A stochastic approach to the synchronization of coupled oscillators

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dc.contributor.authorBiccari, Umberto
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-08-21T09:18:32Z
dc.date.available2025-08-21T09:18:32Z
dc.date.issued2020-06-19
dc.date.updated2025-08-21T09:18:32Z
dc.description.abstractThis paper deals with an optimal control problem associated with the Kuramoto model describing the dynamical behavior of a network of coupled oscillators. Our aim is to design a suitable control function allowing us to steer the system to a synchronized configuration in which all the oscillators are aligned on the same phase. This control is computed via the minimization of a given cost functional associated with the dynamics considered. For this minimization, we propose a novel approach based on the combination of a standard Gradient Descent (GD) methodology with the recently-developed Random Batch Method (RBM) for the efficient numerical approximation of collective dynamics. Our simulations show that the employment of RBM improves the performances of the GD algorithm, reducing the computational complexity of the minimization process and allowing for a more efficient control calculation.en
dc.description.sponsorshipThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement NO.694126-DyCon). The work of both authors was partially supported by the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain) and by the Air Force Office of Scientific Research (AFOSR) under Award NO. FA9550-18-1-0242. The work of EZ was partially funded by 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, the Grant ICON-ANR-16-ACHN-0014 of the French ANR and the Transregio 154 Project Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks of the German DFGen
dc.identifier.citationBiccari, U., & Zuazua, E. (2020). A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, 8. https://doi.org/10.3389/FENRG.2020.00115
dc.identifier.doi10.3389/FENRG.2020.00115
dc.identifier.eissn2296-598X
dc.identifier.urihttps://hdl.handle.net/20.500.14454/3393
dc.language.isoeng
dc.publisherFrontiers Media S.A.
dc.rights© 2020 Biccari and Zuazua
dc.subject.otherCoupled oscillators
dc.subject.otherKuramoto model
dc.subject.otherOptimal control
dc.subject.otherSynchronization
dc.subject.otherGradient descent
dc.subject.otherRandom batch method
dc.titleA stochastic approach to the synchronization of coupled oscillatorsen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.titleFrontiers in Energy Research
oaire.citation.volume8
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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