Equivalent Existence Structures for Temporal-Safety Control

Abstract

This paper shows that beyond the expected basic results on supervisor existence and synthesis, the temporal logic systems analysis for the invariance control of an arbitrary past formula P yields new insights into supremal control. These insights come in the form of equivalent temporal characterizations. One characterization allows a natural-language interpretation which provides a very good intuitive feel of the supremal controllability concept. Another provides a structurally elegant representation revealing that the past formula P must never be stronger than some fixed logic ‘constant’. Finally, a controllable canonical form is exposed and its significance is discussed.