Recursive computation of limited lookahead supervisory controls for discrete event systems

Abstract

We continue the study of limited lookahead policies in supervisory control of discrete event systems undertaken in a previous paper. On-line control of discrete event systems using limited lookahead policies requires, after the execution of each event, the calculation of the supremal controllable sublanguage of a given language with respect to another larger language. These two languages are finite and represented by their tree generators, where one tree is a subtree of the other. These trees change dynamically from step to step, where one step is the execution of one event by the system. We show in this paper how to perform this calculation in a recursive manner, in the sense that the calculation for a new pair of trees can make use of the calculation for the preceding pair, thus substantially reducing the amount of computation that has to be done on-line. In order to make such a recursive procedure possible from step to step, we show how the calculation for a single step (i.e., for a given pair of trees) can itself be performed recursively by means of a backward dynamic programming algorithm on the vertices of the larger tree. These two nested recursive procedures are also extended to the limited lookahead version of the "supervisory control problem with tolerance."

On-Line Synthesis of Permissive Supervisors for Partially Observed Discrete Event Systems under scLTL Constraints

“…Researchers have overcome the difficulty by designing supervisors online. Chung et al (1992Chung et al ( , 1993Chung et al ( , 1994 proposed a method to generate limited lookahead trees on-the-fly instead of constructing a complete supervisor and their methods are extended to the settings of partial observation (Hadj-Alouane et al, 1996) or time-varying DESs (Grigorov and Rudie, 2006). Another way is taken to design on-line supervisors for partially observed DESs, where the supervisor modifies appropriate control actions precomputed in the case of full observation (Heymann and Lin, 1994;Prosser et al, 1998).…”