  Recently we developed supervisor localization, a top-down approach to
distributed control of discrete-event systems (DES) with finite behavior. Its
essence is the allocation of monolithic (global) control action among the local
control strategies of individual agents. In this report, we extend supervisor
localization to study the distributed control of DES with infinite behavior.
Specifically, we first employ Thistle and Wonham's supervisory control theory
for DES with infinite behavior to compute a safety supervisor (for safety
specifications) and a liveness supervisor (for liveness specifications), and
then design a suitable localization procedure to decompose the safety
supervisor into a set of safety local controllers, one for each controllable
event, and decompose the liveness supervisor into a set of liveness local
controllers, two for each controllable event. The localization procedure for
decomposing the liveness supervisor is novel; in particular, a local controller
is responsible for disabling the corresponding controllable event on only part
of the states of the liveness supervisor, and consequently, the derived local
controller in general has states number no more than that computed by
considering the disablement on all the states. Moreover, we prove that the
derived local controllers achieve the same controlled behavior with the safety
and liveness supervisors. We finally illustrate the result by a Small Factory
example.
