Dynamical consistency in hierarchical supervisory control

A hierarchical control theory is presented founded upon the Trace-dynamical consistency (DC) property, which is an extension of the notion of dynamical consistency [1]-[3] to the supervisory case of automata with disablable transitions. Partitions of a system state space are considered for which the Trace-DC and, further, the (nonblocking) IBC conditions hold; it is shown, respectively, that low-level nonblocking controllable languages project up to such languages in the high-level system, and (when the (nonblocking) IBC condition also holds), high-level nonblocking controllable languages map down to such languages in the low-level system. It is demonstrated that the resulting pairs of low-level and high-level languages satisfy a version of the hierarchical consistency condition found in the existing language-based hierarchical supervisory control theory [4]. The structures produced in the formulation of hierarchical control in this paper permit efficient regulator design (and, in particular, repeated redesign) for hierarchy-compatible language specifications; such hierarchy-compatible language specifications consist of low-level languages whose maximal controllable sublanguages are realizable by a combination of a high-level (possibly history dependent) regulator and a set of (state-dependent) low-level regulators (specified block-wise). An algorithm is proposed which facilitates the construction of (nonblocking) IBC partitions of systems with vocalized states. Examples are presented including a material transfer line with re-entrant flow and a double queue.