Formulas for a class of controllable and observable sublanguages larger than the supremal controllable and normal sublanguage
The article continues the research made by \textit{W. M. Wonham} and \textit{P. J. Ramadge} [On the supremal controllable sublanguage of a given language, SIAM J. Control. Optim. 25(3), 635-659 (1987)], \textit{R. Creslak}, \textit{C. Desclaux}, \textit{A. Fawaz} and \textit{P. Varaiya} [Supervisory control of discrete-event processes with partial observations, IEEE Trans. Automat. Control 33(3), 249-260 (1988)], \textit{F. Lin} and \textit{W. M. Wonham} [On observability of discrete event systems, Inform. Sci. 44(3), 173-198 (1988; Zbl 0644.93008)], \textit{P. S. Ramadge} and \textit{W. M. Wonham} [The control of discrete event systems, Proc IEEE 77(1), 81-98 (1984)], \textit{R. D. Brandt}, \textit{V. Garg}, \textit{R. Kumar}, \textit{F. Lin}, \textit{S. I. Marcus} and \textit{W. M. Wonham} [Formulas for calculating supremal controllable and normal sublanguages, Systems Control Lett. 15, 111-117 (1990; Zbl 0715.93044)] and \textit{R. Kumar}, \textit{V. Garg}, \textit{S. I. Marcus} [On controllability and normality of discrete event dynamical systems, Systems Control Lett. 17, 157-168 (1991; Zbl 0759.93013)]. The authors give some explicit formulas for a class of closed, controllable and observable sublanguages larger than the supremal closed, controllable and normal language. It is proved that these algorithms keep regularity invariant, and can be computed effectively; but any one of the languages obtained from these algorithms may not be the maximal controllable and observable sublanguage, so the computation of the regular maximal controllable and observable sublanguages is still an open problem.
scientific article; zbMATH DE number 205548