Title :
Extremal solutions of inequations over lattices with applications to supervisory control
Author :
Kumar, Ratnesh ; Garg, Vijay K.
Author_Institution :
Dept. of Electr. Eng., Kentucky Univ., Lexington, KY, USA
Abstract :
We study the existence and computation of extremal solutions of a system of inequations defined over lattices. Using the Knaster-Tarski fixed point theorem, we obtain sufficient conditions for the existence of supremal as well as infimal solution of a given system of inequations. Iterative techniques are presented for the computation of the extremal solutions whenever they exist, and conditions under which the termination occurs in a single iteration are provided. These results are then applied for obtaining extremal solutions of various inequations that arise in computation of maximally permissive supervisors in control of logical discrete event systems (DESs). Thus our work presents a unifying approach for computation of supervisors in a variety of situations
Keywords :
control system analysis; digital arithmetic; discrete event systems; duality (mathematics); iterative methods; Knaster-Tarski fixed point theorem; discrete event systems; extremal solutions; inequations; iterative techniques; lattices; sufficient conditions; supervisory control; Algorithm design and analysis; Application software; Computer science; Control systems; Discrete event systems; Lattices; Robots; Sufficient conditions; Supervisory control; Terminology;
Conference_Titel :
Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on
Conference_Location :
Lake Buena Vista, FL
Print_ISBN :
0-7803-1968-0
DOI :
10.1109/CDC.1994.411720
