Abstract: We consider the problem of controlling the nonlinear 5-dimensional systems that are induced by horizontal vector fields X and Y which together with their commutators generate some Cartan algebra depending linearly on two piecewise constant controls. We also study the properties of solutions to the systems on interpreting a solution as a horizontal k-broken line Lk on the canonical Cartan group K, where the segments of Lk are segments of integral curves of the vector fields of the form aX +bY with a,b = const. As regards K, we prove that 4 is the minimal number NK such that every two points u,v ∈ K canbe joinedbysomeLk with k ≤ NK. Thus, we obtain the best version of the Rashevskii–Chow theorem on the Cartan group. We also show that the minimal number of segments of a closed horizontal broken line on K equals 6.

Cite: Greshnov A.V. , Zhukov R.I.
Control Theory Problems and the Rashevskii–Chow Theorem on a Cartan Group
Siberian Mathematical Journal. 2024. V.65. N5. P.1096-1111. DOI: 10.1134/s0037446624050100 WOS Scopus РИНЦ OpenAlex

Original: Грешнов А.В. , Жуков Р.И.
Задачи теории управления и теорема Рашевского — Чоу на группе Картана
Сибирский математический журнал. 2024. Т.65. №5. С.901-920. DOI: 10.33048/smzh.2024.65.510 РИНЦ

Dates:

Submitted:	Jun 10, 2024
Accepted:	Aug 20, 2024
Published print:	Sep 25, 2024
Published online:	Sep 25, 2024

Identifiers:

Web of science:	WOS:001320442300013
Scopus:	2-s2.0-85204785285
Elibrary:	69920886
OpenAlex:	W4402843155

Citing: Пока нет цитирований

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