Geodesic
Geometric approach to the problem of optimal scalar control of two nonsynchronous oscillators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 40-51.

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

The problem of optimal scalar control of a system of two independent harmonic oscillators is considered. For the solution, methods of geometric control theory are used. The vertical subsystem of the Hamiltonian system is examined. Optimal solutions are found in control classes with various number of switchings. Analytical results are illustrated by simulation.
Keywords: geometric theory, optimal control, harmonic oscillator, Pontryagin's maximum principle, Lie algebra. 
@article{INTO_2022_215_a3,
     author = {L. M. Berlin and A. A. Galyaev and P. V. Lysenko},
     title = {Geometric approach to the problem of optimal scalar control of two nonsynchronous oscillators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {40--51},
     publisher = {mathdoc},
     volume = {215},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_215_a3/}
}
TY  - JOUR
AU  - L. M. Berlin
AU  - A. A. Galyaev
AU  - P. V. Lysenko
TI  - Geometric approach to the problem of optimal scalar control of two nonsynchronous oscillators
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 40
EP  - 51
VL  - 215
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_215_a3/
LA  - ru
ID  - INTO_2022_215_a3
ER  - 
%0 Journal Article
%A L. M. Berlin
%A A. A. Galyaev
%A P. V. Lysenko
%T Geometric approach to the problem of optimal scalar control of two nonsynchronous oscillators
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 40-51
%V 215
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_215_a3/
%G ru
%F INTO_2022_215_a3
L. M. Berlin; A. A. Galyaev; P. V. Lysenko. Geometric approach to the problem of optimal scalar control of two nonsynchronous oscillators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 40-51. http://geodesic.mathdoc.fr/item/INTO_2022_215_a3/

[1] Agrachev A. A., Sachkov Yu. L., Geometricheskaya teoriya upravleniya, Fizmatlit, M., 2005

[2] Boltyanskii V. G., Matematicheskie metody optimalnogo upravleniya, Nauka, M., 1969

[3] Galyaev A. A., “Skalyarnoe upravlenie gruppoi nesinkhronnykh ostsillyatorov”, Avtomat. telemekh., 9 (2016), 3–18 | MR | Zbl

[4] Galyaev A. A., Lysenko P. V., “O zadache optimalnogo skalyarnogo upravleniya dvumya nesinkhronnymi ostsillyatorami”, Tr. 59 Vseross. nauch. konf. MFTI, MFTI, Dolgoprudnyi, 2016, 1–13

[5] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961 | MR

[6] Sachkov Yu. L., Vvedenie v geometricheskuyu teoriyu upravleniya, LENAND, M., 2021

[7] Chernousko F. L., Akulenko L. D., Sokolov B. N., Upravlenie kolebaniyami, Nauka, M., 1980

[8] Benzaid Z., “Global null controllability of perturbed linear systems with constrained controls”, J. Math. Anal. Appl., 136 (1988), 201–216 | DOI | MR | Zbl

[9] Jakubczyk B., Introduction to Geometric Nonlinear Control. Controllability of Lie Bracket, Warsaw, 2001 | MR

[10] Sussmann H. J., Jurdjevic V., “Controllability of nonlinear systems”, J. Differ. Equations., 12 (1972), 95–116 | DOI | MR | Zbl