2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99439Due to the appearance of uncontrollable events in discrete event systems, one may wish to replace the behavior leading to the uncontrollability of pre-specified language by some quite similar one. To capture this similarity, we introduce metric to traditional supervisory control theory and generalize the concept of original controllability to $\ld$-controllability, where $\ld$ indicates the similarity degree of two languages. A necessary and sufficient condition for a language to be $\ld$-controllable is provided. We then examine some properties of $\ld$-controllable languages and present an approach to optimizing a realization.22 pages, 5 figuresDiscrete MathematicsB.1; I.6.8text