Journal of the
Korean Mathematical Society JKMS

This paper is concerned with the control problem $$\dot x(t)=F(x)+u(t) G(x),\quad t\in [0,T],\quad x(0)=0, $$ where $ F $ and $ G $ are smooth vector fields on $ {\Bbb R}^n, $ and the admissible controls $ u $ satisfy the constraint $|u(t)|\leq 1$. We provide the sufficient condition that the bang-bang trajectories having different switching orders intersect.

Keywords: bang-bang, optimal trajectory, bifurcation

MSC numbers: 49J30