Actuator design for parabolic distributed parameter systems with the moment method
Entity
UAM. Departamento de MatemáticasPublisher
Society for Industrial and Applied MathematicsDate
2017-04-06Citation
10.1137/16M1058418
SIAM Journal on Control and Optimization 55.2 (2017): 1128-1152
ISSN
0363-0129 (print); 1095-7138 (online)DOI
10.1137/16M1058418Funded by
The first author was partially supported by ANR project OPTIFORM. This work was partially supported by Advanced Grant DYCON (Dynamic Control) of the European Research Council Executive Agency, GA 694126, ICON of the French ANR-2016-ACHN-0014-01, FA9550-15-1-0027 of AFOSR, A9550-14-1-0214 of EOARD-AFOSR, and grant MTM2014-52347 of MINECO (Spain)Project
info:eu-repo/grantAgreement/EC/H2020/694126/EU//DYCON; Gobierno de España. MTM2014-52347Editor's Version
https://doi.org/10.1137/16M1058418Subjects
Heat equation; Lumped control; Moment method; Null controllability; Parabolic systems; Shape optimization; MatemáticasNote
First Published in SIAM Journal on Control and Optimization in Volume 55, Issue 2, 2017, Pages 1128-1152, published by the Society for Industrial and Applied Mathematics (SIAM)Rights
© by SIAM 2017. Unauthorized reproduction of this article is prohibitedAbstract
In this paper, we model and solve the problem of designing in an optimal way actuators for parabolic partial differential equations settled on a bounded open connected subset of Rn. We optimize not only the location but also the shape of actuators, by finding what is the optimal distribution of actuators in , over all possible such distributions of a given measure. Using the moment method, we formulate a spectral optimal design problem, which consists of maximizing a criterion corresponding to an average over random initial data of the largest L2-energy of controllers. Since we choose the moment method to control the PDE, our study mainly covers one-dimensional parabolic operators, but we also provide several examples in higher dimensions. We consider two types of controllers: Either internal controls, modeled by characteristic functions, or lumped controls, that are tensorized functions in time and space. Under appropriate spectral assumptions, we prove existence and uniqueness of an optimal actuator distribution, and we provide a simple computation procedure. Numerical simulations illustrate our results
Files in this item
Google Scholar:Privat, Yannick
-
Trelat, Emmanuel
-
Zuazua Iriondo, Enrique
This item appears in the following Collection(s)
Related items
Showing items related by title, author, creator and subject.