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Interpreted Higher-Dimensional Automata for Concurrent Discrete-Event Control

Dylan Bellier, Gregory Faraut, Yan Monier, Philipp Schlehuber-Caissier

Abstract

In recent years the theory of Higher Dimensional Automata (HDA) has seen significant advances from a theoretical point of view, reflecting standard automata theory. There have also been first attempts to use the mathematical framework provided by HDAs to known problems, in particular Petri Net analysis. However real-world applications are still lacking and issues from real-world system, as concurrency, is still opened in the context of controller generation. In this work we show how the framework of HDAs can be adapted to help transforming controllers given as interpreted Petri nets (IPN) into an actual closed loop controller and how the HDA helps in identifying ambiguous or even contradictory specifications that remain hidden in the IPN. We demonstrate the feasibility by connecting the obtain controller to a virtual environment for closed loop control, exemplified by an industrial example.

Interpreted Higher-Dimensional Automata for Concurrent Discrete-Event Control

Abstract

In recent years the theory of Higher Dimensional Automata (HDA) has seen significant advances from a theoretical point of view, reflecting standard automata theory. There have also been first attempts to use the mathematical framework provided by HDAs to known problems, in particular Petri Net analysis. However real-world applications are still lacking and issues from real-world system, as concurrency, is still opened in the context of controller generation. In this work we show how the framework of HDAs can be adapted to help transforming controllers given as interpreted Petri nets (IPN) into an actual closed loop controller and how the HDA helps in identifying ambiguous or even contradictory specifications that remain hidden in the IPN. We demonstrate the feasibility by connecting the obtain controller to a virtual environment for closed loop control, exemplified by an industrial example.
Paper Structure (15 sections, 1 theorem, 4 equations, 7 figures)

This paper contains 15 sections, 1 theorem, 4 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Interpreted Petri Nets
  3. Higher Dimensional Automata
  4. Formal definition
  5. From Petri Nets to HDAs
  6. Introducing Interpreted HDAs
  7. Definitions
  8. From IPN to IHDA
  9. From IHDAs to Controllers
  10. Manufacturing Example
  11. Example presentation
  12. Translation into IHDA
  13. Error Detection and Correction
  14. IHDA controller in simulation tool
  15. CONCLUSIONS

Key Result

Lemma 1

The reachability graph of Petri net $N_{}$ is isomorphic to the $1$-truncation of $\textsf{pn2HDA}(N_{})$: $G_{N_{}}^{}<1>\simeq {\textsf{pn2HDA}(N_{})}^{\leq 1}$

Figures (7)

  • Figure 1: Pipeline depicting the generation and use of the concurrent step controller (CSC).
  • Figure 2: Manufacturing example
  • Figure 3: Manufacturing example designed in the simulation tool Factory I/O
  • Figure 4: Control law designed by Interpreted Petri Net of the manufacturing system
  • Figure 5: The HDA corresponding to the Interpreted Petri Net of Figure \ref{['PN_ex']}.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Lemma 1: 4 in DBLP:conf/apn/AmraneBFHS25
  • Definition 3