  We consider a supervisory control problem of a discrete event system (DES)
under partial observation, where a control specification is given by a fragment
of linear temporal logic. We design an on-line supervisor that dynamically
computes its control action with the complete information of the product
automaton of the DES and an acceptor for the specification. The concepts of
controllability and observability are defined by means of a ranking function
defined on the product automaton, which decreases its value if an accepting
state of the product automaton is being approached. The proposed on-line
control scheme leverages the ranking function and a permissiveness function,
which represents a time-varying permissiveness level. As a result, the on-line
supervisor achieves the specification, being aware of the tradeoff between its
permissiveness and acceptance of the specification, if the product automaton is
controllable and observable.
