Chaos and Control of Ships with Water on Deck Under Periodic Excitation with Lévy Noise

Abstract

Non-linear dynamic and chaotic roll motion response of ships with water on deck induced by uncertain jumps are investigated. The huge wave with random jump can be described as Lévy noise with critical parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Through sensitive study, the stability index [Formula: see text] and the scale parameter [Formula: see text] are specified as two significant parameters in chaotic motion induction. On the same [Formula: see text] condition, the motion histories, phase portraits and Poincare maps are all recorded to highlight the effect of [Formula: see text] upon uncertain jump system, and their global bifurcation characteristics with the fluctuating amplitude [Formula: see text] are analyzed. Results show that the decrement of stability index [Formula: see text] makes the curve much thicker, and leads the acceptable stable [Formula: see text] region becomes smaller. Finally, an adaptive fuzzy sliding mode control is proposed to eliminate the chaotic behavior and stabilize the system. The asymptomatic stability from the perspective of mean square convergence is analyzed and simulated results show the effectiveness of the method.