On Controllability of Timed Continuous Petri Nets

Abstract

Continuous Petri Nets is a subclass of hybrid models representing relaxed views of discrete events systems, in which timing may adopt different semantics. Even if no semantics is strictly superior, we proved in [1] that for an important subclass of models infinite server semantics provides always a better approximation of the underlying discrete model than finite server. This paper then concentrates on controllability under this semantics. First we propose a notion of controllability over subsets of the reachable polytope, and provide a necessary and sufficient condition for markings with no null elements (interior points); later the transformation of an arbitrary initial marking into an interior one is done. The technically more involved part of the paper is the extension of those results to the case in which some transitions are non controllable. An interesting point is that all characterizations depend only on the structure and firing speeds of the timed continuous net.