Supervisory controller synthesis for decomposable deterministic context free specification languages

In this paper we consider a supervisory control problem (SCP) consisting of a regular plant language and a deterministic context free specification language, where the latter can be decomposed into a regular and a deterministic context free part. For this setup we give an implementable algorithm calculating two separate controllers for each part of the specification. We show under which conditions the parallel composition of these controllers solves the original SCP. The latter is done by reducing the problem to a special case of hierarchical decentralized control and using existing results from the literature.