
doi: 10.1007/bf01797154
An abstract hierarchical control theory is developed for discrete-event systems, based on the concepts of control structures and observers. The investigation is set in an elementary framework of formal languages constructed from the simplest principles of sets (languages) and order (lattices). The introduced concept of ``control structure'' is an abstract generalization of the family of controllable sublanguages in the standard Ramadge-Wonham approach. It is shown that, given a system endowed with a control structure, such structure is induced on image (or quotient) systems, establishing ``control consistency'' and as a consequence achieving hierarchical consistency. This abstract generalization allows a natural adaptation of the hierarchical theory to the Brandin-Wonham timed extension. The concept of ``observer'' -- a congruence with respect to a suitably defined dynamic action -- fits into the lattice-theoretic picture and provides conditions for architectural decomposition subject to the requirement of nonblocking. In the course of this development, a bridge is spanned between the observer theory of control engineering and the process-algebraic idea of ``observation equivalence'' in computer science.
Hierarchical systems, Observability, observers, abstract hierarchical control, control structures, control consistency, nonblocking, Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems), discrete-event systems, formal languages, hierarchical consistency
Hierarchical systems, Observability, observers, abstract hierarchical control, control structures, control consistency, nonblocking, Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems), discrete-event systems, formal languages, hierarchical consistency
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