On the existence of Petri net Controller for Discrete Event Systems under Partial Observation

Authors:	Achour Zied, Metz University, France Rezg Nidhal, Metz University, France Xie Xiaolan, Metz University, France
Topic:	1.3 Discrete Event and Hybrid Systems
Session:	Discrete Event and Hybrid Systems
Keywords:	Supervisory Control, Petri Nets, Unobservable Transitions, Forbidden State Problems.

Abstract

This paper addresses the existence of a maximally permissive PN controller for the forbidden state problem of bounded Petri nets (PN) under partial observation. Based on a Ramadge-Wonham theory, the refined controlled observer reachability graph of the controlled PN is determined and represents the most permissive behavior with liveness requirement and uncontrollable / unobservable transitions. The theory of regions is then used to generate a set of control places, if such controller exists, to be added to the plant PN model. Necessary and sufficient conditions for the existence of pure and impure control places are then presented.