A hierarchical and modular control architecture for sequential behaviours

This paper develops a hierarchical and modular control architecture for so called sequential behaviours, i.e. for plant dynamics and specifications that are represented as formal languages of infinite-length words. Our main result is the elaboration of structural properties that allow for abstraction based controller design and that are preserved under closed-loop composition. Thus, we propose to alternate controller design, closed-loop composition and abstraction in order to construct a hierarchical control system in a bottom-up fashion. When the overall plant is composed from a number of components, our approach naturally extends to the alternation of controller design, closed-loop composition, abstraction and component composition. Technically, our results are based on the notion of input-output systems known from behavioural systems theory, with a particular focus on liveness properties represented as sequential behaviours that are not necessarily topologically closed.