Geodesic
An approach problem for a control system with an unknown parameter
Sbornik. Mathematics, Tome 208 (2017) no. 9, pp. 1312-1352 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A control system with an unknown constant parameter is considered on a finite time interval. In the paper the solvability set is taken to contain only those initial positions of the system such that for each admissible value of the parameter a control taking the system to a prescribed target set exists. A numerical algorithm is designed that constructs an approximate solution, that is, a control on a prescribed interval of time which ensures that the motion of the control system occurs in a certain small neighbourhood of the target set. Bibliography: 26 titles.
Keywords: control, control system, differential inclusion, approach problem, target set, unknown constant parameter. 
@article{SM_2017_208_9_a3,
     author = {A. A. Ershov and V. N. Ushakov},
     title = {An approach problem for a~control system with an unknown parameter},
     journal = {Sbornik. Mathematics},
     pages = {1312--1352},
     year = {2017},
     volume = {208},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_9_a3/}
}
TY  - JOUR
AU  - A. A. Ershov
AU  - V. N. Ushakov
TI  - An approach problem for a control system with an unknown parameter
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 1312
EP  - 1352
VL  - 208
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_9_a3/
LA  - en
ID  - SM_2017_208_9_a3
ER  - 
%0 Journal Article
%A A. A. Ershov
%A V. N. Ushakov
%T An approach problem for a control system with an unknown parameter
%J Sbornik. Mathematics
%D 2017
%P 1312-1352
%V 208
%N 9
%U http://geodesic.mathdoc.fr/item/SM_2017_208_9_a3/
%G en
%F SM_2017_208_9_a3
A. A. Ershov; V. N. Ushakov. An approach problem for a control system with an unknown parameter. Sbornik. Mathematics, Tome 208 (2017) no. 9, pp. 1312-1352. http://geodesic.mathdoc.fr/item/SM_2017_208_9_a3/

[1] N. N. Krasovskii, Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970, 420 pp. | MR | Zbl

[2] N. Krassovski, A. Soubbotine, Jeux différentiels, Éditions Mir, Moscow, 1977, 446 pp. | MR | MR | Zbl | Zbl

[3] Yu. S. Osipov, “Alternativa v differentsialno-raznostnoi igre”, Dokl. AN SSSR, 197:5 (1971), 1022–1025 | MR | Zbl

[4] A. B. Kurzhanskii, Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977, 392 pp. | MR | Zbl

[5] A. B. Kurzhanskii, “Alternirovannyi integral Pontryagina v teorii sinteza upravlenii”, Algebra. Topologiya. Differentsialnye uravneniya i ikh prilozheniya, Sbornik statei. K 90-letiyu so dnya rozhdeniya akademika Lva Semenovicha Pontryagina, Tr. MIAN, 224, Nauka, M., 1999, 234–248 | MR | Zbl

[6] A. V. Kryazhimskii, Yu. S. Osipov, “Ob odnom algoritmicheskom kriterii razreshimosti igrovykh zadach dlya lineinykh upravlyaemykh sistem”, Tr. IMM UrO RAN, 6, no. 1, 2000, 131–140 | MR | Zbl

[7] A. I. Subbotin, N. N. Subbotina, “Alternativa dlya differentsialnoi igry sblizheniya-ukloneniya pri ogranicheniyakh na impulsy upravleniya igrokov”, PMM, 39:3 (1975), 397–406 | MR | Zbl

[8] A. I. Subbotin, A. G. Chentsov, Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 288 pp. | MR | Zbl

[9] A. M. Tarasev, V. N. Ushakov, A. P. Khripunov, “Ob odnom vychislitelnom algoritme resheniya igrovykh zadach upravleniya”, PMM, 51:2 (1987), 216–222 | MR | Zbl

[10] M. I. Gomoyunov, N. Yu. Lukoyanov, A. R. Plaksin, “Suschestvovanie tseny i sedlovoi tochki v pozitsionnykh differentsialnykh igrakh dlya sistem neitralnogo tipa”, Tr. IMM UrO RAN, 22, no. 2, 2016, 101–112 | DOI | MR

[11] L. V. Kamneva, V. S. Patsko, “Postroenie maksimalnogo stabilnogo mosta v igrakh s prostymi dvizheniyami na ploskosti”, Tr. IMM UrO RAN, 20, no. 4, 2014, 128–142 ; L. V. Kamneva, V. S. Patsko, “Construction of a maximal stable bridge in games with simple motions on the plane”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 125–139 | MR | Zbl | DOI

[12] Yu. S. Osipov, A. V. Kryazhimskii, V. I. Maksimov, Metody dinamicheskogo vosstanovleniya vkhodov upravlyaemykh sistem, Izd-vo UrO RAN, Ekaterinburg, 2011, 291 pp.

