Optimal strategies to steer and control water waves

In this paper, we propose a new method for controlling surface water waves and their interaction with floating bodies. A floating target rigid body is surrounded by a control region where we design three control strategies of increasing complexity: an active strategy based on controlling the pressure at the air–water interface and two passive strategies where an additional controlled floating device is designed. Such device is modeled both as a membrane and as a thin plate and the effect of this modeling choice on the performance of the overall controlled system is analyzed. We frame this problem as an optimal control problem where the underlying state dynamics is represented by a system of coupled partial differential equations describing the interaction between the surface water waves and the floating target body in the frequency domain. An additional intermediate coupling is then added when considering the control floating device. The optimal control problem then aims at minimizing a cost functional which weights the unwanted motions of the floating body. A system of first-order necessary optimality conditions is derived and numerically solved using the finite element method. The efficacy of this new method for reducing hydrodynamic loads on floating objects has been shown through numerical simulations.