  We propose an on-line supervisory control scheme for discrete event systems
(DESs), where a control specification is described by a fragment of linear
temporal logic. On the product automaton of the DES and an acceptor for the
specification, we define a ranking function that returns the minimum number of
steps required to reach an accepting state from each state. In addition, we
introduce a permissiveness function that indicates a time-varying permissive
level. At each step during the on-line control scheme, the supervisor refers to
the permissiveness function as well as the ranking function in order to
guarantee the control specification while handling the tradeoff between its
permissiveness and acceptance of the specification. The proposed scheme is
demonstrated in a surveillance problem for a mobile robot.
