Control of underwater vehicles in inviscid fluids II. Flows with vorticity
1 CMM – Centro de Modelamiento Matemático., Universidad de
Chile (UMI CNRS 2807), Avenida Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago,
2 Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272 Paris cedex 06, France.
Revised: 6 June 2016
Accepted: 7 June 2016
In a recent paper, the authors investigated the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid, assuming that the flow was irrotational. The aim of the present paper is to pursue this study by considering the more general case of a flow with vorticity. It is shown here that the local controllability of the position and the velocity of the underwater vehicle (a vector in R12) holds in a flow with vorticity whenever it holds in a flow without vorticity.
Mathematics Subject Classification: 35Q35 / 76B03 / 93B05
Key words: Underwater vehicle / fluid-structure interaction / Euler equations / vorticity / exterior domain / exact controllability / return method
© EDP Sciences, SMAI 2016