Optimal Control of 1D Semilinear Heat Equations with Moment-SOS Relaxations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00386949" target="_blank" >RIV/68407700:21230/25:00386949 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.23919/ECC65951.2025.11187245" target="_blank" >http://dx.doi.org/10.23919/ECC65951.2025.11187245</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.23919/ECC65951.2025.11187245" target="_blank" >10.23919/ECC65951.2025.11187245</a>

Result language

angličtina

Original language name

Optimal Control of 1D Semilinear Heat Equations with Moment-SOS Relaxations

Original language description

We use moment-SOS (Sum Of Squares) relaxations to address the optimal control problem of the 1D heat equation perturbed with a nonlinear term. We extend the current framework of moment-based optimal control of PDEs to consider a quadratic cost on the control. We develop a new method to extract a nonlinear controller from approximate moments of the solution. The control law acts on the boundary of the domain and depends on the solution over the whole domain. Our method is validated numerically and compared to a linear-quadratic controller.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

20205 - Automation and control systems

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Proceedings of European Control Conference

ISBN

978-3-907144-12-1

ISSN

2996-8895

e-ISSN

2996-8917

Number of pages

6

Pages from-to

731-736

Publisher name

IEEE

Place of publication

Piscataway

Event location

Thessaloniki

Event date

Jun 24, 2025

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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