Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction

Adrien Camille le Coent; Laurent Fribourg

doi:10.1007/978-3-030-41131-2_9

Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction

Adrien Camille le Coent^*, Laurent Fribourg

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Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

2 Citationer (Scopus)

Abstract

We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By “sufficiently large”, we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method.

Originalsprog	Engelsk
Titel	Cyber Physical Systems. Model-Based Design : 9th International Workshop, CyPhy 2019, and 15th International Workshop, WESE 2019, New York City, NY, USA, October 17-18, 2019, Revised Selected Papers
Redaktører	Roger Chamberlain, Martin Edin Grimheden, Walid Taha
Antal sider	22
Forlag	Springer
Publikationsdato	2020
Sider	181-202
ISBN (Trykt)	978-3-030-41130-5
ISBN (Elektronisk)	978-3-030-41131-2
DOI	https://doi.org/10.1007/978-3-030-41131-2_9
Status	Udgivet - 2020
Begivenhed	9th International Workshop on Model-Based Design of Cyber Physical Systems, CyPhy 2019 and 15th International Workshop on Embedded and Cyber-Physical Systems Education, WESE 2019, held in conjunction with ESWeek 2019 - New York City, USA Varighed: 17 okt. 2019 → 18 okt. 2019

Konference

Konference	9th International Workshop on Model-Based Design of Cyber Physical Systems, CyPhy 2019 and 15th International Workshop on Embedded and Cyber-Physical Systems Education, WESE 2019, held in conjunction with ESWeek 2019
Land/Område	USA
By	New York City
Periode	17/10/2019 → 18/10/2019

Navn	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Vol/bind	11971 LNCS
ISSN	0302-9743

Bibliografisk note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Adgang til dokumentet

10.1007/978-3-030-41131-2_9

https://arxiv.org/pdf/1907.12155.pdf

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Citationsformater

Coent, A. C. L., & Fribourg, L. (2020). Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction. I R. Chamberlain, M. Edin Grimheden, & W. Taha (red.), Cyber Physical Systems. Model-Based Design: 9th International Workshop, CyPhy 2019, and 15th International Workshop, WESE 2019, New York City, NY, USA, October 17-18, 2019, Revised Selected Papers (s. 181-202). Springer. https://doi.org/10.1007/978-3-030-41131-2_9

Coent, Adrien Camille le ; Fribourg, Laurent. / Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction. Cyber Physical Systems. Model-Based Design: 9th International Workshop, CyPhy 2019, and 15th International Workshop, WESE 2019, New York City, NY, USA, October 17-18, 2019, Revised Selected Papers. red. / Roger Chamberlain ; Martin Edin Grimheden ; Walid Taha. Springer, 2020. s. 181-202 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 11971 LNCS).

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title = "Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction",

abstract = "We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By “sufficiently large”, we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method.",

author = "Coent, {Adrien Camille le} and Laurent Fribourg",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 9th International Workshop on Model-Based Design of Cyber Physical Systems, CyPhy 2019 and 15th International Workshop on Embedded and Cyber-Physical Systems Education, WESE 2019, held in conjunction with ESWeek 2019 ; Conference date: 17-10-2019 Through 18-10-2019",

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doi = "10.1007/978-3-030-41131-2_9",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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editor = "Roger Chamberlain and {Edin Grimheden}, Martin and Walid Taha",

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Coent, ACL & Fribourg, L 2020, Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction. i R Chamberlain, M Edin Grimheden & W Taha (red), Cyber Physical Systems. Model-Based Design: 9th International Workshop, CyPhy 2019, and 15th International Workshop, WESE 2019, New York City, NY, USA, October 17-18, 2019, Revised Selected Papers. Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), bind 11971 LNCS, s. 181-202, 9th International Workshop on Model-Based Design of Cyber Physical Systems, CyPhy 2019 and 15th International Workshop on Embedded and Cyber-Physical Systems Education, WESE 2019, held in conjunction with ESWeek 2019, New York City, USA, 17/10/2019. https://doi.org/10.1007/978-3-030-41131-2_9

Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction. / Coent, Adrien Camille le; Fribourg, Laurent.
Cyber Physical Systems. Model-Based Design: 9th International Workshop, CyPhy 2019, and 15th International Workshop, WESE 2019, New York City, NY, USA, October 17-18, 2019, Revised Selected Papers. red. / Roger Chamberlain; Martin Edin Grimheden; Walid Taha. Springer, 2020. s. 181-202 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 11971 LNCS).

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

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AU - Coent, Adrien Camille le

AU - Fribourg, Laurent

PY - 2020

Y1 - 2020

N2 - We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By “sufficiently large”, we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method.

AB - We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By “sufficiently large”, we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method.

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Coent ACL, Fribourg L. Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction. I Chamberlain R, Edin Grimheden M, Taha W, red., Cyber Physical Systems. Model-Based Design: 9th International Workshop, CyPhy 2019, and 15th International Workshop, WESE 2019, New York City, NY, USA, October 17-18, 2019, Revised Selected Papers. Springer. 2020. s. 181-202. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 11971 LNCS). doi: 10.1007/978-3-030-41131-2_9

Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction

Abstract

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