Supervisory control of real-time discrete-event systems using lattice theory

The behaviour of timed discrete-event systems (DES's) can be described by sequences of event occurrence times. These sequences can be ordered to form a lattice. Since logical (untimed) DES behaviours described by regular languages also form a lattice, questions of controllability for timed DES's may be treated in much the same manner as they are for untimed systems. In this paper we establish conditions for the controllability of timed DES performance specification which are expressed as inequations on the lattice of sequences. These specifications may take the form of sets of acceptable event occurrence times, maximum or minimum occurrence times, or limits on the separation times between events. Optimal behaviours are found as extremal solutions to these inequations using fixed point results for lattices.