From Forbidden States to Linear Constraints

Authors: M. Zareiee, A. Dideban, P. Nazemzadeh

Abstract:

This paper deals with the problem of constructing constraints in non safe Petri Nets and then reducing the number of the constructed constraints. In a system, assigning some linear constraints to forbidden states is possible. Enforcing these constraints on the system prevents it from entering these states. But there is no a systematic method for assigning constraints to forbidden states in non safe Petri Nets. In this paper a useful method is proposed for constructing constraints in non safe Petri Nets. But when the number of these constraints is large enforcing them on the system may complicate the Petri Net model. So, another method is proposed for reducing the number of constructed constraints.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1057613

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] 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).
[8] K. Yamalidou, J. Moody, M. Lemmon, and P. Antsaklis, "Feedback control of petri nets based on place invariants," Automatica, 1996, 32(1),15-28.
[9] 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.
[10] 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.
[11] A. Dideban, and H. Alla, "Reduction of Constraints for Controller Synthesis based on Safe Petri Nets," Automatica, 2008, 44(7): 1697-1706.
[12] 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.
[13] R. Kumar, L. Holloway, "Supervisory control of deterministic Petri nets with regular specification languages," IEEE Trans. Automatic Control, 1996 41(2):245-249.