Geodesic
A method for the asymptotic solution of singularly perturbed linear terminal control problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 366-378 
A. I. Kalinin. A method for the asymptotic solution of singularly perturbed linear terminal control problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 366-378. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a2/
@article{ZVMMF_1990_30_3_a2,
     author = {A. I. Kalinin},
     title = {A~method for the asymptotic solution of singularly perturbed linear terminal control problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {366--378},
     year = {1990},
     volume = {30},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a2/}
}
TY  - JOUR
AU  - A. I. Kalinin
TI  - A method for the asymptotic solution of singularly perturbed linear terminal control problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 366
EP  - 378
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a2/
LA  - ru
ID  - ZVMMF_1990_30_3_a2
ER  - 
%0 Journal Article
%A A. I. Kalinin
%T A method for the asymptotic solution of singularly perturbed linear terminal control problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 366-378
%V 30
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a2/
%G ru
%F ZVMMF_1990_30_3_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Terminal control of a singularly perturbed linear system, with constraints on the right endpoint of the trajectory is considered. The asymptotic behaviour of the solution is analysed and on that basis an algorithm is proposed for the asymptotic allocation of optimal control switching points. A computational procedure is outlined which utilizes the asymptotic approximations to obtain an exact solution for any given value of the small parameter.

[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1983 | MR

[2] Rakitskii Yu. V., Ustinov S. M., Chernorutskii N. G., Chislennye metody resheniya zhestkikh sistem, Nauka, M., 1979 | MR

[3] Vasileva A. B., Dmitriev M. G., “Singulyarnye vozmuscheniya v zadachakh optimalnogo upravleniya”, Itogi nauki i tekhn. Ser. Matem. analiz, 20, VINITI, M., 1982, 3–77 | MR

[4] Saksena V. R., O'Reilly J., Kokotovic P. V., “Singular perturbations and time-scale methods in control theory: Survey 1976–1983”, Automatica, 20:3 (1984), 273–293 | DOI | MR | Zbl

[5] Kalinin A. I., Romanyuk G. A., “Optimizatsiya lineinykh singulyarno vozmuschennykh sistem”, Konstruktivnaya teoriya ekstremalnykh zadach, Izd-vo Belorus. un-ta, Minsk, 1984, 100–113

[6] Gabasov R., Kirillova F. M., Kostyukova O. I., “Optimizatsiya sistem upravleniya s pomoschyu kratnykh opor”, Konstruktivnaya teoriya ekstremalnykh zadach, Izd-vo Belorus. un-ta, Minsk, 1984, 62–67

[7] Gabasov R., Kirillova F. M., Konstruktivnye metody optimizatsii, v. 2, Zadachi upravleniya, Izd-vo Belorus. un-ta, Minsk, 1984 | MR

[8] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR

[9] Vainberg M. M., Trenogin V. A., Teoriya vetvleniya reshenii nelineinykh integralnykh uravnenii, Nauka, M., 1969 | MR