Switching in Time-Optimal Problem with Control in a Ball

Abstract

In this paper we analyze local regularity of time-optimal controls and trajectories for an $n$-dimensional affine control system with a control parameter, taking values in a $k$-dimensional closed ball. In the case of $k=n-1$, we give sufficient conditions in terms of Lie bracket relations for all optimal controls to be smooth or to have only isolated jump discontinuities.