Relative Observability and Coobservability of Timed Discrete-Event Systems

We study supervisory control of timed discrete-event systems (TDES) under partial observation, and propose new observability concepts effective for supervisor synthesis. First, we consider monolithic/centralized supervisory control, and introduce timed relative observability and timed relative weak observability. The former concept extends our previous work to the timed case, while the latter exploits choices of forcible events to preempt the clock event tick. We prove that timed relative (respectively, weak) observability is stronger than timed (respectively, weak) observability, weaker than normality, and closed under set union; hence there exists the supremal relatively (respectively, weakly) observable sublanguage of a given language. We move on to study decentralized supervisory control of TDES, and propose timed relative coobservability and timed relative weak coobservability as extensions of their centralized counterparts. It is shown that timed relative (respectively, weak) coobservability is stronger than timed (respectively, weak) coobservability, weaker than conormality, and closed under set union; therefore the supremal relatively (respectively, weakly) coobservable sublanguage of a given language exists. Finally, algorithms are designed to compute the supremal relatively (weakly) (co)observable and controllable sublanguages, which are demonstrated with a Guideway example.