Extension of the lower bound of monitor solutions of maximally permissive supervisors to non-α net systems

Abstract

Traditional region-based liveness-enforcing supervisors focus on (1) maximal permissiveness of not losing legal states, (2) structural simplicity of minimal number of monitors, and (3) fast computation. Lately, a number of similar approaches can achieve minimal configuration using efficient linear programming. However, it is unclear as to the relationship between the minimal configuration and the net structure. It is important to explore the structures involved for the fewest monitors required. Once the lower bound is achieved, further iteration to merge (or reduce the number of) monitors is not necessary. The minimal strongly connected resource subnet (i.e., all places are resources) that contains the set of resource places in a basic siphon is an elementary circuit. Earlier, we showed that the number of monitors required for liveness-enforcing and maximal permissiveness equals that of basic siphons for a subclass of Petri nets modelling manufacturing, called α systems. This paper extends this to systems more powerful than the α one so that the number of monitors in a minimal configuration remains to be lower bounded by that of basic siphons. This paper develops the theory behind and shows examples.

Keywords:

• Petri net
• flexible manufacturing system (FMS)
• deadlock prevention

Additional information

Notes on contributors

W.H. Wu

Wen-Hui Wu is currently a 1ecturer in the College of Information and Electronic Engineering, Zhejiang Gongshang University. She obtained her MS degree from Zhejiang Normal University. Her main research interests include Petri net theory and application.

D.Y. Chao

Daniel-Yuh Chao is a professor in the Department of Management Information Systems, National Chengchi University, Taipei, Taiwan. He received his PhD in electronic engineering and computer science from University of California, Berkeley in 1987. His research interest is in the application of Petri nets to the design and synthesis of communication protocols and the CAD implementation of a multi-function Petri net graphic tool. He has published 110 (including 45 journal) papers in the area of communication protocols, Petri nets, DQDB, networks, FMS, data flow graphs, and neural networks.