Optimal supervisor synthesis for petri nets with uncontrollable transitions: A bottom-up algorithm

Information Sciences

Volumn 363, Issue , 2016, Pages 261-273

  Wang, Shouguang ^a   You, Dan ^a   Wang, Chengying ^a  

^a ZHEJIANG GONGSHANG UNIVERSITY   (China)

Author keywords

Discrete event system; Forbidden state problem; Petri net; Supervisory control

Indexed keywords

ALGORITHMS; PETRI NETS; SUPERVISORY PERSONNEL; WORK SIMPLIFICATION;

AUTOMATED PRODUCTIONS; EXPONENTIAL COMPLEXITY; FORBIDDEN STATE; GENERALIZED MUTUAL EXCLUSION CONSTRAINT; INTELLIGENT TRANSPORTATION; POLYNOMIAL COMPLEXITY; SUPERVISORY CONTROL; WORKFLOW MANAGEMENTS;

DISCRETE EVENT SIMULATION;

EID: 84949656251     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2015.11.003     Document Type: Article

References (61)

1. [1] Basile, F., Carbone, C., Chiacchio, P., An approach to enforce disjunction of GMECs on controlled Petri nets. Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, 2003, 1852–1859.
2. [2] Basile, F., Chiacchio, P., Giua, A., Suboptimal supervisory control of Petri nets in presence of uncontrollable transitions via monitor places. Automatica 42:6 (2006), 995–1004.
3. [3] Basile, F., Carbone, C., Chiacchio, P., Feedback control logic for backward conflict free choice nets. IEEE Trans. Autom. Control 52:3 (2007), 387–400.
4. [4] Chen, H., Net structure and control logic synthesis of controlled Petri nets. IEEE Trans. Autom. Control 43:10 (1998), 1446–1450.
5. [5] Chen, H., Control synthesis of Petri nets based on s-decrease. Discret. Event Dyn. Syst.: Theory Appl. 10:3 (2000), 233–249.
6. [6] Holloway, L.E., Krogh, B.H., Synthesis of feedback control logic for a class of controlled Petri nets. IEEE Trans. Autom. Control 35:5 (1990), 514–523.
7. [7] Holloway, L.E., Krogh, B.H., Giua, A., A survey of Petri net methods for controlled discrete event system. Discret. Event Dyn. Syst.: Theory Appl. 7:2 (1997), 151–190.
8. [8] Holloway, L.E., Khare, A.S., Gong, Y., Computing bounds for forbidden state reachability functions for controlled Petri nets. IEEE Trans. Syst., Man, Cybern. A, Syst., Humans 34:2 (2004), 219–228.
9. [9] Iordache, M.V., Moody, J., Antsaklis, P., Synthesis of deadlock prevention supervisors using Petri nets. IEEE Trans. Robot. Autom. 18:1 (2002), 59–68.
10. [10] Iordache, M.V., Antsaklis, P.J., Synthesis of supervisors enforcing general linear constraints in Petri nets. IEEE Trans. Autom. Control 48:11 (2003), 2036–2039.
11. [11] Iordache, M.V., Antsaklis, P.J., Decentralized supervision of Petri nets. IEEE Trans. Autom. Control 51:2 (2006), 376–381.
12. [12] Ghaffari, A., Rezg, N., Xie, X., Feedback control logic for forbiddenstate problems of marked graphs: application to a real manufacturing system. IEEE Trans. Autom. Control 48:1 (2003), 18–29.
13. [13] Giua, A., DiCesare, F., Silva, M., Generalized mutual exclusion constraints on nets with uncontrollable transitions. IEEE International Conference on Systems, Man, Cybernetics, 1992, 974–979.
14. [14] Li, Y., Wonham, W.M., Control of vector discrete-event systems II—The base model. IEEE Trans. Autom. Control 38:8 (1993), 1214–1227.
15. [15] Li, Y., Wonham, W.M., Control of vector discrete-event systems II—Controller synthesis. IEEE Trans. Autom. Control 39:3 (1994), 512–531.
16. [16] Li, Z.W., Zhou, M.C., Synthesis of structurally simple supervisors enforcing generalized mutual exclusion constraints in Petri nets. IEEE Trans. Syst., Man, Cybern., Part C 40:3 (2010), 330–340.
17. [17] Lien, Y.L., Termination properties of generalized Petri nets. SIAM J. Comput. 5:2 (1976), 251–265.
18. [18] Luo, J., Wu, W., Su, H., Chu, J., Supervisor synthesis for enforcing GMECs on a controlled Petri net. American Control Conference, 2006, 4165–4170.
19. [19] Luo, J., Wu, W., Su, H., Chu, J., Supervisor synthesis for a class of forbidden state problems in Petri nets. American Control Conference, 2006, 4171–4176.
