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.

如果向量中存在一个非负积分向量集合，则表示该集合为右封闭向量，这意味着所有按词项计算的较大向量也都属于该集合。如果在该组中的任何标记处触发任何不可控制的过渡导致在该组中也有新标记，则一组标记相对于Petri网（PN）结构是控制不变的。每个右闭合标记集都有一个唯一的至上控制不变子集，这是相对于PN结构而言控制不变的最大子集。此子集不一定是右封闭的。在本文中，我们提出了一种算法，该算法针对任意PN结构计算右上标记右上角的控制右上不变不变子集。该集合在用于一类PN结构的活动执行监督策略（LESP）的合成中起关键作用，因此，所提出的算法在用于此类PN结构的LESP的合成中起关键作用。