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Minimum energy control of passive tracers advection in point vortices flow

Abstract : In this work we are interested in controlling the displacement of particles in interaction with N point vortices, in a two-dimensional fluid and neglecting the viscous diffusion. We want to drive a passive particle from an initial point to a final point, both given a priori, in a given finite time, the control being due to the possibility of impulsion in any direction of the plane. For the energy cost, the candidates as minimizers are given by the normal extremals of the Pontryagin Maximum Principle (PMP). The transcription of the PMP gives us a set of nonlinear equations to solve, the so-called shooting equations. We introduce these shooting equations and present numerical computations in the cases of N = 1, 2, 3 and 4 point vortices. In the integrable case N = 1, we give complete quadratures of the normal extremals.
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https://hal.archives-ouvertes.fr/hal-02865231
Contributor : Olivier Cots <>
Submitted on : Thursday, June 11, 2020 - 3:44:54 PM
Last modification on : Saturday, June 13, 2020 - 3:46:53 AM

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  • HAL Id : hal-02865231, version 1

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Carlos Balsa, Olivier Cots, Joseph Gergaud, Boris Wembe. Minimum energy control of passive tracers advection in point vortices flow. 2020. ⟨hal-02865231⟩

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