20. [20] Luo, J.L., Wu, W.M., Su, H.Y., Chu, J., Supervisor Synthesis for Enforcing a class of GMECs on Petri Nets. IEEE Trans. Syst.,Man, Cybern., A, Syst., Hum. 39:6 (2009), 1237–1246.
21. [21] Moody, J.O., Antsaklis, P.J., Supervisory Control of Discrete Event Systems Using Petri Nets. 1998, Kluwer Academic Publisher.
22. [22] Moody, J., Antsaklis, P., Petri net supervisors for DBS with uncontrollable and unobservable transitions. IEEE Trans. Autom. Control 45:3 (2000), 462–476.
23. [23] Murata, T., Petri nets: properties, analysis, and applications. Proc. IEEE 77:4 (1989), 541–580.
24. [24] Stremersch, G., Boel, R.K., Enforcing k-safeness in controlled state machine. IEEE 38th Conference Decision Control, 1999, 1737–1742.
25. [25] Stremersch, G., Boel, R.K., Structuring acyclic Petri nets for reachability analysis and control. Discret. Event Dyn. Syst.: Theory Appl. 12:1 (2002), 7–41.
26. [26] Chen, Y.F., Li, Z.W., Barkaoui, K., Maximally permissive liveness-enforcing supervisor with lowest implementation cost for flexible manufacturing systems. Inf. Sci. 256 (2014), 74–90.
27. [27] Chen, Y.F., Li, Z.W., Zhou, M.C., Optimal supervisory control of flexible manufacturing systems by Petri nets: a set classification approach. IEEE Trans. Autom. Sci. Eng. 11:2 (2014), 549–563.
28. [28] Liu, D., Li, Z.W., Zhou, M.C., A parameterized liveness and ratio-enforcing supervisor for a class of generalized Petri nets. Automatica 49:11 (2013), 3167–3179.
29. [29] Li, Z.W., Liu, G.Y., Hanisch, H., Zhou, M.C., Deadlock prevention based on structure reuse of Petri net supervisors for flexible manufacturing systems. IEEE Trans. Syst., Man, Cybern., Part A 42:1 (2012), 178–191.
30. [30] Li, Z., Zhou, M., Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems. IEEE Trans. Syst., Man, Cybern. A, Syst., Humans 34:1 (2004), 38–51.
31. [31] Li, Z.W., Hu, H.S., Wang, A.R., Design of liveness-enforcing supervisors for flexible manufacturing systems using Petri nets. IEEE Trans. Syst., Man, Cybern., Part C: Appl. Rev. 37:4 (2007), 517–526.
32. [32] Li, Z., Wu, N., Zhou, M., Deadlock control of automated manufacturing systems based on Petri nets—A literature review. IEEE Trans. Syst., Man, Cybern., Part C: Appl. Rev. 42:4 (2012), 437–462.
33. [33] Hu, H.S., Zhou, M.C., Li, Z.W., Tang, Y., Deadlock-free control of automated manufacturing systems with flexible routes and assembly operations using Petri nets. IEEE Trans. Ind. Inf. 9:1 (2013), 109–121.
34. [34] Chen, Y.F., Li, Z.W., Al-Ahmari, A., Nonpure Petri net supervisors for optimal deadlock control of flexible manufacturing systems. IEEE Trans. Syst., Man, Cybern.: Syst. 43:2 (2013), 252–265.
35. [35] Hu, H.S., Zhou, M.C., Li, Z.W., Liveness and ratio-enforcing supervision of automated manufacturing systems using Petri nets. IEEE Trans. Syst., Man, Cybern., Part A 42:2 (2012), 392–403.
36. [36] Wang, A., Li, Z.W., Zhou, M.C., Al-Ahmari, A., Iterative deadlock control by using Petri nets. IEEE Trans. Syst., Man, Cybern., Part C 42:6 (2012), 1204–1218.
37. [37] Li, Z., Zhou, M., Deadlock Resolution in Automated manufacturing Systems: A Novel Petri Net Approach. 2009, Springer-Verlag, London.
38. [38] Qin, M., Li, Z.W., Zhou, M.C., Khalgui, M., Mosbahi, O., Deadlock prevention for a class of Petri nets with uncontrollable and unobservable transitions. IEEE Trans. Systems, Man, Cybern., Part A 42:3 (2012), 727–738.
39. [39] Wonham, W.M., Ramadge, P.J., On the supremal controllable sublanguage of a given language. SIAM J. Control Opt. 25:3 (1987), 637–659.
40. [40] Yamalidou, K., Moody, J., Lemmon, M., Antsaklis, P., Feedback control of Petri nets based on place invariants. Automatica 32:1 (1996), 15–28.
41. [41] Tarjan, R.E., Depth first search and linear graph algorithms. SIAM J. Comput. 1:2 (1972), 146–160.
