Extremal Solutions of Inequations over Lattices with Applications to Supervisory Control

We study the existence and computation of extremal solutions of a system of inequations de ned over lattices. Using the Knaster-Tarski xed point theorem, we obtain sucient conditions for the existence of supremal as well as inmal 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) rst studied by Ramadge and Wonham. Thus our work presents a unifying approach for computation of supervisors in a variety of situations