Implicit Function. Controllability and Perturbation of Optimal Control Problems
Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 483-499.

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

We prove a special implicit function theorem which is used to obtain meaningful results about the controllability of dynamical systems and perturbations of optimal control problems.
Keywords: controllability, optimal control problem
Mots-clés : perturbation, convexification, local infimum.
@article{MZM_2021_109_4_a0,
     author = {E. R. Avakov and G. G. Magaril-Il'yaev},
     title = {Implicit {Function.} {Controllability} and {Perturbation} of {Optimal} {Control} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--499},
     publisher = {mathdoc},
     volume = {109},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a0/}
}
TY  - JOUR
AU  - E. R. Avakov
AU  - G. G. Magaril-Il'yaev
TI  - Implicit Function. Controllability and Perturbation of Optimal Control Problems
JO  - Matematičeskie zametki
PY  - 2021
SP  - 483
EP  - 499
VL  - 109
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a0/
LA  - ru
ID  - MZM_2021_109_4_a0
ER  - 
%0 Journal Article
%A E. R. Avakov
%A G. G. Magaril-Il'yaev
%T Implicit Function. Controllability and Perturbation of Optimal Control Problems
%J Matematičeskie zametki
%D 2021
%P 483-499
%V 109
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a0/
%G ru
%F MZM_2021_109_4_a0
E. R. Avakov; G. G. Magaril-Il'yaev. Implicit Function. Controllability and Perturbation of Optimal Control Problems. Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 483-499. http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a0/

[1] R. V. Gamkrelidze, Osnovy optimalnogo upravleniya, URSS, M., 2019 | MR

[2] E. R. Avakov, G. G. Magaril-Ilyaev, “Teorema o neyavnoi funktsii dlya vklyuchenii, zadavaemykh blizkimi otobrazheniyami”, Matem. zametki, 103:4 (2018), 483–489 | DOI | Zbl

[3] E. R. Avakov, G. G. Magaril-Ilyaev, “Lokalnyi infimum i semeistvo printsipov maksimuma v optimalnom upravlenii”, Matem. sb., 211:6 (2020), 3–39 | DOI | Zbl

[4] V. A. Zorich, Matematicheskii analiz, Ch. 2, Nauka, M, 1984 | MR | Zbl

[5] E. B. Li, L. Markus, Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972 | MR

[6] E. R. Avakov, G. G. Magaril-Ilyaev, “Upravlyaemost i neobkhodimye usloviya optimalnosti vtorogo poryadka”, Matem. sb., 210:1 (2019), 3–26 | DOI | Zbl

[7] A. F. Filippov, “O nekotorykh voprosakh teorii optimalnogo regulirovaniya”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1959, no. 2, 25–32 | MR | Zbl

[8] E. R. Avakov, G. G. Magaril-Ilyaev, “Ovypuklenie po Gamkrelidze i teorema Bogolyubova”, Matem. zametki, 107:4 (2020), 483–497 | DOI | Zbl