E. R. Avakov, G. G. Magaril-Il'yaev, “Implicit Function. Controllability and Perturbation of Optimal Control Problems”, Mat. Zametki, 2021, Volume 109, Issue 4,Pages <nobr>483–499</nobr>

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Mat. Zametki, 2021 Volume 109, Issue 4, Pages 483–499 (Mi mzm12824)

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Implicit Function. Controllability and Perturbation of Optimal Control Problems

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: We prove a special implicit function theorem which is used to obtain meaningful results about the controllability of dynamical systems and perturbations of optimal control problems.

Keywords: controllability, optimal control problem, perturbation, convexification, local infimum.

UDC: 517.97

Received: 30.06.2020
Revised: 30.11.2020

DOI: 10.4213/mzm12824

English version: Mathematical Notes, 2021, 109:4, 503–516

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© Steklov Math. Inst. of RAS, 2024