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In the supervisory control framework of discrete-event systems (DES) withinfinite behavior initiated by Thistle and Wonham, a supervisor satisfying theminimal acceptable specification and the maximal legal specification issynthesized. However, this supervisor may incur livelocks as it cannot ensurethat the infinite behavior under supervision will always visit some markerstates. To tackle this problem, we propose the definition of markability byrequiring that all infinite cycles include at least one marker state. Then weformulate the problem of $\omega-$nonblocking supervisory control of DES withinfinite behavior to synthesize an $\omega-$nonblocking (i.e. nonblocking,deadlock-free and livelock-free) supervisor. An algorithm is proposed toachieve $\omega-$nonblockingness by computing the supremal $*-$controllable,$*-$closed, $\omega-$controllable and markable sublanguage. We utilize theexample of a robot as a running example.

$\omega-$nonblocking supervisory control of discrete-event systems with infinite behavior