We analyze the properties of smooth trajectories subject to a constant differential inclusion which constrains the first derivative to belong to a given convex polyhedron. We present the first exact symbolic 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 prove that this set of points remains the same if the smoothness constraint is replaced by a weaker differentiability constraint, but not if it is replaced by almost everywhere differentiability. We discuss the connection with (Linear) Hybrid Automata and in particular the relationship with the classical algorithm for reachability analysis for Linear Hybrid Automata.
Tracking smooth trajectories in linear hybrid systems / Benerecetti, Massimo; Faella, Marco. - In: INFORMATION AND COMPUTATION. - ISSN 0890-5401. - 257:(2017), pp. 114-138. [10.1016/j.ic.2017.10.004]
Tracking smooth trajectories in linear hybrid systems
Benerecetti, Massimo
;Faella, Marco
2017
Abstract
We analyze the properties of smooth trajectories subject to a constant differential inclusion which constrains the first derivative to belong to a given convex polyhedron. We present the first exact symbolic 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 prove that this set of points remains the same if the smoothness constraint is replaced by a weaker differentiability constraint, but not if it is replaced by almost everywhere differentiability. We discuss the connection with (Linear) Hybrid Automata and in particular the relationship with the classical algorithm for reachability analysis for Linear Hybrid Automata.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.