CAJ | 학술논문

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。
연구사랍색비선성수궤진동적최우유계반련속공제。건립수공랍색적횡향비선성운동방정，운용가료금법추도다모태우합적진동방정；고필공제력적유계성，건립다자유도비선성색계통적수궤최우공제문제방정，응용수궤평균법、동태규화원리여변분원리학정HJB방정병득도최우유계반련속공제률，최후통과수치결과설명해최우공제대우사랍색비선성수궤진동능구체도교호적실제공제효과。
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.