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Markov Clustering based Fully Automated Nonblocking Hierarchical Supervisory Control of Large-Scale Discrete-Event Systems

Yingying Liu, Zhaojian Cai, Kai Cai

TL;DR

This work addresses the computational challenge of designing nonblocking, decentralized supervisory control for large-scale discrete-event systems. It introduces a Markov clustering–based integration with a DSM/Domain Mapping Matrix encoding to automatically group supervisors and higher-level abstractions into clusters, enabling scalable hierarchical synthesis. The authors prove that the resulting hierarchy remains globally nonblocking and maximally permissive under the same projection conditions as established in prior abstraction-based methods, and provide practical guidance on tuning the inflation parameter $\beta$ to control cluster sizes. A benchmark case with automated guided vehicles demonstrates automation, compact coordinators, and performance close to monolithic control. The approach offers a structured, automatic pathway to apply hierarchical DES control in industry with adjustable computational trade-offs.

Abstract

In this paper we revisit the abstraction-based approach to synthesize a hierarchy of decentralized supervisors and coordinators for nonblocking control of large-scale discrete-event systems (DES), and augment it with a new clustering method for automatic and flexible grouping of relevant components during the hierarchical synthesis process. This method is known as Markov clustering, which not only automatically performs grouping but also allows flexible tuning the sizes of the resulting clusters using a single parameter. Compared to the existing abstraction-based approach that lacks effective grouping method for general cases, our proposed approach based on Markov clustering provides a fully automated and effective hierarchical synthesis procedure applicable to general large-scale DES. Moreover, it is proved that the resulting hierarchy of supervisors and coordinators collectively achieves global nonblocking (and maximally permissive) controlled behavior under the same conditions as those in the existing abstraction-based approach. Finally, a benchmark case study is conducted to empirically demonstrate the effectiveness of our approach.

Markov Clustering based Fully Automated Nonblocking Hierarchical Supervisory Control of Large-Scale Discrete-Event Systems

TL;DR

This work addresses the computational challenge of designing nonblocking, decentralized supervisory control for large-scale discrete-event systems. It introduces a Markov clustering–based integration with a DSM/Domain Mapping Matrix encoding to automatically group supervisors and higher-level abstractions into clusters, enabling scalable hierarchical synthesis. The authors prove that the resulting hierarchy remains globally nonblocking and maximally permissive under the same projection conditions as established in prior abstraction-based methods, and provide practical guidance on tuning the inflation parameter to control cluster sizes. A benchmark case with automated guided vehicles demonstrates automation, compact coordinators, and performance close to monolithic control. The approach offers a structured, automatic pathway to apply hierarchical DES control in industry with adjustable computational trade-offs.

Abstract

In this paper we revisit the abstraction-based approach to synthesize a hierarchy of decentralized supervisors and coordinators for nonblocking control of large-scale discrete-event systems (DES), and augment it with a new clustering method for automatic and flexible grouping of relevant components during the hierarchical synthesis process. This method is known as Markov clustering, which not only automatically performs grouping but also allows flexible tuning the sizes of the resulting clusters using a single parameter. Compared to the existing abstraction-based approach that lacks effective grouping method for general cases, our proposed approach based on Markov clustering provides a fully automated and effective hierarchical synthesis procedure applicable to general large-scale DES. Moreover, it is proved that the resulting hierarchy of supervisors and coordinators collectively achieves global nonblocking (and maximally permissive) controlled behavior under the same conditions as those in the existing abstraction-based approach. Finally, a benchmark case study is conducted to empirically demonstrate the effectiveness of our approach.

Paper Structure

This paper contains 5 sections, 1 theorem, 6 equations, 1 figure, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. PRELIMINARIES AND PROBLEM STATEMENT
  3. Abstraction-based Approach with Markov Clustering
  4. Case study
  5. Conclusions

Key Result

Theorem 1

The outputs of Algorithm 1 --- $\textbf{SUP}_i$ ($i \in I$) and ${\bf CO}_j$ ($j \in J$) --- collectively solve the Nonblocking Hierarchical Control Problem; namely (co) holds.

Figures (1)

  • Figure 1: 10-state coordinator CO ($\beta = 4$)

Theorems & Definitions (2)

  • Theorem 1
  • Remark 1