Geodesic
Time optimality and the power moment problem
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 185-206 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A solution of the problem of exact determination of a time optimal control for the equation $x^{(n)}=u$, $|u|\le1$, in the open loop form as well as in the closed loop form is presented in this paper. A system of special polynomials, called canonical variables, is introduced. The solution is obtained in terms of Hankel determinants and a sequence of Markov determinants in the canonical variables. A connection between the solution obtained and the power moment problem is investigated. Bibliography: 6 titles. 
@article{SM_1989_62_1_a12,
     author = {V. I. Korobov and G. M. Sklyar},
     title = {Time optimality and the power moment problem},
     journal = {Sbornik. Mathematics},
     pages = {185--206},
     year = {1989},
     volume = {62},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_62_1_a12/}
}
TY  - JOUR
AU  - V. I. Korobov
AU  - G. M. Sklyar
TI  - Time optimality and the power moment problem
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 185
EP  - 206
VL  - 62
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1989_62_1_a12/
LA  - en
ID  - SM_1989_62_1_a12
ER  - 
%0 Journal Article
%A V. I. Korobov
%A G. M. Sklyar
%T Time optimality and the power moment problem
%J Sbornik. Mathematics
%D 1989
%P 185-206
%V 62
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1989_62_1_a12/
%G en
%F SM_1989_62_1_a12
V. I. Korobov; G. M. Sklyar. Time optimality and the power moment problem. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 185-206. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a12/

[1] Pontryagin L. S, Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961

[2] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968 | MR

[3] Markov A. A., Izbrannye trudy, Gostekhizdat, M., 1948

[4] Korobov V. I., “Obschii podkhod k resheniyu zadachi sinteza ogranichennykh upravlenii v zadache upravlyaemosti”, Matem. sb., 109(151) (1979), 582–606 | MR | Zbl

[5] Chebyshev P. L., Polnoe sobranie sochinenii, T. III, Izd-vo AN SSSR, M., 1948 | MR

[6] Stiltes T., Issledovanie nepreryvnykh drobei, Kharkov, 1936