Synthesis of deadlock prevention supervisors using Petri nets

Given an arbitrary Petri net (PN) structure, which may have uncontrollable and unobservable transitions, the deadlock prevention procedure presented here determines a set of linear inequalities on the PN markings. When the PN is supervised so that its markings satisfy these inequalities, the supervised net is proved to be deadlock-free for all initial markings that satisfy the supervision constraints. Deadlock-freedom implies that there will always be at least one transition that is enabled in the closed-loop (supervised) system. The method is not guaranteed to ensure liveness, as it can be applied to systems that cannot be made live under any circumstances. However, for controllable and observable PNs, it is shown that, when the method ensures liveness as well, the liveness-ensuring supervisor is least restrictive. Moreover, it is shown that the method is not restrictive even for PNs in which not all transitions can be made live. The procedure allows automated synthesis of the supervisors.

[1]  Javier Martínez,et al.  A Petri net based deadlock prevention policy for flexible manufacturing systems , 1995, IEEE Trans. Robotics Autom..

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

[5]  Kamel Barkaoui,et al.  On Liveness and Controlled Siphons in Petri Nets , 1996, Application and Theory of Petri Nets.

[6]  Kamel Barkaoui,et al.  Deadlock avoidance in FMS based on structural theory of Petri nets , 1995, Proceedings 1995 INRIA/IEEE Symposium on Emerging Technologies and Factory Automation. ETFA'95.

[7]  Kamel Barkaoui,et al.  Structural Analysis of Workflow Nets with Shared Resources , 1998 .

[8]  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.

[9]  Panos J. Antsaklis,et al.  Generalized Conditions for Liveness Enforcement and Deadlock Prevention in Petri Nets , 2001, ICATPN.

[10]  Leslie Lloyd Glasgow,et al.  Contributions to the knowledge of the ecology of the American woodcock, Philohela minor (Gmelin), on the wintering range in Louisiana , 1958 .

[11]  Haoxun Chen,et al.  Deadlock avoidance policy for Petri-net modeling of flexible manufacturing systems with shared resources , 1996 .

[12]  John-Warren Reynolds.  The earthworms of South Carolina (Oligochaeta: Acanthodrilidae, Lumbricidae, Megascolecidae, Ocnerodrilidae and Sparganophilidae) , 2001 .

[13]  W. Sheldon,et al.  The Book of the American Woodcock , 1968 .

[14]  H. H. Prince,et al.  Feeding-site selection and foraging strategies of American woodcock , 1983 .

[15]  Kelley,et al.  AMERICAN WOODCOCK POPULATION STATUS, 2000 , 2000 .

[16]  Kamel Barkaoui,et al.  Supervisory control of discrete event systems based on structure theory of Petri nets , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

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

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

[19]  Panos J. Antsaklis,et al.  Automated Synthesis of Deadlock Prevention Supervisors Using Petri Nets , 2001 .

[20]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[21]  K. Barkaoui,et al.  A deadlock prevention method for a class of FMS , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[22]  H. L. Stribling,et al.  Nocturnal use of fields by American woodcock , 1985 .