Balsa, CarlosCots, OlivierGergaud, JosephWembe, Boris2023-05-102023-05-102020Balsa, Carlos; Cots, Olivier; Gergaud, Joseph; Wembe, Boris (2020). Minimum energy control of passive tracers advection in point vortices flow. In 14th International Conference on Automatic Control and Soft-Computing CONTROLO’2020. Bragançahttp://hdl.handle.net/10198/28260withNpoint 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 givena priori, in a given finite time, the control being due to the possibility of impulsionin any direction of the plane. For the energy cost, the candidates asminimizers are given by the normal extremals of the Pontryagin Maximum Principle (PMP). The transcription of the PMP gives us a set ofnonlinear equations to solve, the so-called shooting equations. We introduce these shooting equations and present numerical computationsin 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.engconference object