Geodesic
Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 5-13

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

We consider the problem of optimal control for a linear system with constant coefficients with convex integral performance index contains small parameter in integral part in the class of piecewise continuous controls with a smooth control constraints. The article is based on asymptotic of the initial vector of the adjoint state, which determines the type of optimal control. In the time-optimal control problem limit problem has a solution with discontinuous control but the perturbed problem has continuous control. It is proved that in this case the solution is decomposed in an series with a complex structure. But optimal control is decomposed in a power series of expansion in small parameter in the cheap control problem.
Keywords: optimal control, cheap controls, asymptotic expansion, small parameter. . 
@article{SJIM_2022_25_3_a0,
     author = {A. R. Danilin and A. A. Shaburov},
     title = {Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {5--13},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a0/}
}
TY  - JOUR
AU  - A. R. Danilin
AU  - A. A. Shaburov
TI  - Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2022
SP  - 5
EP  - 13
VL  - 25
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a0/
LA  - ru
ID  - SJIM_2022_25_3_a0
ER  - 
%0 Journal Article
%A A. R. Danilin
%A A. A. Shaburov
%T Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2022
%P 5-13
%V 25
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a0/
%G ru
%F SJIM_2022_25_3_a0
A. R. Danilin; A. A. Shaburov. Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 5-13. http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a0/