Geodesic
External estimates and construction of attainability sets for controlled systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 4, pp. 483-490 
D. L. Kondratiev; A. V. Lotov. External estimates and construction of attainability sets for controlled systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 4, pp. 483-490. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A numerical method for constructing external estimates of attainability sets for non-linear controlled systems of ordinary differential equations is proposed. In some cases the method enables the attainability set itself to be approximated.

[1] Krasovskii N. N., Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970 | MR

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

[3] Chernousko F. L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem. Metod ellipsoidov, Nauka, M., 1988 | MR

[4] Lotov A. V., “Chislennyi metod postroeniya mnozhestv dostizhimosti dlya lineinoi upravlyaemoi sistemy”, Zh. vychisl. matem. i matem. fiz., 12:3 (1972), 785–788 | MR | Zbl

[5] Lotov A. V., “Chislennyi metod postroeniya mnozhestv dostizhimosti dlya lineinykh upravlyaemykh sistem s fazovymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 15:1 (1975), 67–78 | MR | Zbl

[6] Lotov A. V., “O skhodimosti metodov chislennoi approksimatsii mnozhestv dostizhimosti dlya lineinykh differentsialnykh sistem s vypuklymi fazovymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 19:1 (1979), 44–55 | MR | Zbl

[7] Konstantinov G. N., Normirovanie vozdeistvii na dinamicheskie sistemy, Izd-vo Irkutskogo un-ta, Irkutsk, 1983 | Zbl

[8] Blagodatskikh V. I., Filippov A. F., “Differentsialnye vklyucheniya i optimalnoe upravlenie”, Topologiya, obyknovennye differents. ur-niya, dinamich. sistemy, Tr. MIAN SSSR, 169, Nauka, M., 1985, 194–252 | MR

[9] Bushenkov V. A., Lotov A. V., “Paket prikladnykh programm “Potentsial””, Pakety prikl. programm. Sistemnoe napolnenie. (Algoritmy i algoritmich. yazyki), Nauka, M., 1984, 120–132

[10] Sidorenko G. V., Vneshnie otsenki mnozhestv dostizhimosti upravlyaemykh sistem s prilozheniyami k zadache normirovaniya vozdeistvii, Dis. ...kand. fiz.-matem. nauk, VTs SO AN SSSR, Irkutsk, 1987

[11] Bushenkov V. A., “Iteratsionnyi metod postroeniya ortogonalnykh proektsii vypuklykh mnogogrannykh mnozhestv”, Zh. vychisl. matem. i matem. fiz., 25:9 (1985), 1285–1292 | MR | Zbl

[12] Chernykh O. L., “Postroenie vypukloi obolochki konechnogo mnozhestva tochek pri priblizhennykh vychisleniyakh”, Zh. vychisl. matem. i matem. fiz., 28:9 (1988), 1386–1396 | MR | Zbl