A hierarchical control architecture for sequential behaviours

This paper develops a hierarchical 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 (a) allow for abstraction based controller design and that (b) 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. Technically, our results are based on a variation of input-output systems as introduced by Willems (1991), with a particular focus on liveness properties, i.e., sequential behaviours that are not necessarily topologically closed.