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Identification of controllable transitions to decide the existence of an optimal liveness-enforcing supervisor for a class of Petri nets

¹ School of Electro-Mechanical Engineering, Xidian University, Xi'an, China
² School of Electro-Mechanical Engineering, Xidian University, Xi'an and Dalian Jianting Institute, Dalian, China

^* To whom correspondence should be addressed. E-mail: zhwli{at}xidian.edu.cn.

	Abstract

Behaviour permissiveness is an important criterion in evaluating the performance of a liveness-enforcing supervisor for discrete event systems. The existence of uncontrollable events is a standard feature in the supervisory control of discrete event systems. A natural problem arising in this area is the existence of an optimal supervisor when there exist uncontrollable events in a plant. For a class of Petri net models of flexible manufacturing systems, whose optimal liveness-enforcing Petri net supervisors can be synthesized by a particular method through the addition of a set of monitors, this paper aims to identify a set of transitions such that the existence of an optimal liveness-enforcing net supervisor depends on their controllability. The controllability of a transition is decided by solving a linear programming problem to verify whether a monitor with arcs to the transition can act to inhibit it when it is otherwise enabled. A number of examples are presented to demonstrate the application of the proposed methods.

First published on September 8, 2009
Transactions of the Institute of Measurement and Control 2009, doi:10.1177/0142331208100103


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