  Due 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.
