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

摘要

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 Levy noise with critical parameters alpha, sigma, beta, and mu. Through sensitive study, the stability index alpha and the scale parameter sigma are specified as two significant parameters in chaotic motion induction. On the same D = sigma(alpha) condition, the motion histories, phase portraits and Poincare maps are all recorded to highlight the effect of alpha upon uncertain jump system, and their global bifurcation characteristics with the alpha fluctuating amplitude A are analyzed. Results show that the decrement of stability index alpha makes the curve much thicker, and leads the acceptable stable A 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.