A Preliminary Study of Barrier Stopping Points in Constrained Nonlinear Systems

We first recall results on the boundary of the so-called admissible set for state and input constrained nonlinear systems, namely that the boundary is made up of two parts: one included in the state constraints and its complement called the barrier, made of integral curves that satisfy a minimum-like principle. Then we define the notions of barrier stopping points by intersection and by self-intersection. We then prove that all regular intersection points of the integral curves running along the barrier are barrier stopping points. Then we present, on systems of two and three dimensions, examples where barriers with stopping points occur.