42. [42] Kumar, R., Holloway, L.E., Supervisory control of deterministic Petri nets with regular specification languages. IEEE Trans. Autom. Control. 41:2 (1996), 245–249.
43. [43] Dideban, A, Zareiee, M., Orouji, A.A., A simple Petri net controller by solving some integer linear programming problems. J. Control Eng. Appl. Inf. 16:4 (2014), 3–11.
44. [44] Zareiee, M, Dideban, A., Orouji, A.A., Soltanizadeh, H., Solving the problem of forbidden states in discrete event systems: a novel systematic method for reducing the number of control places. Asian J. Control. 17:3 (2015), 1006–1015.
45. [45] Zareiee, M., Dideban, A., Orouji, A.A., Safety analysis of discrete event systems using a simplified Petri net controller. ISA Trans. 53:1 (2014), 44–49.
46. [46] Dideban, A., Zareiee, M., Alla, H., Controller synthesis with highly simplified linear constraints in PN model. Asian J. Control 15:1 (2013), 80–94.
47. [47] Nazemzadeh, P., Dideban, A., Zareiee, M., Fault modeling in discrete event systems using Petri Nets. ACM Trans. Embedded Comput. Syst., 12(1), 2013.
48. [48] Zareiee, M., Dideban, A., Orouji, A.A., Soleymanpour, H.R., Simplification of a Petri net controller in industrial systems by using an optimization algorithm. Int. J. Ind. Eng. Prod. Res. 24:1 (2013), 59–70.
49. [49] Zareiee, M., Dideban, A., Nazemzadeh, P., From forbidden states to linear constraints. World Academy of Science, Engineering and Technology, Dubai, UME, January 2011.
50. [50] Nazeem, A., Reveliotis, S., Wang, Y., Lafortune, S., Designing compact and maximally permissive deadlock avoidance policies for complex resource allocation systems through classification theory: the linear case. IEEE Trans. Autom. Control 56:8 (2011), 1818–1833.
51. [51] Cordone, R., Nazeem, A., Piroddi, L., Reveliotis, S., Designing optimal deadlock avoidance policies for sequential resource allocation systems through classification theory: existence results and customized algorithms. IEEE Trans. Autom. Control 58:11 (2013), 2772–2787.
52. [52] Basile, F., Cordone, R., Piroddi, L., Compact supervisors for general constraint enforcement in Petri net models with uncontrollable transitions. European Control Conference, 2013, 143–148.
53. [53] Li, Z.W., Zhou, M.C., Two-stage method for synthesizing liveness-enforcing supervisors for flexible manufacturing systems using Petri nets. IEEE Trans. Ind. Inf. 2:4 (2006), 313–325.
54. [54] Li, Z.W., Zhou, M.C., Control of elementary and dependent siphons in Petri nets and their application. IEEE Trans. Syst., Man, Cybern., Part A 38:1 (2008), 133–148.
55. [55] Li, Z.W., Zhou, M.C., Wu, N.Q., A survey and comparison of Petri net-based deadlock prevention policies for flexible manufacturing systems. IEEE Trans. Syst., Man, Cybern., Part C 38:2 (2008), 173–188.
56. [56] Li, Z.W., Zhou, M.C., Jeng, M.D., A maximally permissive deadlock prevention policy for FMS based on Petri net siphon control and the theory of regions. IEEE Trans. Autom. Sci. Eng. 5:1 (2008), 182–188.
57. [57] Li, Z.W., Zhao, M., On controllability of dependent siphons for deadlock prevention in generalized Petri nets. IEEE Trans. Syst., Man, Cybern., Part A 38:2 (2008), 369–384.
58. [58] Wu, N.Q., Zhou, M., Li, Z.W., Resource-oriented Petri net for deadlock avoidance in flexible assembly systems. IEEE Trans. Syst., Man, Cybern., Part A 38:1 (2008), 56–69.
59. [59] Ma, Z.Y., Li, Z.W., Giua, A., Design of optimal Petri net controllers for disjunctive generalized mutual exclusion constraints. IEEE Trans. Autom. Control 60:7 (2015), 1774–1785.
60. [60] Ma, Z.Y., Li, Z.W., Giua, A., Comments on “Maximally permissive supervisor synthesis based on a new constraint transformation method”. Automatica 51:1 (2015), 131–134.
61. [61] Ma, Z.Y., Li, Z.W., Giua, A., A constraint transformation technique in Petri nets with backward-conflict-free uncontrollable structures. To appear in Proceedings of the American Control Conference, Chicago, US, 2015.