Extremal solutions of inequations over lattices with applicationsto supervisory control

摘要

We study the existence and computation of extremal solutions of asystem of inequations defined over lattices. Using the Knaster-Tarskifixed point theorem, we obtain sufficient conditions for the existenceof supremal as well as infimal solution of a given system ofinequations. Iterative techniques are presented for the computation ofthe extremal solutions whenever they exist, and conditions under whichthe termination occurs in a single iteration are provided. These resultsare then applied for obtaining extremal solutions of various inequationsthat arise in computation of maximally permissive supervisors in controlof logical discrete event systems (DESs). Thus our work presents aunifying approach for computation of supervisors in a variety ofsituations