Title :
A declarative theory for rational controllers
Author_Institution :
Boeing Comput. Services, Seattle, WA, USA
Abstract :
The author presents a computationally effective representation theory for a class of digital controllers referred to as rational controllers. The theory, which is expressed in terms of first-order predicate logic with some meta-extensions, characterizes the dynamic behavior of an element of the class using equations and inequalities that declare the structure of the controller in an algebraic variety V whose algebras satisfy the central factorization principle. The central factorization principle states that an element of an algebraic variety V is either primitive or can be expressed in finitely many different ways, in terms of operations of the algebra, on primitive elements. Important elements of V are the algebra of rational sets over the ring of real numbers, the algebra of rational trees, the algebra of rational functions on a module, the algebra of modular lattices, and direct products and limits of these algebras
Keywords :
automata theory; control system CAD; digital control; discrete systems; formal logic; knowledge based systems; IKBS; algebras; automata theory; control system CAD; declarative theory; digital controllers; discrete systems; dynamic behavior; first-order predicate logic; formal logic; meta-extensions; modular lattices; rational controllers; rational functions; rational trees; representation theory; Actuators; Algebra; Algorithm design and analysis; Analytical models; Centralized control; Computational modeling; Computer architecture; Databases; Performance analysis; Process design;
Conference_Titel :
Decision and Control, 1988., Proceedings of the 27th IEEE Conference on
Conference_Location :
Austin, TX
DOI :
10.1109/CDC.1988.194283