Non-blocking Supervisory Control of Nondeterministic Systems via Prioritized Synchronization 1

In a previous paper [15], we showed that supervisory control of nondeterministic discrete event systems, in the presence of driven events, can be achieved using prioritized synchronous composition as a mechanism of control, and trajectory models as a modeling formalism, rst introduced by Heymann [4]. The speci cations considered in [15] were given by pre x-closed languages. In this paper, we extend this work to to include markings so that non-closed speci cations and issues such as blocking can be addressed. It is shown that the usual notion of non-blocking, called language model non-blocking, may not be adequate in the setting of nondeterministic systems, and a stronger notion, called trajectory model non-blocking, is introduced. Necessary and su cient conditions for the existence of language model non-blocking as well as trajectory model non-blocking supervisors are obtained for nondeterministic systems in the presence of driven events in terms of extended controllability and relative-closure conditions, and a new condition called the trajectory-closure condition.