The infimal closed controllable superlanguage and its application in supervisory control

The authors address the supervisory control of discrete event systems in the case where nonblocking solutions are deemed inadequate because too conservative. For this purpose, they first contribute to the theory of controllability by studying the infimal closed controllable superlanguage of a given language. The authors give two characterizations of this language, present some of its properties, and propose algorithms for its computation in the general case and in the regular case. They also present a new algorithm for the computation of the supremal controllable sublanguage. The authors then turn their attention to supervisory control problems and show that the operation of computing the infimal closed controllable superlanguage plays a central role in problems that involve a trade-off between ‘satisficing’ and ‘blocking.’ They characterize the ‘completely satisficing solution’ in supervisory control and introduce a general control problem that the authors call ‘supervisory control problem with blocking.’