The infimal closed controllable superlanguage and its application in supervisory control

The supervisory control of discrete-event systems is investigated for the case in which nonblocking solutions are deemed inadequate because they are too conservative. For this purpose the infimal closed controllable superlanguage of a given language is studied. Two characterizations of the superlanguage are given, some of its properties are presented, and algorithms for its computation in the general case and in the regular case are proposed. An algorithm for the computation of the supremal controllable sublanguage is presented. It is shown that the computation of the infimal closed controllable superlanguage plays a central role in problems that involve a tradeoff between satisficing and blocking. The completely satisficing solution in supervisory control is characterized, and a general control problem called the supervisory control problem with blocking is introduced