Alexey Davydov
Current position:
Head of the Chair of the Dynamical System Theory, Lomonosov Moscow State University, Moscow, Russia;
Head of Chair of the Mathematics, National University of Science and Technology MISiS (part time), Moscow, Russia.
Main research areas:
singularity theory, structural stability of dynamical systems, mathematical control theory, optimization and parametric optimization
Previous positions:
1982-1990: assistant professor (1982-1984) and associated professor (1984-1990), Vladimir State University, Russia;
1990-1993: research fellow (doctorant), Steklov Mathematical Institute RAS;
1994-2006: Full Professor, Vladimir State University, Russia;
2006-2014: Head of the Chair of the Functional Analysis and its Applications, Vladimir State University, Russia (2014-2016 – part time);
2016-2020: Leading Researcher, National University of Science and Technology MISiS, Moscow, Russia;
2016-2020: Head of Chair, National University of Science and Technology MISiS, Moscow, Russia;
2014-2016; 2016-2020, part time; 2021 – now: Head of the Chair of the Dynamical System Theory, Lomonosov Moscow State University, Moscow, Russia.
Education:
Master Thesis in Mathematics (1979) and PhD in Mathematics and Physics (1982), Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Russia;
Doctor of Science in Mathematics and Physics (1993), Steklov Mathematical Institute RAS.
Editorial board member/associate editor:
«Journal of Dynamical and Control Systems» (since 1995) and of «Izvestia:Mathematics» (since 2010) .
Awards:
Moscow Mathematical Society awards a young mathematician for his/her outstanding work in the field (1986);
MAIK/INTERPERIODICA award (2002).
Publications:
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Davydov A. A., Shutkina T. S.
Abstract
We prove the existence of solution in the problem of time averaged optimization of cyclic processes with both profit and effort discounts and find the respective necessary optimality condition. It is shown that optimal strategy could be selected piecewise continuous if a differentiable profit density has a finite number of critical points. In such a case the optimal motion uses only maximum and minimum velocities as in Arnold’s case without any discount.
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