[13] V. I. Maksimov, Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, Izd-vo UrO RAN, Ekaterinburg, 2000, 305 pp.

[14] A. M. Denisov, Vvedenie v teoriyu obratnykh zadach, Izd-vo Mosk. un-ta, M., 1994, 208 pp.

[15] L. S. Pontryagin, “Matematicheskaya teoriya optimalnykh protsessov i differentsialnye igry”, Topologiya, obyknovennye differentsialnye uravneniya, dinamicheskie sistemy, Sbornik obzornykh statei. 2. K 50-letiyu instituta, Tr. MIAN SSSR, 169, Izd-vo AN SSSR, M., 1985, 119–158 | MR | Zbl

[16] B. N. Pshenichnyi, “Struktura differentsialnykh igr”, Dokl. AN SSSR, 184:2 (1969), 285–287 | MR | Zbl

[17] F. L. Chernousko, A. A. Melikyan, Igrovye zadachi upravleniya i poiska, Nauka, M., 1978, 270 pp. | MR | Zbl

[18] M. S. Nikolskii, “Ob alternirovannom integrale L. S. Pontryagina”, Matem. sb., 116(158):1(9) (1981), 136–144 ; M. S. Nikol'skii, “On the alternating integral of Pontryagin”, Math. USSR-Sb., 44:1 (1983), 125–132 | MR | Zbl | DOI

[19] E. S. Polovinkin, “Stabilnost terminalnogo mnozhestva i optimalnost vremeni presledovaniya v differentsialnykh igrakh”, Differents. uravneniya, 20:3 (1984), 433–446 | MR | Zbl

[20] F. L. Chernousko, I. M. Ananevskii, S. A. Reshmin, Metody upravleniya nelineinymi mekhanicheskimi sistemami, Fizmatlit, M., 2006, 328 pp.

[21] A. M. Tarasev, A. A. Usova, “Chuvstvitelnost fazovykh portretov gamiltonovykh sistem dlya modeli rosta resursozavisimoi ekonomiki”, Dinamika sistem i protsessy upravleniya, Trudy Mezhdunarodnoi konferentsii, posvyaschennoi 90-letiyu so dnya rozhdeniya akademika N. N. Krasovskogo (Ekaterinburg, 2014 g.), IMM UrO RAN, Ekaterinburg, 2015, 317–324

[22] V. N. Afanasev, V. B. Kolmanovskii, V. R. Nosov, Matematicheskaya teoriya konstruirovaniya sistem upravleniya, 2-e izd., ispr. i dop., Vyssh. shk., M., 2003, 614 pp. ; V. N. Afanas'ev, V. B. Kolmanovskii, V. R. Nosov, Mathematical theory of control systems design, Math. Appl., 341, Kluwer Acad. Publ., Dordrecht, 1996, xxiv+668 pp. | MR | Zbl | DOI | MR | Zbl

[23] A. S. Bratus, A. S. Novozhilov, A. P. Platonov, Dinamicheskie sistemy i modeli biologii, Fizmatlit, M., 2010, 400 pp.

[24] A. P. Khripunov, Postroenie oblastei dostizhimostei i stabilnykh mostov v nelineinykh zadachakh upravleniya, Diss. ... kand. fiz.-matem. nauk, IMM UrO RAN, Ekaterinburg, 1992, 140 pp.

[25] A. V. Ushakov, “Ob odnom variante priblizhennogo postroeniya razreshayuschikh upravlenii v zadache o sblizhenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 94–107 | Zbl

[26] V. N. Ushakov, V. I. Ukhobotov, A. V. Ushakov, G. V. Parshikov, “K resheniyu zadach o sblizhenii upravlyaemykh sistem”, Optimalnoe upravlenie, Sbornik statei. K 105-letiyu so dnya rozhdeniya akademika Lva Semenovicha Pontryagina, Tr. MIAN, 291, MAIK, M., 2015, 276–291 | DOI | Zbl