On the enforcement of a class of constraint in Petri nets

This paper addresses the enforcement of a class of linear inequality constraint defined on the marking of a Petri net (PN). The constraint may be regarded as the conjunction of 'less-than-or-equal-to' inequality and 'greater-than-or-equal-to' inequality. The extended Petri nets such as inhibitor arc PN and its complementary net, the so-called enabling arc PN, are exploited to design a PN supervisor such that the constraint is enforced in the controlled net. The supervisor is optimal in the sense that it allows the net evolves with least restriction while the given constraint is satisfied. An example is provided for illustration.

[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.  Supervisory Control of Discrete Event Systems Using Petri Nets , 1998, The International Series on Discrete Event Dynamic Systems.

[3]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[4]  Murat Uzam.  Petri-net-based supervisory control of discrete event systems and their ladder logic diagram implementations , 1998 .

[5]  Panos J. Antsaklis,et al.  Synthesis of deadlock prevention supervisors using Petri nets , 2002, IEEE Trans. Robotics Autom..

[6]  Weimin Wu,et al.  Supervisory control of discrete event systems using enabling arc Petri nets , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[7]  Yong Li,et al.  Control of Vector Discrete-Event Systems , 1993 .

[8]  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).

[9]  Chun-Hung Chen,et al.  Simulation Budget Allocation for Further Enhancing the Efficiency of Ordinal Optimization , 2000, Discret. Event Dyn. Syst..

[10]  Chen Haoxun.  Control Synthesis of Petri Nets Based on S-Decreases , 2000 .

[11]  Hongye Su,et al.  Petri net controller synthesis for discrete event systems using weighted inhibitor arc , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

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

[13]  René Boel,et al.  On forbidden state problems for a class of controlled Petri nets , 1995, IEEE Trans. Autom. Control..

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

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

[16]  Wook Hyun Kwon,et al.  On forbidden state problems in a general class of non-ordinary controlled Petri nets , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).