Local controllability and the boundary of the attainable set of a control system

E. R. Avakov^a, G. G. Magaril-Il'yaev<sup>bcd

a</sup> V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
^b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
^d Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia

Abstract: Given a control system of ordinary differential equations, the attainable set of trajectories admissible for it with respect to certain maps is defined. The aim of the work is to state necessary and sufficient conditions describing boundary points of this set. Interesting examples are considered, which illustrate the results obtained.
Bibliography: 11 titles.

Keywords: control system, controllability, boundary of the attainable set.

MSC: Primary 93B03, 93B05, 93C15; Secondary 49K15

Received: 17.09.2024 and 13.11.2024

DOI: 10.4213/sm10197

 English version: Sbornik: Mathematics, 2025, 216:3, 273–291

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