Tracking smooth trajectories in linear hybrid systems

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 gi...

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Bibliographic Details
Published inInformation and computation Vol. 257; pp. 114 - 138
Main Authors Benerecetti, Massimo, Faella, Marco
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2017
Subjects
Controller synthesis
Hybrid automata
Reachability
Hybrid automata
Controller synthesis
Reachability
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ISSN0890-5401
1090-2651
DOI10.1016/j.ic.2017.10.004

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Summary: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.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2017.10.004