The controllability prefix for supervisory control under partial observation with an application to fault-tolerant control

Abstract

The controllability prefix is known as a useful concept for the discussion and solution of synthesis problems in supervisory control of cp-languages, i.e., formal languages of infinite-length words. There, the controllability prefix is defined as the set of all finite-length prefixes that can be controlled to satisfy prescribed liveness and safety properties. In this paper, we discuss a variation of the controllability prefix to address supervisory control under partial observation for regular *-languages, i.e., formal languages of finite-length words. We derive algebraic properties that are useful for a quantitative analysis on how an upper-bound language-inclusion specification affects achievable lower-bound specifications. Our study is motivated by the synthesis of fault-tolerant supervisory controllers, where the possible occurrence of a fault may restrict the achievable pre-fault behaviour so severe, that a relaxation of the upper-bound specification becomes a practical option. As our study shows, such a relaxation can be systematically constructed in terms of the controllability prefix. (