| Fairness in supervisory control is defined and studied for discrete-event systems when they are represented by finite deterministic automata, or correspondingly by regular languages. The notions of weak and strong fairness are adapted to address the issue of fairness in open- and closed-loop systems. It is argued that since all controllers in practice are finite-state, when synthesizing a controller one need only consider the bounded fair designs. When a bound is specified, the supremal fair restriction of a system exists in both cases and is computed in time polynomial in the state size of the system. Priority relations are reintroduced as a convenient way to describe precedence among events; however, it is shown that under priorities a supremal fair design may not exist in general. Lastly, queues are introduced as an efficient way to implement fairness hierarchically. |
