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拉索非线性随机振动的最优有界半连续控制

     

摘要

The optimal bounded semi-continuous control of nonlinear random vibration of an inclined taut cable is studied. The nonlinear equation for transverse motion of the cable with control and excitation is derived and then converted into the vibration equations with multi-modal coupling by using Galerkin method. Considering the limitation of the control force, the equation for the random optimal control of the nonlinear cable system with multi-degree-of-freedom is established. Then, the HJB equation is determined, and the optimal bounded semi-continuous control law is obtained based on the random averaging method, dynamical programming principle and variational principle. Numerical results show that the proposed control method has good effect for the nonlinear random vibration control of the cables.%研究斜拉索非线性随机振动的最优有界半连续控制。建立受控拉索的横向非线性运动方程,运用伽辽金法推导多模态耦合的振动方程;考虑控制力的有界性,建立多自由度非线性索系统的随机最优控制问题方程,应用随机平均法、动态规划原理与变分原理确定HJB方程并得到最优有界半连续控制律,最后通过数值结果说明该最优控制对于斜拉索非线性随机振动能够达到较好的实际控制效果。

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