A reversibility enforcement approach for petri nets using invariants

Petri net model which is one of the most common modelling method of discrete event systems, is considered to enforce reversibility in this work. Reversibility guarantees that the intial state is reachable from any state in the reachability set of given Petri net. An approach, enforcing reversibility, is presented in this work. In this approach, the minimal T-invariants and the firing sequences coressponding to the determined T-invariants are determined. Then, a set of markings, which is a subset of reachability set, is constructed by using those firing sequences. In this set, any state can reach to the initial state. Furthemore, the algorithms are developed for the presented enforcement approach and implemented by using Matlab.

[1]  Buket Yılmaz Applications of Petri nets , 2008 .

[2]  Wil M. P. van der Aalst,et al.  Applications and Theory of Petri Nets , 1983, Informatik-Fachberichte.

[3]  Hirozumi Yamaguchi,et al.  Petri net-based protocol synthesis with minimum communication costs , 2006, J. Frankl. Inst..

[4]  Aydin Aybar,et al.  Centralized and decentralized supervisory controller design to enforce boundedness, liveness, and reversibility in Petri nets , 2005 .

[5]  Qiang Ye,et al.  Combining Petri nets and ns-2: a hybrid method for analysis and simulation , 2006, 4th Annual Communication Networks and Services Research Conference (CNSR'06).

[6]  Aydin Aybar,et al.  Decentralized supervisory controller design to avoid deadlock in Petri nets , 2003 .

[7]  S. Toumodge Applications of Petri Nets in Manufacturing systems; Modeling, Control, and Performance Analysis [Book review] , 1995, IEEE Control Systems.

[8]  M. Nielsen,et al.  Decidability Issues for Petri Nets , 1994 .

[9]  Branislav Hrúz,et al.  Solution of the manufacturing transport control using Petri Nets , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[10]  Altug Iftar,et al.  Overlapping decompositions and expansions of Petri nets , 2002, IEEE Trans. Autom. Control..

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

[12]  MuDer Jeng,et al.  Augmented reachability trees for 1-place-unbounded generalized Petri nets , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[13]  Manuel Silva,et al.  A Simple and Fast Algorithm to Obtain All Invariants of a Generalized Petri Net , 1980, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets.

[14]  A. Iftar,et al.  A program for analysis and control of petri nets' , 2004, Second IEEE International Conference on Computational Cybernetics, 2004. ICCC 2004..

[15]  Aydõn Aybar,et al.  Decentralized structural control approach for Petri nets , 2007 .

[16]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[17]  Aydin Aybar,et al.  REVERSIBILITY ENFORCEMENT FOR UNBOUNDED PETRI NETS , 2005 .

[18]  Yu-Chi Ho,et al.  Discrete event dynamic systems : analyzing complexity and performance in the modern world , 1992 .

[19]  Abdellah El Moudni,et al.  On the analysis of some structural properties of Petri nets , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[20]  MengChu Zhou,et al.  Petri net synthesis for discrete event control of manufacturing systems , 1992, The Kluwer international series in engineering and computer science.

[21]  Luca Ferrarini,et al.  On the Reachability and Reversibility Problems in a Class of Petri Nets , 1994, IEEE Trans. Syst. Man Cybern. Syst..