超长索缆作为连接深海机器人与母船的重要纽带，在海洋扰动以及其自身的弹性特性等因素下，索缆的运动将导致中继器偏离期望轨迹、高频振动以及响应时滞等问题、索缆的过度振动极可能造成疲劳断裂，因此深海机器人索缆的控制受到了极大的关注。在极端工况下深海机器人索缆系统为时滞和强非线性奇异性动力学模型，现有求解方法计算效率低和收敛慢、被动控制难以抑制系统振动。本项目拟采用小波随机有限元求解系统的耦合模型，获得索缆的非线性响应、分析时滞和随机非线性对时变索缆系统的动力学相关特性。针对时变索缆耦合系统提出基于动力学模型非线性自适应鲁棒反馈控制器，从而抑制索缆与中继器的振动。本项目将深入认识具有非线性振动和时滞联合作用的分布参数系统的复杂动力学，基于动力学模型构造边界反馈控制策略、实现减小索缆的冲击载荷、延长索缆的使用寿命和提高系统的安全性，为深海机器人索缆系统的动力学分析和控制奠定理论基础。

Super-length umbilical cable is an important link between deep sea robot and mothership. However, the umbilical cable system is subjected to the harsh marine conditions and flexible stiffness, which would lead to an offset from the cage target position, high frequency vibration and response hysteresis. Since the excessive vibration would lead to premature fatigue failure of the umbilical cable, the vibration active control of the super-length umbilical cable is well motivated. The dynamic modelling of umbilical cable for the deep sea robot under extreme conditions is hysteresis, strong nonlinearity and singularity. The existing solution method has low computational efficiency and slow convergence, and passive control is not suitable for suppressing system vibration. System coupling model is solved by wavelet stochastic finite element method, which can obtain the random nonlinear response of the umbilical cable, and dynamic relation characteristics of stochastic nonlinearity and hysteresis of the time-varying umbilical cable system. A nonlinear adaptive robust feedback control will be proposed based on the time varying umbilical cable coupling system, which will effectively reduce vibration of the cage and cable. The purpose of the study is to have a deep understanding of complex dynamics of distributed parameter system with nonlinear vibration and hysteresis. The boundary feedback control strategy, constructed on the dynamic model, will reduce the impact load of the umbilical cable, extend the service life of the umbilical cable, and improve the safety of the system, which will lay the theoretical basis for the dynamic analysis and control of the deep sea robot cable system.