This article is cited in 7 papers

Relaxation and controllability in optimal control problems

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

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

Abstract: The paper is concerned with the relationships between necessary minimum conditions in an optimal control problem, minimum conditions in the corresponding relaxed problem and sufficient conditions for local controllability of the system. The results obtained are applied to a fairly general optimal control problem.
Bibliography: 7 titles.

Keywords: optimal control, Pontryagin maximum principle, controllability, regularity, relaxation, mix of controls.

UDC: 517.977.52

MSC: 49J27, 49J15

Received: 21.04.2016 and 03.02.2017

DOI: 10.4213/sm8721

 English version: Sbornik: Mathematics, 2017, 208:5, 585–619

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