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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 321, Pages 7–30
DOI: https://doi.org/10.4213/tm4312 (Mi tm4312) 		 
Controllability and Second-Order Necessary Conditions for Local Infimum Trajectories in Optimal Control

E. R. Avakova, G. G. Magaril-Il'yaevbcd

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997 Russia
b Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia
c Southern Mathematical Institute, Vladikavkaz Scientific Center of Russian Academy of Sciences, ul. Vatutina 53, Vladikavkaz, 362027 Russia
d Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm4312
Abstract: We introduce the concept of local controllability of a dynamical system and present sufficient conditions for such controllability. As an immediate consequence, we prove necessary second-order conditions for a local infimum trajectory in an optimal control problem. These conditions strengthen the well-known second-order optimality conditions and extend them to more general classes of problems.
Received: February 1, 2022
Revised: September 6, 2022
Accepted: December 7, 2022
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 321, Pages 1–23
DOI: https://doi.org/10.1134/S0081543823020013
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
Language: Russian
Citation: E. R. Avakov, G. G. Magaril-Il'yaev, “Controllability and Second-Order Necessary Conditions for Local Infimum Trajectories in Optimal Control”, Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, Steklov Math. Inst., Moscow, 2023, 7–30; Proc. Steklov Inst. Math., 321 (2023), 1–23
Citation in format AMSBIB
\Bibitem{AvaMag23}
\by E.~R.~Avakov, G.~G.~Magaril-Il'yaev
\paper Controllability and Second-Order Necessary Conditions for Local Infimum Trajectories in Optimal Control
\inbook Optimal Control and Dynamical Systems
\bookinfo Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 321
\pages 7--30
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4312}
\crossref{https://doi.org/10.4213/tm4312}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 321
\pages 1--23
\crossref{https://doi.org/10.1134/S0081543823020013}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85170833090}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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