Reducing the Number of Constraints in Non Safe Petri Net

This paper addresses the problem of forbidden states in non safe Petri Nets. In the system, for preventing it from entering the forbidden states, some linear constraints can be assigned to them. Then these constraints can be enforced on the system using control places. But when the number of constraints in the system is large, a large number of control places must be added to the model of system. This concept complicates the model of system. There are some methods for reducing the number of constraints in safe Petri Nets. But there is no a systematic method for non safe Petri Nets. In this paper we propose a method for reducing the number of constraints in non safe Petri Nets which is based on solving an integer linear programming problem.

Authors:

• M. Zareiee
• A. Dideban

Keywords:

• discrete event system
• Supervisory control
• Petri Net
• Constraint

References:

[1] P. Ramadge, W. Wonham, "Modular feedback logic for discrete event
systems," SIAM Journal of Control and Optimization, 1987, 25(5),
1202-1218.
[2] P. Ramadge, W. Wonham, "The control of discrete event systems,"
Dynamics of discrete event systems [Special issue]. Proceedings of the
IEEE, 1989, 77(1), 81-98.
[3] A. Giua, Petri Nets as Discrete Event Models for Supervisory Control.
Ph.D. Thesis, 1992.
[4] J. Moody, P. Antsaklis, "Petri net supervisor for DES with
uncontrollable and unobservable transition," IEEE Trans. Automatic
Control, 2000, 45(3): 462-476.
[5] B. Krogh, L. Holloway, "Synthesis of feedback control logic for discrete
manufacturing systems," Automatica, 1991, vol. 27, no. 4, pp. 641-651.
[6] L. Holloway, X. Guan, and L. Zhang, "A Generalisation of state
avoidance Policies for Controlled Petri Nets," IEEE Trans. Autom.
Control, 1996, AC-41, 6, 804- 816.
[7] Dideban, A., & Alla, H. (2006). Solving the problem of forbidden states
by feedback control logical synthesis. The 32nd Annual Conference of
the IEEE Industrial Electronics Society, Paris, FRANCE.
[8] A. Ghaffari, N. Rezg, and X. Xie, "Design of live and maximally
permissive petri net controller using the theory of regions," IEEE
Transactions on Robotics and Automation, 2003, 19(1).
[9] K. Yamalidou, J. Moody, M. Lemmon, and P. Antsaklis, "Feedback
control of petri nets based on place invariants," Automatica, 1996, 32(1),
15-28.
[10] A. Giua, F. DiCesare, M. Silva, Generalized Mutual Exclusion
Constraints on Nets with Uncontrollable Transitions. In Proc. IEEE int.
conf. on systems, man, and cybernetics, 1992, pp. 974-799.
[11] A. Dideban, and H. Alla, "From forbidden state to linear constraints for
the optimal supervisory control," Control Engineering and applied
Informaics (CEAI), 2005, 7(3), 48-55.
[12] A. Dideban, and H. Alla, "Reduction of Constraints for Controller
Synthesis based on Safe Petri Nets," Automatica, 2008, 44(7): 1697-
1706.
[13] A. Dideban, M. Zareiee, and H. Alla, Controller synthesis with very
simplified linear constraints in PN model. The 2nd IFAC workshop on
Depebdable Control of Discrete Systems, June 10-12, Bari, Italy, 2009,
265-270.
[14] R. Kumar, L. Holloway, "Supervisory control of deterministic Petri nets
with regular specification languages," IEEE Trans. Automatic Control,
1996 41(2):245-249.