Geodesic
Approximation of control for singularly perturbed system with delay with geometric constraints
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 142-151 
I. V. Grebennikova; A. G. Kremlev. Approximation of control for singularly perturbed system with delay with geometric constraints. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 142-151. http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a2/
@article{ISU_2015_15_2_a2,
     author = {I. V. Grebennikova and A. G. Kremlev},
     title = {Approximation of control for singularly perturbed system with delay with geometric constraints},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {142--151},
     year = {2015},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a2/}
}
TY  - JOUR
AU  - I. V. Grebennikova
AU  - A. G. Kremlev
TI  - Approximation of control for singularly perturbed system with delay with geometric constraints
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2015
SP  - 142
EP  - 151
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a2/
LA  - ru
ID  - ISU_2015_15_2_a2
ER  - 
%0 Journal Article
%A I. V. Grebennikova
%A A. G. Kremlev
%T Approximation of control for singularly perturbed system with delay with geometric constraints
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2015
%P 142-151
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a2/
%G ru
%F ISU_2015_15_2_a2

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

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and geometric constraints on the control resources according to the minimax criterion is considered. A limiting problem is formulated for which a specially selected quality functional is chosen. We propose the procedure for initial approximation construction of a control response in the control minimax problem.

[1] Krasovskii N. N., The Theory of Motion Control, Nauka, M., 1968, 475 pp. (in Russian) | MR

[2] Kurzhanskij A. B., Control and Surveillance in the Face of Uncertainty, Nauka, M., 1977, 392 pp. (in Russian) | MR

[3] Kremlev A. G., “Asymptotic properties of a set of trajectories of a singularly perturbed system in the optimal control problem”, Autom. Remote Control, 54:9 (1993), 1353–1367 | MR | Zbl

[4] Grebennikova I. V., “Solution approximation in a minimax control problem for a singularly perturbed system with delay”, Russian Math., 55:10 (2011), 23–33 | DOI | MR | Zbl

[5] Grebennikova I. V., “The problem of optimal control for singularly perturbed system with delay with integral quadratic constraints”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 12:4 (2012), 3–11 (in Russian)

[6] Kremlev A. G., Grebennikova I. V., “About asymptotic of a set of trajectories of a singularly perturbed system with delay”, News of Scientific Thought, Proceedings of the international conference, v. 4, Nauka i obrazovanie, Dneproperovsk, 2006, 65–69 (in Russian)

[7] Rokafellar R., Convex Analysis, Mir, M., 1973, 492 pp. (in Russian)

[8] Krasovskii N. N., Some Problems in the Theory of Stability of Motion, Fizmatgiz, M., 1959, 468 pp. (in Russian) | MR

[9] Kirillova F. M., “Relative controllability of linear dynamic systems with delay”, Doklady AN SSSR, 174:6 (1967), 1260–1263 (in Russian) | MR | Zbl

[10] Bellman R., Kuk K., Differential-Difference Equations, Mir, M., 1967, 547 pp. (in Russian) | MR

[11] Natanson I. P., Theory of Functions of a Real Variable, Nauka, M., 1974, 468 pp. (in Russian) | MR