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The existence of marker-progressive supervisory control &#x2013; about ensuring constant marker progress under specified temporal safety for a class of fair discrete-event systems (DES&#x2019;s) &#x2013; is a new control problem formulation that has been studied in terms of DES marker-controllability of a linear-time temporal logic (LTL) safety formula given in canonical form. In this paper, provided it exists, the supremal marker-controllable subformula of a given canonical temporal-safety formula for the fair DES model considered is characterized as the weakest fixpoint of some monotone operator <inline-formula> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula>. In the case where the DES model is finite state and the complete specification for constant marker progress under temporal safety is a formula of a decidable LTL fragment, it is shown that this fixpoint can be computed as the limit of the (finite) sequence of iterations of computing operator <inline-formula> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> in the syntax of LTL. Marker-progressive control synthesis by fixpoint computation can therefore be made in the same natural-language motivated algebra of LTL as writing the specification, providing the unique opportunity to exploit not only the role of fair events in DES&#x2019;s, but also the human readability of LTL formulas and the associated, syntax-based calculational approach that is transparent; such fixpoint computation is illustrated with four examples. A discussion examines and illuminates the significance of this paper and its potential impact on the logic foundation of supervisory control; it includes making comparisons with related work, and explaining a straightforward generalization of DES marker-controllability that directly extends the proposed fixpoint computation to cover the full specification hierarchy of canonical LTL.

Supremal Marker-Controllable Subformula of a Given Canonical Temporal-Safety Formula