On Relative Observability of Timed Discrete-Event Systems

We study new observability concepts in supervisory control of timed discrete-event systems (DES) under partial observation. Known concepts in the literature are timed observability and weak observability; neither, however, is closed under set union, and consequently the supremal (weak) observable sublanguage of a given language need not exist in general. In the first part of this paper, we extend our previous work on relative observability to timed DES: a fixed, ambient language is given, relative to which timed observability is tested. Relative observability is stronger than timed observability, weaker than normality, and closed under set union. An algorithm is presented for computing the supremal relatively observable sublanguage of a given language. In the second part, we identify relative weak observability by exploiting forcible events to preempt the clock event tick. Relative weak observability is stronger than weak observability, weaker than normality, and closed under set union; we present an algorithm for computing the supremal relatively weakly observable sublanguage of a given language.