Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download
Contributor : Olivier Cots Connect in order to contact the contributor
Submitted on : Thursday, June 11, 2020 - 3:44:54 PM
Last modification on : Tuesday, January 11, 2022 - 3:37:06 PM


Files produced by the author(s)


  • HAL Id : hal-02865231, version 1


Carlos Balsa, Olivier Cots, Joseph Gergaud, Boris Wembe. Minimum energy control of passive tracers advection in point vortices flow. 14th International Conference on Automatic Control and Soft Computing (CONTROLO 2020), Jul 2020, Bragança, Portugal. ⟨hal-02865231⟩



Record views


Files downloads