Minimizing Underwater Noise Generated by Submarine Maneuvering: An Optimal Control Approach

In this paper, the problem of minimizing the noise generated by the propeller and the control surfaces of a manned submarine is addressed. Cavitation attached to propeller blades and hydrofoils as well as vortex cavitation occurring at a distance from propeller blades and hydrofoils which is generated by turbulent boundary layers is considered. The main goal is to compute trajectories for different tactically relevant maneuvers that minimize the noise generated by its associated prevalent source. To this end, we consider a constrained, nonlinear, optimal control problem which has a system of 12 nonlinear differential equations as the underlaying state law and a Bolza-type cost function. The control variables are propeller revolutions, deflections of control surfaces, and the rate at which they change. After a suitable change of variables, the existence of a solution for the control problem is proved by using Filippov's theory. The problem is solved numerically with a descent method. A couple of numerical simulations complete our study.