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XDU & NJIT 1 On Iterative Liveness-enforcement for a Class of Generalized Petri Nets YiFan Hou, Ding Liu, MengChu Zhou CASE 2012 Aug. 20-24, 2012.

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Presentation on theme: "XDU & NJIT 1 On Iterative Liveness-enforcement for a Class of Generalized Petri Nets YiFan Hou, Ding Liu, MengChu Zhou CASE 2012 Aug. 20-24, 2012."— Presentation transcript:

1 XDU & NJIT 1 On Iterative Liveness-enforcement for a Class of Generalized Petri Nets YiFan Hou, Ding Liu, MengChu Zhou CASE 2012 Aug , 2012

2 XDU & NJIT 2 Outline Background and Motivation Background and Motivation Intrinsically Live Structure (ILS) Intrinsically Live Structure (ILS) Liveness and Ratio-enforcing Supervisor (LRS) Liveness and Ratio-enforcing Supervisor (LRS) MIP & LRS MIP & LRS Conclusion and Future Work Conclusion and Future Work

3 XDU & NJIT 3 Outline Background and Motivation Background and Motivation Intrinsically Live Structure (ILS) Intrinsically Live Structure (ILS) Liveness and Ratio-enforcing Supervisor (LRS) Liveness and Ratio-enforcing Supervisor (LRS) MIP & LRS MIP & LRS Conclusion and Future Work Conclusion and Future Work

4 XDU & NJIT 4 Background and Motivation Two oxen and a single-log bridge (picture from Internet) DEADLOCK

5 XDU & NJIT 5 Background and Motivation (a) (b) (c) (d)

6 XDU & NJIT 6 Background and Motivation siphons do not carry any weight information; the siphon-based method originally developed for ordinary Petri nets mostly cannot be directly used in generalized ones; the siphon-based method originally developed for ordinary Petri nets yield a controlled system with very limited reachable states; a new kind of structural objects tied with deadlock-freeness and liveness? a new policy for deadlock-control / liveness-enforcement?

7 XDU & NJIT 7 Outline Background and Motivation Background and Motivation Intrinsically Live Structure (ILS) Intrinsically Live Structure (ILS) Liveness and Ratio-enforcing Supervisor (LRS) Liveness and Ratio-enforcing Supervisor (LRS) MIP & LRS MIP & LRS Conclusion and Future Work Conclusion and Future Work

8 XDU & NJIT 8 Intrinsically Live Structure (ILS) a structural object carrying weight information; a structural intuitively reflecting circular waits; a numerical relationship between initial marking and arc weights; (a) (b)

9 XDU & NJIT 9 Intrinsically Live Structure (ILS) A WSDC is a subnet consisting of places, transitions, and their arcs that form a simple circuit of the digraph; The competition path t 2 r 2 t 3 ; The upstream activity place p r2 up and downstream one p r2 down compete against each other; The numerical relationship between the arc weights of and the initial number of tokens in the resource place;

10 XDU & NJIT 10 Intrinsically Live Structure (ILS) A revised dining philosopher problem modeled by WS 3 PR; A WSDC t 2 r 1 t 14 t 5 t 11 r 4 t 8 r 3 t 5 r 2 t 2 expresses the circular wait relation among all resource places;

11 XDU & NJIT 11 Intrinsically Live Structure (ILS) A competition path is a link of the whole chain of resource places; Break the chain of circular wait by breaking a link of it; The basic idea is to ensure that after a prioritized and maximal acquirement of tokens in the resource place by the upstream activity place, the remaining ones are still adequate for the downstream one to complete one operation; Implemented by the numerical relationship between arc weights and initial markings;

12 XDU & NJIT 12 Intrinsically Live Structure (ILS) A weight matrix is used to deal with the situation that multiple competition path with the same resource places;

13 XDU & NJIT 13 Intrinsically Live Structure (ILS) Main results - Restriction 1;

14 XDU & NJIT 14 Intrinsically Live Structure (ILS) Main results - Theorems;

15 XDU & NJIT 15 Intrinsically Live Structure (ILS) A Live WS 3 PR with all WSDC satisfying Restriction 1;

16 XDU & NJIT 16 Outline Background and Motivation Background and Motivation Intrinsically Live Structure (ILS) Intrinsically Live Structure (ILS) Liveness and Ratio-enforcing Supervisor (LRS) Liveness and Ratio-enforcing Supervisor (LRS) MIP & LRS MIP & LRS Conclusion and Future Work Conclusion and Future Work

17 XDU & NJIT 17 Liveness and Ratio-enforcing Supervisor (LRS) Basic idea: Impose a well-designed supervisor with intrinsically live structures to break the chain of circular waits; Consider the resource usage ratios of upstream and downstream activity places and the relation between them;

18 XDU & NJIT 18 Liveness and Ratio-enforcing Supervisor (LRS) Resource usage ratio (RU-ratio): an admissible range of RU-ratios

19 XDU & NJIT 19 Liveness and Ratio-enforcing Supervisor (LRS) All RU-ratios

20 XDU & NJIT 20 Liveness and Ratio-enforcing Supervisor (LRS) Rephrase Restriction 1 from the pespective of RU-ratio; Make sure the structures of LRS monitors satisfy Restriction 2;

21 XDU & NJIT 21 Liveness and Ratio-enforcing Supervisor (LRS) Design a control path satisfying Restriction 2; Impose the control path to a competition one; Make a competition path to be a puppet;

