Open AccessSub-Finsler problem on Cartan group
Author(s) -
A. A. Ardentov,
Yu. L. Sachkov
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524842138-141
Subject(s) - mathematics , invariant (physics) , infinity , group (periodic table) , pure mathematics , upper and lower bounds , mathematical analysis , mathematical physics , physics , quantum mechanics
Left invariant l-infinity sub-Finsler problem on Cartan group is considered as time-optimal control problem. We describe abnormal and singular normal trajectories, then prove that all such trajectories are optimal. We construct the bang-bang flow and obtain upper bounds on the number of switchings on bang-bang and mixed minimizers.