Combined Top-down and Bottom-up Approach to Multilevel Supervisory Control

TL;DR

This paper integrates top-down and bottom-up methods for multilevel supervisory control of discrete-event systems, enhancing efficiency and generality, and provides polynomial-time solutions for complex cases.

Contribution

It introduces a combined approach that leverages the strengths of both methods and extends the theory to non-prefix-closed languages with polynomial-time algorithms.

Findings

Combined approach reduces complexity and maintains permissiveness.

A posteriori supervisors do not affect maximal permissiveness in prefix-closed cases.

Polynomial-time procedure for non-prefix-closed languages is developed.

Abstract

Recently, we have proposed two complementary approaches, top-down and bottom-up, to multilevel supervisory control of discrete-event systems. In this paper, we compare and combine these approaches. The combined approach has strong features of both approaches, namely, a lower complexity of the top-down approach with the generality of the bottom-up approach. We show that, for prefix-closed languages, a posteriori supervisors computed in the bottom-up manner do not alter maximal permissiveness within the three-level coordination control architecture, that is, the supremal three-level conditionally-controllable and conditionally-normal language can always be computed in a distributed way using multilevel coordination. Moreover, a general polynomial-time procedure for non-prefix closed case is proposed based on coordinators for nonblockingness and a posteriori supervisors.