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Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

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Li and Zhou developed a method to compute elementary siphons and indicated that it may be extended to weighted resource allocation systems. The author shows a better way to find elementary siphons for weighted S3PR (systems of simple sequential processes with resources) or WS3PR via an example where there is no dependent siphon based on the approach by Li and Zhou. Yet, the author is able to locate one; thus, reducing the number of monitors required. Redefining the characteristic P-vector by weighting each component by that of a P-invariant, the author shows via a theorem and an example that an S3PR and its weighted S3PR have the same sets of elementary, dependent siphons and systems of equations of characteristic T-vectors. Applying their siphon-synthesis theory, the time to find elementary siphons for WS3PR is reduced from exponential to polynomial. The author also derives the controllability condition for a WS3PR and discuss how to extend to S3PGR2 (systems of simple sequential processes with general resources requirement).

Inspec keywords: Petri nets; resource allocation; flexible manufacturing systems; control system synthesis

Other keywords: petri nets; weighted resource allocation systems; S3PGR2; p-vector characteristic; flexible manufacturing systems; weighted S3PR; Li and Zhou method; elementary siphons

Subjects: Control applications in manufacturing processes; Control system analysis and synthesis methods; Combinatorial mathematics; Control technology and theory (production); Manufacturing systems

References

    1. 1)
      • K. Barkaoui , J. Pradat-Peyre , Reisig . (1996) On liveness and controlled siphons in Petri nets, Petri nets, theory and application.
    2. 2)
      • Z.W. Li , J. Zhang , M. Zhao . Liveness-enforcing supervisor design for a class of generalized Petri net models of flexible manufacturing systems. IEE Proc. Control Theory Appl. , 4 , 955 - 967
    3. 3)
      • Z.W. Li , M. Zhao . (2009) Deadlock resolution in automated manufacturing systems: a novel petri net approach.
    4. 4)
      • M.D. Jeng , X. Xie , S.L. Chung . ERCN* merged nets for modeling degraded behavior and parallel processes in semiconductor manufacturing systems. IEEE Trans. Syst., Man, Cybern. A , 1 , 102 - 112
    5. 5)
      • Lipton, R.J.: `The reachability problem requires exponential space', Report no. 62, Research, 1976, Department of Computer Science, Yale University, New Haven, CT.
    6. 6)
      • Z.W. Li , M.C. Zhou . Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems. IEEE Trans. Syst., Man, Cybern. A , 38 - 51
    7. 7)
      • D.Y. Chao . Reachability of nonsynchronized choice Petri nets and its applications. IEEE Trans. Syst., Man, and Cybern. – PART B: Cybernet. , 6 , 1013 - 1023
    8. 8)
      • J. Ezpeleta , J.M. Colom , J. Martinez . A Petri net based deadlock prevention policy for flexible manufacturing systems. IEEE Trans. Robot. Automat. , 173 - 184
    9. 9)
      • Iordache, M.V., Moody, J.O., Antsaklis, P.J.: `A method for the synthesis liveness enforcing supervisors in Petri nets', Proc. Am. Control Conf., 2001, p. 4943–4948.
    10. 10)
      • J. Park , S.A. Reveliotis . Deadlock avoidance in sequential resource allocation systems with multiple resource acquisitions and flexible routings. IEEE Trans. Automat. Contr. , 1572 - 1583
    11. 11)
      • D.Y. Chao . Computation of elementary siphons in Petri nets for deadlock control. Comput. J. , 4 , 470 - 479
    12. 12)
      • Tricas, F., Martinez, J.: `An extension of the liveness of concurrent sequential processes competing for shared resources', Proc. IEEE Int. Conf. System, Man, Cybernetics, 1995, Vancouver, BC, Canada, p. 4119–4124.
    13. 13)
      • D.Y. Chao , D.T. Wang . Two theoretical and practical aspects of knitting technique – invariants and a new class of Petri net. IEEE Trans. Syst., Man, Cybern. , 962 - 977
    14. 14)
      • D.Y. Chao . Revised dependent siphons. Int. J. Adv. Manuf. Technol. , 1 , 182 - 188
    15. 15)
      • T. Murata . Petri nets: properties, analysis and applications. Proc. IEEE , 4 , 541 - 580
    16. 16)
      • I.B. Abdallah , H.A. ElMaraghy . Deadlock prevention and avoidance in FMS: a Petri net based approach. Int. J. Adv. Manuf. Technol. , 10 , 704 - 715
    17. 17)
      • D.Y. Chao . Incremental approach to computation of elementary siphons for arbitrary S3PR. Control Theory Appl. IET , 2 , 168 - 179
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