Effective computation of an Lm(G)-closed, controllable, and observable sublanguage arising in supervisory control

In this paper we study nonblocking, supervisory control of discrete event systems under partial observation. A nonblocking supervisor can be synthesized for the supremal L_m(G)-closed, controllable, and normal sublanguage of a given (non-closed) marked language. However, such a supervisor may be too restrictive as a solution to the supervisory control problem. We identify a subclass of observable sublanguages of a given language, which has the supremal element larger than the supremal normal sublanguage. By using the supremal element, we present an iterative algorithm for computing an L_m(G)-closed, controllable and observable sublanguage of a given marked language, which is larger than the supremal L_m(G)-closed, controllable and normal sublanguage.