Balsa, CarlosCots, OlivierGergaud, JosephWembe, Boris2023-02-282023-02-282021Balsa, Carlos; Cots, Olivier; Gergaud, Joseph; Wembe, Boris (2021). Minimum energy control of passive tracers advection in point vortices flow. In 14th APCA International Conference on Automatic Control and Soft Computing, CONTROLO 2020. Cham: Springer Nature, p. 232-242. ISBN 978-3-030-58652-2978-3-030-58652-2http://hdl.handle.net/10198/27297In 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 is 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.engHelhmoltz-Kirchhoff N vortices modelEnergy minimizationPontryagin maximum principleIndirect shooting methodconference paper10.1007/978-3-030-58653-9_22