Deadlock Prevention for a Class of Petri Nets With Uncontrollable and Unobservable Transitions

This study deals with deadlock problems in a system with uncontrollable and unobservable events, which is modeled with a subclass of Petri nets. We design monitors to enforce constraints for minimal siphons in a Petri net model. A key point of this paper is how to select the input and output arcs of a monitor when there exist uncontrollable and unobservable transitions. After the enforcement of constraints, an iterative algorithm is developed to obtain a controlled system with liveness. A sufficient and necessary condition is established to decide the existence of a monitor enforcing a constraint in a plant with uncontrollable and unobservable transitions.

[1]  MengChu Zhou,et al.  Petri net synthesis and analysis of a flexible manufacturing system cell , 1993, IEEE Trans. Syst. Man Cybern..

[2]  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.

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

[4]  MengChu Zhou,et al.  Modeling, analysis, simulation, scheduling, and control of semiconductor manufacturing systems: A Petri net approach , 1998 .

[5]  MengChu Zhou,et al.  Automated Modeling of Dynamic Reliability Block Diagrams Using Colored Petri Nets , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[6]  MengChu Zhou,et al.  Deadlock control methods in automated manufacturing systems , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[7]  Mark Lawley,et al.  Polynomial-complexity deadlock avoidance policies for sequential resource allocation systems , 1997, IEEE Trans. Autom. Control..

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

[9]  MengChu Zhou,et al.  Modeling, Simulation, and Control of Flexible Manufacturing Systems - A Petri Net Approach , 1999, Series in Intelligent Control and Intelligent Automation.

[10]  Panos J. Antsaklis,et al.  Supervisory Control of Discrete Event Systems Using Petri Nets , 1998, The International Series on Discrete Event Dynamic Systems.

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

[12]  MengChu Zhou,et al.  Petri nets and industrial applications: A tutorial , 1994, IEEE Trans. Ind. Electron..

[13]  Philippe Darondeau,et al.  Theory of Regions , 1996, Petri Nets.

[14]  Nidhal Rezg,et al.  Design of a live and maximally permissive Petri net controller using the theory of regions , 2003, IEEE Trans. Robotics Autom..

[15]  Spyros A. Reveliotis,et al.  A correct and scalable deadlock avoidance policy for flexible manufacturing systems , 1998, IEEE Trans. Robotics Autom..

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

[17]  MengChu Zhou,et al.  Resource-Transition Circuits and Siphons for Deadlock Control of Automated Manufacturing Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[18]  Victor R. L. Shen,et al.  Supervised and Unsupervised Learning by Using Petri Nets , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[19]  Spyros A. Reveliotis,et al.  Deadlock avoidance policies for automated manufacturing cells , 1996, IEEE Trans. Robotics Autom..

[20]  Joaquín Ezpeleta,et al.  A Class of Well Structured Petri Nets for Flexible Manufacturing Systems , 1998, ICATPN.

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

[22]  Feng Chu,et al.  Deadlock analysis of Petri nets using siphons and mathematical programming , 1997, IEEE Trans. Robotics Autom..

[23]  MengChu Zhou,et al.  Petri Nets in Flexible and Agile Automation , 1995 .

[24]  Alessandro Giua,et al.  Suboptimal supervisory control of Petri nets in presence of uncontrollable transitions via monitor places , 2006, Autom..

[25]  MengChu Zhou,et al.  Petri net modelling of buffers in automated manufacturing systems , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[26]  MengChu Zhou,et al.  Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[27]  MengChu Zhou,et al.  Supervisor Design to Enforce Production Ratio and Absence of Deadlock in Automated Manufacturing Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[28]  René K. Boel,et al.  A Continuous Petri Net Approach for Model Predictive Control of Traffic Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[29]  Gabriel Alves,et al.  Automatic Modeling for Performance Evaluation of Inventory and Outbound Distribution , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[30]  Ugo Buy,et al.  Enforcing Periodic Transition Deadlines in Time Petri Nets With Net Unfoldings , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[31]  Basil K. Papadopoulos,et al.  Fuzzy Performance Evaluation of Workflow Stochastic Petri Nets by Means of Block Reduction , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[32]  MengChu Zhou,et al.  An Effective Algorithm to Find Elementary Siphons in a Class of Petri Nets , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[33]  MengChu Zhou,et al.  Design and implementation of a petri net based supervisor for a flexible manufacturing system , 1992, Autom..

[34]  MengChu Zhou,et al.  Design of industrial automated systems via relay ladder logic programming and Petri nets , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[35]  Ming C. Leu,et al.  Modeling and Performance Analysis of a Flexible PCB Assembly Station Using Petri Nets , 1991 .

[36]  MuDer Jeng,et al.  Deadlock prevention policy based on Petri nets and siphons , 2001 .

[37]  Pavlos S. Georgilakis,et al.  A Novel Colored Fluid Stochastic Petri Net Simulation Model for Reliability Evaluation of Wind/PV/Diesel Small Isolated Power Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[38]  Quan Z. Sheng,et al.  A Petri Net Approach to Analyzing Behavioral Compatibility and Similarity of Web Services , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[39]  MengChu Zhou,et al.  A Petri Net Approach to Analysis and Composition of Web Services , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[40]  Philippe Darondeau,et al.  Linear control of live marked graphs , 2003, Autom..

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

[42]  David K. Smith.  Theory of Linear and Integer Programming , 1987 .

[43]  Dimitri Lefebvre,et al.  Stochastic Petri Net Identification for the Fault Detection and Isolation of Discrete Event Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[44]  MengChu Zhou,et al.  Adaptive design of Petri net controllers for error recovery in automated manufacturing systems , 1989, IEEE Trans. Syst. Man Cybern..

[45]  Murat Uzam,et al.  An Optimal Deadlock Prevention Policy for Flexible Manufacturing Systems Using Petri Net Models with Resources and the Theory of Regions , 2002 .

[46]  Fernando D. Von Borstel,et al.  Model-Based Development of Virtual Laboratories for Robotics Over the Internet , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[47]  MengChu Zhou,et al.  A hybrid methodology for synthesis of Petri net models for manufacturing systems , 1992, IEEE Trans. Robotics Autom..

[48]  MengChu Zhou,et al.  Parallel and sequential mutual exclusions for petri net modeling of manufacturing systems with shared resources , 1991, IEEE Trans. Robotics Autom..

[49]  Zhiwu Li,et al.  Liveness-enforcing supervisor design for a class of generalised petri net models of flexible manufacturing systems , 2007 .

[50]  Yoram Reich,et al.  Formalizing a Workflow-Net Implementation of Design-Structure-Matrix-Based Process Planning for New Product Development , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[51]  Zhiwu Li,et al.  Identification of controllable transitions to decide the existence of an optimal liveness-enforcing supervisor for a class of Petri nets , 2011 .

[52]  Chengying Wang,et al.  Comments on "Siphon-Based Deadlock Prevention Policy for Flexible Manufacturing Systems" , 2011, IEEE Trans. Syst. Man Cybern. Part A.

[53]  MengChu Zhou.  Deadlock avoidance schemes in a distributed robotic system: Petri net modeling and analysis , 1995, J. Field Robotics.

[54]  Hyunbo Cho,et al.  Graph-theoretic deadlock detection and resolution for flexible manufacturing systems , 1995, IEEE Trans. Robotics Autom..

[55]  Zhiwu Li,et al.  Deadlock Resolution in Automated Manufacturing Systems: A Novel Petri Net Approach , 2009 .