access icon free Optimal controllability of 3-composed siphons in a class of Petri nets

A controllability condition of a siphon composed of three elementary ones in a class of Petri nets, namely S3PR, is developed. Under the condition, a maximally permissive liveness-enforcing supervisor expressed by a set of monitors (control places) can be decided by an algorithm with polynomial complexity for an S3PR if every dependent siphon is m-composed with m ≤ 3.

Inspec keywords: polynomials; flexible manufacturing systems; computational complexity; controllability; optimal control; Petri nets

Other keywords: Petri nets; flexible manufacturing systems; optimal controllability; S3PR; maximally permissive liveness-enforcing supervisor; polynomial complexity; 3-composed siphons

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

References

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      • 3. Uzam, M.: ‘An optimal deadlock prevention policy for flexible manufacturing systems using Petri net models with resources and the theory of regions’, Int. J. Adv. Manuf. Tech., 2002, 19, pp. 192208.
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      • 1. Fanti, M.P., Zhou, M.: ‘Deadlock control methods in automated manufacturing systems’, IEEE Trans. Syst., Man, Cybern., A., 2004, 34, pp. 522 (doi: 10.1109/TSMCA.2003.820590).
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      • 2. Li, Z.W., Zhou, M.C.: ‘Deadlock resolution in automated manufacturing systems: a novel Petri net approach’ (Springer, Berlin, 2009).
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      • 4. Hou, Y.F., Li, Z.W., Al-Ahmari, A.M.: ‘On optimal controllability of 2-composed siphons in a class of Petri nets’, Electron. Lett., 2012, 48, (24), pp. 15351537 (doi: 10.1049/el.2012.2336).
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      • 5. Li, Z.W., Zhou, M.C.: ‘On siphon computation for deadlock control in a class of Petri nets’, IEEE Trans. Syst., Man, Cybern., A., 2008, 38, pp. 667679.
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