An approach to enforce disjunction of GMECs on controlled Petri Nets

The problem of enforcing disjunction of Generalized Mutual Exclusion Constraints (GMECs) on a Petri Net (PN) system is discussed in this paper. It has been proved that in presence of uncontrollable transitions a GMEC has to be transformed into a proper disjunction of GMECs to be enforced in a maximally permissive way. In addition, some control problems have to be directly specified as a disjunction of GMECs; this is the case when the legal markings belong to a non-convex region. In the literature the problem has been solved by extending the standard enabling rule for PNs by using OR-logic and Inhibitor Arcs. In this paper we propose an algorithm to synthesize a standard PN based controller to enforce a limited non-convex legal marking region under some restrictions.

[1]  W. Wonham,et al.  Control of vector discrete-event systems. II. Controller synthesis , 1994, IEEE Trans. Autom. Control..

[2]  Panos J. Antsaklis,et al.  Feedback control of Petri nets based on place invariants , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  P. Antsaklis,et al.  Reduced-order controllers for continuous and discrete-time singular H ∞ control problems based on LMI , 1996 .

[4]  Panos J. Antsaklis,et al.  Supervisory Control of Discrete Event Systems Using Petri Nets , 1998, The International Series on Discrete Event Dynamic Systems.

[5]  Alessandro Giua,et al.  Generalized mutual exclusion contraints on nets with uncontrollable transitions , 1992, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics.

[6]  Wook Hyun Kwon,et al.  Inhibitor arc based state avoidance controller for non-convex forbidden state problems in Petri nets , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[7]  Bruce H. Krogh,et al.  Synthesis of feedback control logic for discrete manufacturing systems , 1991, Autom..

[8]  René K. Boel,et al.  Structuring Acyclic Petri Nets for Reachability Analysis and Control , 2002, Discret. Event Dyn. Syst..

[9]  Panos J. Antsaklis,et al.  Petri net supervisors for DES with uncontrollable and unobservable transitions , 2000, IEEE Trans. Autom. Control..

[10]  Francesco Basile,et al.  Petri net controllers to enforce disjunction of GMECs , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).