Dynamics and control for multi-agent networked systems: a finite-difference approach

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dc.contributor.authorBiccari, Umberto
dc.contributor.authorKo, Dongnam
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2024-12-12T10:40:28Z
dc.date.available2024-12-12T10:40:28Z
dc.date.issued2019-04
dc.date.updated2024-12-12T10:40:28Z
dc.description.abstractWe analyze the dynamics of multi-agent collective behavior models and its control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the nonlocal transport equations commonly derived as the mean-field limit, are subordinated to the first one. In other words, the solution of the nonlocal transport model can be obtained by a suitable averaging of the diffusive one. We then address the control problem in the linear setting, linking the multi-agent model with the spatial semi-discretization of parabolic equations. This allows us to use the existing techniques for parabolic control problems in the present setting and derive explicit estimates on the cost of controlling these systems as the number of agents tends to infinity. We obtain precise estimates on the time of control and the size of the controls needed to drive the system to consensus, depending on the size of the population considered. Our approach, inspired on the existing results for parabolic equations, possibly of fractional type, and in several space dimensions, shows that the formation of consensus may be understood in terms of the underlying diffusion process described by the heat semi-group. In this way, we are able to give precise estimates on the cost of controllability for these systems as the number of agents increases, both in what concerns the needed control time horizon and the size of the controls.en
dc.description.sponsorshipThis project has received funding from the European Research Council, under the European Union’s Horizon 2020 research and innovation programme (ERC-2015-AdG-694126-DyCon). The work of the first and of the third author was partially supported by the Grants MTM2017-92996 and MTM2017-82996-C2-1-R COSNET of MINECO (Spain), by the ELKARTEK project KK-2018/00083 ROAD2DC of the Basque Government, and by the Grant FA9550-18-1-0242 of AFOSR. The work of the second author was partially supported by CNCS-UEFISCDI Grant No. PN-III-P4-ID-PCE-2016-0035. The work of the third author was partially supported by the Grant ICON of the French ANRen
dc.identifier.citationBiccari, U., Ko, D., & Zuazua, E. (2019). Dynamics and control for multi-agent networked systems: A finite-difference approach. Mathematical Models and Methods in Applied Sciences, 29(4), 755-790. https://doi.org/10.1142/S0218202519400050
dc.identifier.doi10.1142/S0218202519400050
dc.identifier.issn0218-2025
dc.identifier.urihttp://hdl.handle.net/20.500.14454/2162
dc.language.isoeng
dc.publisherWorld Scientific Publishing Co. Pte Ltd
dc.rights© 2019 World Scientific Publishing Co Pte Ltd.
dc.subject.otherCollective dynamics
dc.subject.otherConsensus
dc.subject.otherControllability
dc.subject.otherNonlocal diffusion equations
dc.subject.otherSemi-discretization of PDEs
dc.titleDynamics and control for multi-agent networked systems: a finite-difference approachen
dc.typejournal article
dcterms.accessRightsmetadata only access
oaire.citation.endPage790
oaire.citation.issue4
oaire.citation.startPage755
oaire.citation.titleMathematical Models and Methods in Applied Sciences
oaire.citation.volume29
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