Geodesic
Operator methods of the search for extremal controls in linear-quadratic optimal control problems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 19-27.

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

In the class of bilinear control systems with a state-quadratic optimality criterion, new methods of the search for extremal controls are considered. The approach proposed is based on special versions of the maximum principle that have the form of operator fixed-point problems in the space of controls, which are equivalent to the well-known condition of the maximum principle in the class of linear-quadratic optimal control problems. The operator forms of optimality conditions allows one to construct new iterative algorithms for finding controls satisfy the maximum principle. The comparative efficiency of the operator methods is illustrated by numerical simulations of a well-known model optimization problem for a quantum system characterized by degenerate extremal controls.
Keywords: linear-quadratic optimal control problem, extremal control, fixed point, iterative algorithm. 
@article{INTO_2023_224_a2,
     author = {A. S. Buldaev and I. D. Kazmin},
     title = {Operator methods of the search for extremal controls in linear-quadratic optimal control problems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {19--27},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a2/}
}
TY  - JOUR
AU  - A. S. Buldaev
AU  - I. D. Kazmin
TI  - Operator methods of the search for extremal controls in linear-quadratic optimal control problems
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 19
EP  - 27
VL  - 224
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_224_a2/
LA  - ru
ID  - INTO_2023_224_a2
ER  - 
%0 Journal Article
%A A. S. Buldaev
%A I. D. Kazmin
%T Operator methods of the search for extremal controls in linear-quadratic optimal control problems
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 19-27
%V 224
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_224_a2/
%G ru
%F INTO_2023_224_a2
A. S. Buldaev; I. D. Kazmin. Operator methods of the search for extremal controls in linear-quadratic optimal control problems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 19-27. http://geodesic.mathdoc.fr/item/INTO_2023_224_a2/

[8] Bartenev O. V., Fortran dlya professionalov. Matematicheskaya biblioteka IMSL, Dialog-MIFI, M., 2001

[9] Baturina O. V., Morzhin O. V., “Optimalnoe upravlenie sistemoi spinov na osnove metoda globalnogo uluchsheniya”, Avtomat. telemekh., 2011, no. 6, 79–86 | MR | Zbl

[10] Buldaev A. S., “Operatornye uravneniya i algoritmy printsipa maksimuma v zadachakh optimalnogo upravleniya”, Vestn. Buryat. gos. un-ta. Mat. Inform., 2020, no. 1, 35–53

[11] Vasilev O. V., Lektsii po metodam optimizatsii, Irkutsk, 1994 | MR

[12] Kiselev Yu. N., “Lineino-kvadratichnaya zadacha optimalnogo upravleniya: analiz s pomoschyu printsipa maksimuma”, Problemy dinamicheskogo upravleniya: Sb. nauch. tr. Vyp. 1, Izd-vo MGU, M., 2005, 166–182

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

[14] Khlebnikov M. V., Scherbakov P. S., Chestnov V. N., “Zadacha lineino-kvadratichnogo upravleniya: I. Novoe reshenie”, Avtomat. telemekh., 2015, no. 12, 65–79 | Zbl

[15] Trentelman H., “Linear quadratic optimal control”, Encyclopedia of Systems and Control, eds. Baillieul J., Samad T., Springer, London, 2013, 1–8 | MR