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Pregled bibliografske jedinice broj: 1143009

Optimal control of parabolic equations - a spectral calculus based approach.


Grubišić, Luka; Lazar, Martin; Nakić, Ivica; Tauttenhahn, Martin
Optimal control of parabolic equations - a spectral calculus based approach. // INdAM Workshop 2021 – Analysis and Numerics of Design, Control and Inverse Problems
Rim, Italija, 2021. str. 1-1 (pozvano predavanje, recenziran, sažetak, znanstveni)


CROSBI ID: 1143009 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

Naslov
Optimal control of parabolic equations - a spectral calculus based approach.

Autori
Grubišić, Luka ; Lazar, Martin ; Nakić, Ivica ; Tauttenhahn, Martin

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
INdAM Workshop 2021 – Analysis and Numerics of Design, Control and Inverse Problems / - , 2021, 1-1

Skup
INdAM Workshop 2021 – Analysis and Numerics of Design, Control and Inverse Problems

Mjesto i datum
Rim, Italija, 01.07.2021. - 07.07.2021

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Recenziran

Ključne riječi
Optimal control ; Parabolic equations ; spectral measures ; rational Krylov approximations

Sažetak
We consider an optimal control problem for a general linear parabolic equation governed by a self-adjoint operator on an abstract Hilbert space. The task consists in identifying a control (entering the system through the initial condition) that minimises a given cost functional, while steering the final state close to the given target. This can be considered as an inverse prob- lem (of initial source identification) for parabolic equations from the optimal control viewpoint. In order to efficiently deal with this problem, we propose a novel approach based on the spectral calculus for self adjoint operators and geometrical rep- resentation of the problem. We obtain closed form expression for the control solution as a function of the operator governing the dynamics of the system. Its numerical computation is performed by exploring efficient Krylov subspace tech- niques, by which one constructs a rational approximation of the aforementioned function of the operator. The efficiency of the proposed algorithm method is confirmed through nu- merical examples, which will be also presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekti:
IP-2016-06-2468 - Upravljanje dinamičkim sustavima (ConDyS) (Lazar, Martin, HRZZ - 2016-06) ( CroRIS)

Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb,
Sveučilište u Dubrovniku

Profili:

Avatar Url Martin Lazar (autor)

Avatar Url Ivica Nakić (autor)

Avatar Url Luka Grubišić (autor)

Poveznice na cjeloviti tekst rada:

indam2020.files.wordpress.com

Citiraj ovu publikaciju:

Grubišić, Luka; Lazar, Martin; Nakić, Ivica; Tauttenhahn, Martin
Optimal control of parabolic equations - a spectral calculus based approach. // INdAM Workshop 2021 – Analysis and Numerics of Design, Control and Inverse Problems
Rim, Italija, 2021. str. 1-1 (pozvano predavanje, recenziran, sažetak, znanstveni)
Grubišić, L., Lazar, M., Nakić, I. & Tauttenhahn, M. (2021) Optimal control of parabolic equations - a spectral calculus based approach.. U: INdAM Workshop 2021 – Analysis and Numerics of Design, Control and Inverse Problems.
@article{article, author = {Grubi\v{s}i\'{c}, Luka and Lazar, Martin and Naki\'{c}, Ivica and Tauttenhahn, Martin}, year = {2021}, pages = {1-1}, keywords = {Optimal control, Parabolic equations, spectral measures, rational Krylov approximations}, title = {Optimal control of parabolic equations - a spectral calculus based approach.}, keyword = {Optimal control, Parabolic equations, spectral measures, rational Krylov approximations}, publisherplace = {Rim, Italija} }
@article{article, author = {Grubi\v{s}i\'{c}, Luka and Lazar, Martin and Naki\'{c}, Ivica and Tauttenhahn, Martin}, year = {2021}, pages = {1-1}, keywords = {Optimal control, Parabolic equations, spectral measures, rational Krylov approximations}, title = {Optimal control of parabolic equations - a spectral calculus based approach.}, keyword = {Optimal control, Parabolic equations, spectral measures, rational Krylov approximations}, publisherplace = {Rim, Italija} }




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