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Control of underwater vehicles in inviscid fluids. (English) Zbl 1301.35098

The authors investigate the controllability of a vehicle in a 3D inviscid incompressible and irrotational fluid. They consider a neutrally buoyant underwater vehicle without rudder, and actuated by a few number of propellers located into some tunnels inside the rigid body. The motion of such a 3D rigid body is described by twelve functions: the three dimensional position, the attitude, the linear velocity, and the angular velocity of the vehicle. The authors give a rigorous analysis of the control of these functions.
Considering the Euler equations, they derive an initial-boundary value problem for the corresponding functions, and apply the return method of Coron. They prove that if the rigid body of the vehicle is symmetric in some sense, and a rank condition is satisfied, then the system is locally controllable around the origin in a finite time.
They give examples with six, four, or only three control inputs for a vehicle with an ellipsoidal shape.

MSC:

35Q31 Euler equations
76B75 Flow control and optimization for incompressible inviscid fluids
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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