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JOURNALS // Matematicheskii Sbornik // Archive
Mat. Sb., 2019 Volume 210, Number 1, Pages 3–26 (Mi sm9013)
This article is cited in 7 papers

Controllability and second-order necessary conditions for optimality

E. R. Avakovab, G. G. Magaril-Il'yaevbc

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 Kharkevich Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, Russia

Abstract: Sufficient conditions for the local controllability of a control system of ordinary differential equations are presented. These conditions are meaningful in the case where the linear approximation of the system is not completely controllable. Second-order necessary conditions for optimality for the problem of optimal control are obtained as a corollary.
Bibliography: 13 titles.

Keywords: controllability, optimal control, second-order conditions.

UDC: 517.977.52

MSC: 49J21, 49J15

Received: 22.09.2017 and 18.09.2018

DOI: 10.4213/sm9013


 English version: Sbornik: Mathematics, 2019, 210:1, 1–23

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© Steklov Math. Inst. of RAS, 2024