, Differents. uravneniya, 28:11 (1992), 1907–1915 | MR | Zbl
[53] Ivanov A. G., “Ob odnom svoistve pochti periodicheskogo integrala, zavisyaschego ot parametra”, Izv. vuzov. Matematika, 2001, no. 6(469), 34–43
[54] Danilov L. I., “O meroznachnykh pochti periodicheskikh funktsiyakh”, Vestn. Udm. un-ta, 1992, no. 1, 51–58 | MR
[55] Danilov L. I., “Pochti periodicheskie secheniya mnogoznachnykh otobrazhenii”, Izv. In-ta matem. i inform., 1993, no. 1, 16–78
[56] Danilov L. I., “O ravnomernoi approksimatsii pochti periodicheskikh po Stepanovu funktsii”, Izv. vuzov. Matematika, 1998, no. 5, 10–18
[57] Fink A. M., Almost periodic differential equation, Lect. Notes Math., 377, 1974, 336 pp. | MR | Zbl
[58] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Nauka, M., 1979, 429 pp.
[59] Berezanskii Yu. M., Us G. F., Sheftel Z. G., Funktsionalnyi analiz: Kurs lektsii, Vischa shkola, Kiev, 1990, 600 pp.
[60] Danford N., Shvarts Dzh., Lineinye operatory. Obschaya teoriya, Inostr. lit., M., 1962
[61] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976, 544 pp.
[62] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., Vvedenie v teoriyu mnogoznachnykh otobrazhenii, Voronezh, 1986, 104 pp.
[63] Samoilenko A. M., Perestyuk N. A., Differentsialnye uravneniya s impulsnym vozdeistviem, Vischa shkola, Kiev, 1987, 288 pp.
[64] Khalanai A., Veksler D., Kachestvennaya teoriya impulsnykh sistem, Mir, M., 1971, 309 pp.
[65] Dolbilov A. M., Shneiberg I. Ya., “Pochti periodicheskie mnogoznachnye otobrazheniya i ikh secheniya”, Sib. matem. zhurn., 32:2 (1991), 172–175 | MR | Zbl
[66] Krasnoselskii M. A., Burd V. Sh., Kolesov Yu. S., Nelineinye pochti periodicheskie kolebaniya, Nauka, M., 1970, 352 pp.
[67] Ivanov A. G., Elementy apparata zadach upravleniya pochti periodicheskimi dvizheniyami, I, Dep. v VINITI 28.06.2001, No 1536-B91, UdGU, Izhevsk, 2001, 49 pp.
[68] Castaing C., Valadier M., Convex analysis and measure able multifunction, Lect. Notes Math., 459, Springer-Verlag, Berlin–Heidelberg–New York, 1977, 279 pp. | DOI | MR
[69] Danilov L. I., Ivanov A. G., “K teoreme o potochechnom maksimume v pochti periodicheskom sluchae”, Izv. vuzov. Matematika, 1994, no. 6, 50–59
[70] Krein M. G., Nudelman A. A., Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973, 522 pp.