22 XDU & NJIT 22 Liveness and Ratio-enforcing Supervisor (LRS) Designed a control path according to the control specification; Impose the control path to the competition one virtually replacing its role in the chain; Take over the token allocation of the resource place by the numerical relationship between arc weights and initial markings; Design the control parameters of the competition path by setting a minimal RU-ratio of downstream activity place and solving the following mathematical programming problem;

23 XDU & NJIT 23 Liveness and Ratio-enforcing Supervisor (LRS)

24 XDU & NJIT 24 Liveness and Ratio-enforcing Supervisor (LRS) The differences between LRS and siphon-monitor-based methods: (1)Basic idea; (2)Structural object; (3)Supervisor’s size; (4)RU-ratios and parameters;

25 XDU & NJIT 25 Liveness and Ratio-enforcing Supervisor (LRS) The advantages of LRS: (1) The size of an LRS; (2) No new problematic structures; (3) Adjusting control parameters; (4) Intuitive and easy to understand; (5) A precise usage and robustness of resources; The limitation of LRS: (1)The existence is decided by the initial marking of a plant model;

26 XDU & NJIT 26 Outline Background and Motivation Background and Motivation Intrinsically Live Structure (ILS) Intrinsically Live Structure (ILS) Liveness and Ratio-enforcing Supervisor (LRS) Liveness and Ratio-enforcing Supervisor (LRS) MIP & LRS MIP & LRS Conclusion and Future Work Conclusion and Future Work

27 XDU & NJIT 27 MIP & LRS Avoid enumerate all WSDCs in a plant net modeled with WS 3 PR; Only find the problematic structure;

28 XDU & NJIT 28 MIP & LRS Find a maximal insufficiently marked siphon by solving MIP problem 2; Select a resource place from the maximal insufficiently marked siphon; Design an LRS monitor for the resource place;

29 XDU & NJIT 29 MIP & LRS Process idle places: 2 Activity places: 11 Resource places: 6 Transitions: 14 3,334,653 states Including 30 dead ones

30 XDU & NJIT 30 MIP & LRS Iteration 1: Find the maximal insufficiently marked siphon by MIP; Control resource place p 19 by v 1 ; 2,663,888 states Including 6 dead ones

31 XDU & NJIT 31 MIP & LRS Iteration 2: Find the maximal insufficiently marked siphon by MIP; Control resource place p 15 by v 2 ; 2,613,824 states Including 1 dead ones

32 XDU & NJIT 32 MIP & LRS Iteration 3: Find the maximal insufficiently marked siphon by MIP; Control resource place p 17 by v 3 ; 2,500,037 states No dead ones LIVE

33 XDU & NJIT 33 MIP & LRS

34 XDU & NJIT 34 Outline Background and Motivation Background and Motivation Intrinsically Live Structure (ILS) Intrinsically Live Structure (ILS) Liveness and Ratio-enforcing Supervisor (LRS) Liveness and Ratio-enforcing Supervisor (LRS) MIP & LRS MIP & LRS Conclusion and Future Work Conclusion and Future Work

35 XDU & NJIT 35 Conclusion and Future Work Conclusion: (1) Avoid the enumeration of all WSDC; (2) All strict minimal siphons are minimally controlled; (3) The number of iterations is bounded by that of resource places; Future work: (1)How to optimally select a shared resource place given a maximal insufficiently marked siphon; (2)How to extend this method to more general nets than WS 3 PR;

36 XDU & NJIT 36 Thanks for your attention!

37 XDU & NJIT 37 Related Publications [1] D. Liu, Z. W. Li, and M. C. Zhou, “Liveness of an Extended S 3 PR,” Automatica, vol. 46, no. 6, pp – 1018, [2] D. Liu, Z.W. Li, andM. C. Zhou, “Erratum to “Liveness of an Extended S 3 PR [Automatica 46 (2010) ]”,” Automatica, vol. 48, no. 5, pp – 1004, [3] D. Liu, Z. W. Li, and M. C. Zhou, “Hybrid Liveness-enforcing Policy for Generalized Petri Net Models of Flexible Manufacturing Systems,” accepted by IEEE Transactions on Systems, Man, and Cybernetics, Part A, [4] D. Liu, Z. W. Li, and M. C. Zhou, “A Parameterized Liveness and Ratio-Enforcing Supervisor for a Class of Generalized Petri Nets,” submitted to Automatica, [5] D. Liu, Z. W. Li, Y. F. Hou, and M. C. Zhou, “On Divide-and-Conquer Liveness enforcing strategy for Flexible Manufacturing Systems Modeled by a Class of Generalized Petri Nets,” Technical report, Xidian University, [6] Y. F. Hou, D. Liu, Z. W. Li, and M. Zhao, “Deadlock Prevention Using Divide-and-Conquer Strategy for WS 3 PR,“in Proceedings of IEEE ICMA 2010, pp – 1640, [7] D. Liu, M. Zhao, H. S. Hu, and A. R. Wang, “Hybrid Liveness-enforcing Method for Petri Net Models of Flexible Manufacturing Systems,“ in Proceedings of IEEE ICMA 2010, pp – 1818, [8] M. Zhao, Yifan Hou, and Ding Liu, “Liveness-enforcing Supervisors Synthesis for a class of Generalized Petri Nets based on Two-stage Deadlock Control and Mathematical Programming,“ International Journal of Control, vol. 83, no. 10, pp – 2066, 2010.


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