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A Numerical Algorithm for Optimal Control Problems with a Viscous Point Vortex

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CONTROLO 2022 (CONTROLO 2022)

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Abstract

The dynamics of passive tracers in flows dominated by perfect or viscous point vortices is a broad area of research that continues to attract the attention of numerous studies. Recently, there has been a particular interest in the application of control theory to these issues. Viscous point vortices are singular solutions of the two-dimensional incompressible Navier-Stokes equations in which the vorticity is concentrated at a finite number of points in the flow domain, each of which carries a certain amount of time-invariant circulation. By definition, a passive tracer is a point vortex with zero circulation. This paper describes some numerical investigations of passive tracers performed by viscous point vortices to find the energy-optimal displacement of a passive particle. The numerical results show the existence of near/quasi-optimal controls.

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Acknowledgements

SG was partially supported by CMUP, which is financed by national funds through FCT (Fundação para a Ciência e a Tecnologia, I.P.) within the framework of the project ref. UIDB/00144/2020; by project MAGIC POCI-01-0145-FEDER-032485, funded by FEDER via COM- PETE 2020 - POCI and by FCT/MCTES via PIDDAC; and by project SNAP NORTE-01-0145- FEDER-000085, co-financed by the European Regional Development Fund (ERDF) through the North Portugal Regional Operational Programme (NORTE2020) under Portugal 2020 Partnership Agreement.

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Authors and Affiliations

  1. Research Centre in Digitalization and Intelligent Robotics (CeDRI) - Instituto Politécnico de Bragança, Bragança, Portugal

    Carlos Balsa

  2. Centro de Matemática (Faculdade de Ciências) da Universidade do Porto, Porto, Portugal

    Sílvio M. A. Gama

Authors
  1. Carlos Balsa
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  2. Sílvio M. A. Gama
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Corresponding author

Correspondence to Carlos Balsa .

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Editors and Affiliations

  1. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Luís Brito Palma

  2. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Rui Neves-Silva

  3. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Luís Gomes

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Balsa, C., Gama, S.M.A. (2022). A Numerical Algorithm for Optimal Control Problems with a Viscous Point Vortex. In: Brito Palma, L., Neves-Silva, R., Gomes, L. (eds) CONTROLO 2022. CONTROLO 2022. Lecture Notes in Electrical Engineering, vol 930. Springer, Cham. https://doi.org/10.1007/978-3-031-10047-5_64

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