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Marking Data-Informativity and Data-Driven Supervisory Control of Discrete-Event Systems

Yingying Liu, Kuma Fuchiwaki, Kai Cai

TL;DR

This paper identifies and formalizes a novel concept called marking data-informativity and designs an algorithm for the verification of this concept, and develops an algorithm to compute the largest subset of control specification for which the data set is least restricted marking informative.

Abstract

In this paper we develop a data-driven approach for marking nonblocking supervisory control of discrete-event systems (DES). We consider a setup in which models of DES to be controlled are unknown, but a set of data concerning the behaviors of DES is available. We ask the question: Under what conditions of the available data set can a valid marking noblocking supervisor be designed for the unknown DES to satisfy a given specification? Answering this question, we identify and formalize a novel concept called marking data-informativity. Moreover, we design an algorithm for the verification of this concept. Next, if the data set fails to be marking informative, we propose two related new concepts of restricted marking data-informativity and marking informatizability. Finally, we develop an algorithm to compute the largest subset of control specification for which the data set is least restricted marking informative.

Marking Data-Informativity and Data-Driven Supervisory Control of Discrete-Event Systems

TL;DR

This paper identifies and formalizes a novel concept called marking data-informativity and designs an algorithm for the verification of this concept, and develops an algorithm to compute the largest subset of control specification for which the data set is least restricted marking informative.

Abstract

In this paper we develop a data-driven approach for marking nonblocking supervisory control of discrete-event systems (DES). We consider a setup in which models of DES to be controlled are unknown, but a set of data concerning the behaviors of DES is available. We ask the question: Under what conditions of the available data set can a valid marking noblocking supervisor be designed for the unknown DES to satisfy a given specification? Answering this question, we identify and formalize a novel concept called marking data-informativity. Moreover, we design an algorithm for the verification of this concept. Next, if the data set fails to be marking informative, we propose two related new concepts of restricted marking data-informativity and marking informatizability. Finally, we develop an algorithm to compute the largest subset of control specification for which the data set is least restricted marking informative.
Paper Structure (13 sections, 8 theorems, 44 equations, 15 figures, 3 algorithms)

This paper contains 13 sections, 8 theorems, 44 equations, 15 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. PRELIMINARIES AND PROBLEM STATEMENT
  3. Data-Driven Marking Supervisory Control and Marking Data-Informativity
  4. Problem Formulation of Data-Driven Marking Supervisory Control
  5. Marking Data-Informativity and Its Criterion
  6. Verification of Marking Data-Informativity
  7. Restricted Marking Data-Informativity
  8. K-informativity
  9. Marking Informatizability
  10. Least Restricted Marking Data-Informativity
  11. Non-Informative State
  12. Algorithm for Checking Marking Informatizability and Computing $K_{sup}$
  13. Conclusions

Key Result

Proposition 1

There exists a consistent plant with $(D, D_m, D^-)$ if and only if $D_m\subseteq \overline{D}$ is regular and $\overline{D} \cap D^- = \emptyset$. If $G$ is consistent with $(D, D_m, D^-)$, then $G$ is also consistent with $(\overline{D}, D_m, D^-)$. Moreover, it holds that

Figures (15)

  • Figure 1: Robot navigation: plant $G_1$.
  • Figure 2: Robot navigation: specification $K_1(\subseteq L_m(G_1))$.
  • Figure 3: $G_2$ in Example \ref{['ex2:set up']}.
  • Figure 4: $G_3$ in Example \ref{['ex2:set up']}.
  • Figure 5: Illustration of transtion for $s\in\overline{K_{D_m}}$ and $\sigma\in\Sigma_u$ in (\ref{['eq:informativity']}).
  • ...and 10 more figures

Theorems & Definitions (33)

  • Definition 1
  • Example 1
  • Example 2
  • Definition 2
  • Remark 1
  • Proposition 1
  • Definition 3
  • Definition 4
  • Theorem 1
  • Remark 2
  • ...and 23 more