Dynamical consistency in hierarchical supervisory control

Abstract

A hierarchical control theory is presented founded upon the trace-dynamical consistency property, which is an extension of the notion of dynamical consistency (DC) to the supervisory case of automata with disablable transitions. Partitions of a system state space are considered for which both the trace-DC and the (non-blocking) in-block controllability (IBC) conditions hold; it is shown that low-level non-blocking controllable languages project up to such languages in the high-level system, and that, when the (non-blocking) IBC condition also holds, high-level non-blocking 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. The structures produced in the formulation of hierarchical control in this paper permit efficient regulator design (and, in particular, repeated re-design) for hierarchy-compatible language specifications; such 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 (non-blocking) IBC partitions of systems with vocalized states. Examples are presented, including a material transfer line with re-entrant flow and a double queue.