Effectiveness and mechanism of broaching-to prevention using global optimal control with evolution strategy (CMA-ES)

This paper demonstrates the effectiveness of using global optimal rudder control with the covariance matrix adaptation evolution strategy, applied to a surge-sway-yaw-roll coupled numerical model, in preventing broaching-to, occurring under conventional PD rudder controls in stern quartering waves. In particular, the PD control with optimized PD parameters is more efficient than the time history-optimized approach. With the help of stability analysis of surf-riding equilibria, two different mechanisms to successfully prevent broaching-to were identified: one is to tend to a periodic orbit with additional slight rudder actions and the other is to stay in surf-riding on a position of unstable equilibrium in regular waves for a longer duration with a larger differential gain. These outcomes could facilitate real-time prevention of broaching-to in actual seas.