Seminars
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Search
RSS
Forthcoming seminars






Cohomological geometry of differential equations
October 9, 2019 19:20, Moscow, Independent University of Moscow, room 308
 


Convex trigonometry in problems with two-dimensional control

L. V. Lokutsievskiy

Number of views:
This page:60

Abstract: The talk will discuss a new convenient method of describing flat convex compact sets and their polar sets, which generalizes classical trigonometric functions $cos$ and $sin$. The properties of this pair of functions in the case of unit circle are inherited by two pairs of functions $cos_\Omega$, $sin_\Omega$, and $\cos_{\Omega^\circ}$, $\sin_{\Omega^\circ}$ for the set $\Omega$ and its polar set $\Omega^\circ$. This method turned out to be very useful in optimal control problems with two-dimensional control. In 2018, using this method the explicit geodesic flows in a series of sub-Finsler problems for the cases of Heisenberg, Grushin, Martinet, Engel, and Cartan were found. In 2019, jointly with Yu.L. Sachkov and A.A. Ardentov, more than 10 classical problems were explicitly solved. For instance, I will talk on Finsler geodesic flows on the Lobachevsky plane.

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021