Supervisory control of deterministic Petri nets with regular specification languages

Ratnesh Kumar; Lawrence E. Holloway

doi:10.1109/9.481527

Supervisory control of deterministic Petri nets with regular specification languages

Ratnesh Kumar, Lawrence E. Holloway

Institute for Sustainable Manufacturing (ISM)

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

Algorithms for computing a minimally restrictive control in the context of supervisory control of discrete-event systems have been well developed when both the plant and the desired behavior are given as regular languages. In this paper we extend such prior results by presenting an algorithm for computing a minimally restrictive control when the plant behavior is a deterministic Petri net language and the desired behavior is a regular language. As part of the development of the algorithm, we establish the following results that are of independent interest: i) the problem of determining whether a given deterministic Petri net language is controllable with respect to another deterministic Petri net language is reducible to a reachability problem of Petri nets and ii) the problem of synthesizing the minimally restrictive supervisor so that the controlled system generates the supremal controllable sublanguage is reducible to a forbidden marking problem. In particular, we can directly identify the set of forbidden markings without having to construct any reachability tree.

Original language	English
Pages (from-to)	245-249
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	41
Issue number	2
DOIs	https://doi.org/10.1109/9.481527
State	Published - 1996

Bibliographical note

Funding Information:
Algorithms for testing controllability of K with respect to L and those for computing KT have been developed when both K and L Manuscript received August 9, 1994; revised March 23, 1995, July 5, 1995, and August 21, 1995. This work was supported in part by the Center for Robotics and Manufacturing at the University of Kentucky, the NSF under Grants NSF-ECS-9308737 and NSF-ECS-9409712, NASA under Grant NGT-40049, and Rockwell International The authors are with the Department of Electrical Engineering, University of Kentucky, Lexington, KY 40506-0046 USA. Publisher Item Identifier S 0018-9286(96)00988-9.

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/9.481527

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title = "Supervisory control of deterministic Petri nets with regular specification languages",

abstract = "Algorithms for computing a minimally restrictive control in the context of supervisory control of discrete-event systems have been well developed when both the plant and the desired behavior are given as regular languages. In this paper we extend such prior results by presenting an algorithm for computing a minimally restrictive control when the plant behavior is a deterministic Petri net language and the desired behavior is a regular language. As part of the development of the algorithm, we establish the following results that are of independent interest: i) the problem of determining whether a given deterministic Petri net language is controllable with respect to another deterministic Petri net language is reducible to a reachability problem of Petri nets and ii) the problem of synthesizing the minimally restrictive supervisor so that the controlled system generates the supremal controllable sublanguage is reducible to a forbidden marking problem. In particular, we can directly identify the set of forbidden markings without having to construct any reachability tree.",

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note = "Funding Information: Algorithms for testing controllability of K with respect to L and those for computing KT have been developed when both K and L Manuscript received August 9, 1994; revised March 23, 1995, July 5, 1995, and August 21, 1995. This work was supported in part by the Center for Robotics and Manufacturing at the University of Kentucky, the NSF under Grants NSF-ECS-9308737 and NSF-ECS-9409712, NASA under Grant NGT-40049, and Rockwell International The authors are with the Department of Electrical Engineering, University of Kentucky, Lexington, KY 40506-0046 USA. Publisher Item Identifier S 0018-9286(96)00988-9.",

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PY - 1996

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N2 - Algorithms for computing a minimally restrictive control in the context of supervisory control of discrete-event systems have been well developed when both the plant and the desired behavior are given as regular languages. In this paper we extend such prior results by presenting an algorithm for computing a minimally restrictive control when the plant behavior is a deterministic Petri net language and the desired behavior is a regular language. As part of the development of the algorithm, we establish the following results that are of independent interest: i) the problem of determining whether a given deterministic Petri net language is controllable with respect to another deterministic Petri net language is reducible to a reachability problem of Petri nets and ii) the problem of synthesizing the minimally restrictive supervisor so that the controlled system generates the supremal controllable sublanguage is reducible to a forbidden marking problem. In particular, we can directly identify the set of forbidden markings without having to construct any reachability tree.

AB - Algorithms for computing a minimally restrictive control in the context of supervisory control of discrete-event systems have been well developed when both the plant and the desired behavior are given as regular languages. In this paper we extend such prior results by presenting an algorithm for computing a minimally restrictive control when the plant behavior is a deterministic Petri net language and the desired behavior is a regular language. As part of the development of the algorithm, we establish the following results that are of independent interest: i) the problem of determining whether a given deterministic Petri net language is controllable with respect to another deterministic Petri net language is reducible to a reachability problem of Petri nets and ii) the problem of synthesizing the minimally restrictive supervisor so that the controlled system generates the supremal controllable sublanguage is reducible to a forbidden marking problem. In particular, we can directly identify the set of forbidden markings without having to construct any reachability tree.

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Supervisory control of deterministic Petri nets with regular specification languages

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