Tracking differentiable trajectories across polyhedra boundaries
Massimo Benerecetti, Marco Faella · 2013
We analyze the properties of differentiable trajectories subject to a constant differential inclusion which constrains the first derivative to belong to a given convex polyhedron. We present the first exact algorithm that computes the set of points from which there is a trajectory that reaches a given polyhedron while avoiding another (possibly non-convex) polyhedron. We discuss the connection with (Linear) Hybrid Automata and in particular the relationship with the classical algorithm for reachability analysis for Linear Hybrid Automata.