Bang-Bang Extremals in Sub-Finsler Problems on Engel Group

Abstract

We consider a one-parameter family of left-invariant rank 2 sub-Finsler problems on the Engel group with the set of control parameters given by a square centered at the origin and rotated by an arbitrary angle. We describe the phase portrait for bang-bang extremals. Further, we obtain an upper bound on the number of bang arcs on optimal bang-bang extremals.