The Markov-Dubins problem with angular acceleration control

We study a modified version of the well known Markov-Dubins problem, in which the control is angular acceleration rather than angular velocity. We show that an optimal trajectory cannot contain a junction of a bang-bang and a singular piece, and use the results of Zelikin and Borisov (1994) to show that there are Pontryagin extremals involving infinite chattering.