Supervisor Synthesis for Enforcing a Class of Generalized Mutual Exclusion Constraints on Petri Nets

The considered class of generalized mutual exclusion constraints (GMECs) on a controlled Petri net are such that the influence-uncontrollable subnets are forward-concurrent-free nets. Some structural properties of forward-concurrent-free nets are firstly proposed. Utilizing these properties, a method is then proposed to transform a given conjunction of GMECs into a conjunction of admissible GMECs. Furthermore, the necessary and sufficient condition of the existence of the permissive supervisor is obtained, and the optimal supervisor with a complexity of polynomial time is designed. The theoretic results are illustrated by an example that synthesizes a maximally permissive supervisor for a manufacturing system.

[1]  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.

[2]  Hongye Su,et al.  Supervisor synthesis for a class of forbidden state problems in Petri nets , 2006, 2006 American Control Conference.

[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]  Bruce H. Krogh,et al.  Synthesis of feedback control logic for discrete manufacturing systems , 1991, Autom..

[5]  Michel Hack,et al.  ANALYSIS OF PRODUCTION SCHEMATA BY PETRI NETS , 1972 .

[6]  Y. Edmund Lien.  Termination Properties of Generalized Petri Nets , 1976, SIAM J. Comput..

[7]  P. Ramadge,et al.  Supervisory control of a class of discrete event processes , 1987 .

[8]  Francesco Basile,et al.  Feedback Control Logic for Backward Conflict Free Choice Nets , 2007, IEEE Transactions on Automatic Control.

[9]  Alessandro Giua,et al.  A Survey of Petri Net Methods for Controlled Discrete Event Systems , 1997, Discret. Event Dyn. Syst..

[10]  Yu Gong,et al.  Computing bounds for forbidden State reachability functions for controlled Petri nets , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[11]  Lawrence E. Holloway,et al.  A generalization of state avoidance policies for controlled Petri nets , 1996 .

[12]  Hongye Su,et al.  Normalized cascade structures and state feedback control logic synthesis , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[13]  Hongye Su,et al.  Supervisor synthesis for enforcing GMECs on a controlled Petri net , 2006, 2006 American Control Conference.

[14]  Chen Haoxun.  Net structure and control logic synthesis of controlled Petri nets , 1998, IEEE Transactions on Automatic Control.

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

[16]  G. Stremersch,et al.  Enforcing k-safeness in controlled state machines , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[17]  Bruce H. Krogh,et al.  Synthesis of feedback control logic for a class of controlled Petri nets , 1990 .

[18]  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.

[19]  Mi Zhao,et al.  On Controllability of Dependent Siphons for Deadlock Prevention in Generalized Petri Nets , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[20]  Haoxun Chen,et al.  Control Synthesis of Petri Nets Based on S-Decreases , 2000, Discret. Event Dyn. Syst..

[21]  Panos J. Antsaklis,et al.  Synthesis of supervisors enforcing general linear constraints in Petri nets , 2003, IEEE Trans. Autom. Control..

[22]  René K. Boel,et al.  Structuring Acyclic Petri Nets for Reachability Analysis and Control , 2002, Discret. Event Dyn. Syst..

[23]  René Boel,et al.  On forbidden state problems for a class of controlled Petri nets , 1995, IEEE Trans. Autom. Control..

[24]  Nidhal Rezg,et al.  Feedback control logic for forbidden-state problems of marked graphs: application to a real manufacturing system , 2003, IEEE Trans. Autom. Control..

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

[26]  W. M. Wonham,et al.  The control of discrete event systems , 1989 .

[27]  Zhiwu Li,et al.  ON SUPERVISORY CONTROL OF A CLASS OF DISCRETE EVENT SYSTEMS , 2006 .

[28]  Panos J. Antsaklis,et al.  Supervision Based on Place Invariants: A Survey , 2006, Discret. Event Dyn. Syst..

[29]  W. Wonham,et al.  Control of vector discrete-event systems. II. Controller synthesis , 1994, IEEE Trans. Autom. Control..

[30]  F. Basile,et al.  An approach to enforce disjunction of GMECs on controlled 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).

[31]  P. Ramadge,et al.  Modular Feedback Logic for Discrete Event Systems , 1987 .

[32]  Behzad Bordbar,et al.  A Min-plus Polynomial Approach to Forbidden State Control for General Petri Nets , 1998 .

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

[34]  Chen Haoxun.  Control Synthesis of Petri Nets Based on S-Decreases , 2000 .

[35]  MengChu Zhou,et al.  Clarifications on the Definitions of Elementary Siphons in Petri Nets , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[36]  Alessandro Giua,et al.  Supervisory Control of Petri NetsBased on Suboptimal Monitor Places , 1998 .

[37]  Panos J. Antsaklis,et al.  Feedback Petri net control design in the presence of uncontrollable transitions , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[38]  Noureddine Zerhouni,et al.  Some subclasses of Petri nets and the analysis of their structural properties: a new approach , 1999, IEEE Trans. Syst. Man Cybern. Part A.

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

[40]  MengChu Zhou,et al.  Control of Elementary and Dependent Siphons in Petri Nets and Their Application , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

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

[42]  Murat Uzam.  Synthesis of feedback control elements for discrete event systems using Petri net models and theory of regions , 2003 .