Duality between invariant spaces for max-plus linear discrete event systems

Michael Di Loreto; Stéphane Gaubert; Ricardo D. Katz; Jean Jacques Loiseau

doi:10.1137/090747191

Duality between invariant spaces for max-plus linear discrete event systems

Michael Di Loreto
, Stéphane Gaubert
, Ricardo D. Katz
, Jean Jacques Loiseau

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

Abstract

We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.

Original language	English
Pages (from-to)	5606-5628
Number of pages	23
Journal	SIAM Journal on Control and Optimization
Volume	48
Issue number	8
DOIs	https://doi.org/10.1137/090747191
Publication status	Published - 1 Jan 2010

Keywords

Conditioned invariance
Controlled invariance
Discrete event systems
Duality
Dynamic observer
Geometric control
Max-plus algebra
Tropical semiring

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10.1137/090747191

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abstract = "We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.",

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AB - We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.

KW - Conditioned invariance

KW - Controlled invariance

KW - Discrete event systems

KW - Duality

KW - Dynamic observer

KW - Geometric control

KW - Max-plus algebra

KW - Tropical semiring

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M3 - Article

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JF - SIAM Journal on Control and Optimization

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ER -

Duality between invariant spaces for max-plus linear discrete event systems

Abstract

Keywords

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