A framework for randomized time-splitting in linear-quadratic optimal control

Vista sencilla de Ć­tem
dc.contributor.authorVeldman, Daniƫl W. M.
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-09-04T11:14:41Z
dc.date.available2025-09-04T11:14:41Z
dc.date.issued2022-05-11
dc.date.updated2025-09-04T11:14:41Z
dc.description.abstractInspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal control. In our proposed framework, the linear dynamics of the original problem is replaced by a randomized dynamics. To obtain the randomized dynamics, the system matrix is split into simpler submatrices and the time interval of interest is split into subintervals. The randomized dynamics is then found by selecting randomly one or more submatrices in each subinterval. We show that the dynamics, the minimal values of the cost functional, and the optimal control obtained with the proposed randomized time-splitting method converge in expectation to their analogues in the original problem when the time grid is refined. The derived convergence rates are validated in several numerical experiments. Our numerical results also indicate that the proposed method can lead to a reduction in computational cost for the simulation and optimal control of large-scale linear dynamical systems.en
dc.description.sponsorshipEuropean Research Council (ERC) under the European Unionā€™s Horizon 2020 research and innovation programme (Grant agreement No: 694126-DyCon), the Alexander von Humboldt-Professorship program, the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No.765579-ConFlex and the Transregio 154 Project ā€œMathematical Modelling, Simulation and Optimization Using the Example of Gas Networksā€, project C08, of the German DFG, the grant PID2020-112617GB-C22, ā€œKinetic equations and learning controlā€ of the Spanish MINECO, and the COST Action grant CA18232, ā€œMathematical models for interacting dynamics on networksā€ (MAT-DYN-NET)
dc.identifier.citationVeldman, & Zuazua. (2022). A framework for randomized time-splitting in linear-quadratic optimal control. Numerische Mathematik, 151(2), 495-549. https://doi.org/10.1007/S00211-022-01290-3
dc.identifier.doi10.1007/S00211-022-01290-3
dc.identifier.eissn0945-3245
dc.identifier.issn0029-599X
dc.identifier.urihttps://hdl.handle.net/20.500.14454/3504
dc.language.isoeng
dc.publisherSpringer Science and Business Media Deutschland GmbH
dc.rightsĀ© The Author(s) 2022
dc.titleA framework for randomized time-splitting in linear-quadratic optimal controlen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage549
oaire.citation.issue2
oaire.citation.startPage495
oaire.citation.titleNumerische Mathematik
oaire.citation.volume151
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
Archivos
Bloque original
Mostrando 1 - 1 de 1
Miniatura
Nombre:
veldman_framework_2022.pdf
TamaƱo:
1.15 MB
Formato:
Adobe Portable Document Format
Descargar
Colecciones
ArtĆ­culos