Geodesic
Optimal control of linear systems with interval constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 758-775 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For linear systems with interval constraints, a method for computing a time-optimal control is proposed. The method is based on transforming a quasi-optimal control. The properties and features of the quasi-optimal control are examined. A technique is described for dividing the domain of initial conditions into reachable sets over different times and for approximating each set by a family of hyperplanes. An iterative method for computing an optimal control with interval constraints is developed. The convergence of the method is proved, and a sufficient condition for the convergence of the computational process is obtained. The radius of local quadratic convergence is found. Numerical results are presented. 
@article{ZVMMF_2015_55_5_a2,
     author = {V. M. Aleksandrov},
     title = {Optimal control of linear systems with interval constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {758--775},
     year = {2015},
     volume = {55},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a2/}
}
TY  - JOUR
AU  - V. M. Aleksandrov
TI  - Optimal control of linear systems with interval constraints
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 758
EP  - 775
VL  - 55
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a2/
LA  - ru
ID  - ZVMMF_2015_55_5_a2
ER  - 
%0 Journal Article
%A V. M. Aleksandrov
%T Optimal control of linear systems with interval constraints
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 758-775
%V 55
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a2/
%G ru
%F ZVMMF_2015_55_5_a2
V. M. Aleksandrov. Optimal control of linear systems with interval constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 758-775. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a2/

[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1976

[2] Agrachev A. A., Gamkrelidze R. V., “Geometriya printsipa maksimuma”, Trudy MIAN, 273, 2011, 5–27 | MR | Zbl

[3] Gabasov R., Kirillova F. M., “Optimalnoe upravlenie i nablyudenie v realnom vremeni”, Izv. RAN. Teoriya i sistemy upravleniya, 2006, no. 3, 90–111

[4] Milyutin A. A., Dmitruk A. V., Osmolovskii N. P., Printsip maksimuma v optimalnom upravlenii, Izd-vo MGU, M., 2004

[5] Arguchintsev A. V., Dykhta V. A., Srochko V. A., “Optimalnoe upravlenie: nelokalnye usloviya, vychislitelnye metody i variatsionnyi printsip maksimuma”, Izv. vuzov. Matem., 2009, no. 1, 3–43

[6] Milyutin A. A., Printsip maksimuma v obschei zadache optimalnogo upravleniya, Fizmatlit, M., 2001

[7] Kalmykov S. A., Shokin Yu. I., Yuldashev Z. Kh., Metody intervalnogo analiza, Nauka, Novosibirsk, 1986 | MR

[8] Polyak B. T., Nazin S. A., “Otsenivanie parametrov v lineinykh mnogomernykh sistemakh s intervalnoi neopredelennostyu”, Probl. upravleniya i informatiki, 2006, no. 1–2, 103–115

[9] Aschepkov L. T., “Lineinye intervalnye uravneniya s simmetrichnymi mnozhestvami reshenii”, Zh. vychisl. matem. i matem. fiz., 48:4 (2008), 562–569 | MR | Zbl

[10] Sharyi S. P., “Razreshimost intervalnykh lineinykh uravnenii i analiz dannykh s neopredelennostyami”, Avtomat. i telemekhan., 2012, no. 2, 111–125

[11] Gusev Yu. M., Efanov V. N., Krymskii V. G., Rutkovskii V. Yu., “Analiz i sintez lineinykh intervalnykh dinamicheskikh sistem (sostoyanie problemy). I; II”, Izv. RAN. Tekhn. kibernetika, 1991, no. 1, 3–23; No 2, 3–30

[12] Aleksandrov V. M., “Reshenie zadach optimalnogo upravleniya na osnove metoda kvazioptimalnogo upravleniya”, Modeli i metody optimizatsii, Tr. In-ta matem. SO AN SSSR, 10, Nauka, Novosibirsk, 1988, 18–54 | MR | Zbl

[13] Aleksandrov V. M., “Priblizhennoe reshenie zadach optimalnogo upravleniya”, Probl. kibernetiki, 41, Nauka, M., 1984, 143–206 | Zbl

[14] Aleksandrov V. M., “Vychislenie optimalnogo upravleniya v realnom vremeni”, Zh. vychisl. matem. i matem. fiz., 52:10 (2012), 1778–1800 | Zbl

[15] Aleksandrov V. M., “Zadanie nachalnogo priblizheniya i metod vychisleniya optimalnogo upravleniya”, Sibirskie elektronnye matem. izvestiya, 11 (2014), 87–118 http://semr.math.nsc.ru/v11/p87-118.pdf | Zbl

[16] Aleksandrov V. M., “Chislennyi metod resheniya zadachi lineinogo bystrodeistviya”, Zh. vychisl. matem. i matem. fiz., 38:6 (1998), 918–931 | MR | Zbl

[17] Srochko V. A., Iteratsionnye metody resheniya zadach optimalnogo upravleniya, Fizmatlit, M., 2000