E. R. Avakov, G. G. Magaril-Il'yaev, “Gamkrelidze Convexification and Bogolyubov's Theorem”, Mat. Zametki, 2020, Volume 107, Issue 4,Pages <nobr>483

This article is cited in 1 paper

Gamkrelidze Convexification and Bogolyubov's Theorem

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

^a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
^b Lomonosov Moscow State University
^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 interconnection between an optimal control problem and its convexification in the sense of Gamkrelidze and Bogolyubov is studied. Bogolyubov's classical result for the simplest problem of variational calculus is obtained as a corollary.

Keywords: optimal control problem, second conjugate function, convexification.

UDC: 517.977.52

Received: 02.08.2019
Revised: 19.09.2019

DOI: 10.4213/mzm12530