Monotonic reach control on polytopes

The paper studies the problem of making an affine system defined on a polytopic state space reach a prescribed facet of the polytope in finite time without first leaving the polytope. The focus is on solvability by continuous piecewise affine feedback, and we formulate a variant of the problem in which trajectories exit in a monotonic sense. This allows to obtain necessary and sufficient conditions for solvability in certain geometric situations. Next, we show that, generically, solvability via arbitrary triangulations is equivalent to monotonic solvability. In contrast with existing simplex-based methods, this provides an avenue for reach control on polytopes that does not depend on the choice of triangulation of the polytope.