Sub-Finsler Problem on the Cartan Group

A. A. Ardentov^a^,* and Yu. L. Sachkov^a
Translated by I. Ruzanova

^aAilamazyan Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl oblast, 152020 Russia

Correspondence to: *e-mail: aaa@pereslavl.ru

Received 2 July, 2018

Abstract—A left-invariant ${{l}_{\infty }}$-sub-Finsler problem on Cartan group is treated as a time-optimal control problem. Abnormal and singular normal trajectories are described, and their optimality is proved. A bang-bang phase flow is constructed, and estimates for the number of switchings on bang-bang and mixed trajectories are obtained.

DOI: 10.1134/S1064562419010071