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On computing the supremal right-closed control invariant subset of a right-closed set of markings for an arbitrary petri net

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Abstract

A set of non-negative integral vectors is said to be right-closed if the presence of a vector in the set implies all term-wise larger vectors also belong to the set. A set of markings is control invariant with respect to a Petri Net (PN) structure if the firing of any uncontrollable transition at any marking in this set results in a new marking that is also in the set. Every right-closed set of markings has a unique supremal control invariant subset, which is the largest subset that is control invariant with respect to the PN structure. This subset is not necessarily right-closed. In this paper, we present an algorithm that computes the supremal right-closed control invariant subset of a right-closed of markings with respect to an arbitrary PN structure. This set plays a critical role in the synthesis of Liveness Enforcing Supervisory Policies (LESPs) for a class of PN structures, and consequently, the proposed algorithm plays a key role in the synthesis of LESPs for this class of PN structures.

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Authors and Affiliations

  1. Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Roshanak Khaleghi

  2. Coordinated Science Laboratory, Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Ramavarapu S. Sreenivas

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  1. Roshanak Khaleghi
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  2. Ramavarapu S. Sreenivas
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Correspondence to Roshanak Khaleghi.

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Khaleghi, R., Sreenivas, R.S. On computing the supremal right-closed control invariant subset of a right-closed set of markings for an arbitrary petri net. Discrete Event Dyn Syst 31, 373–405 (2021). https://doi.org/10.1007/s10626-021-00340-6

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  • DOI: https://doi.org/10.1007/s10626-021-00340-6

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