在模态坐标下对结构降阶进行最优控制，用近似离散化的方法得到结构闭环响应的近似解来代替精确解。考虑结构中物理参数和几何参数的随机性，将这些随机参数用随机因子来表示。在此基础上，利用求解随机变量函数矩的方法，导出了在最优控制的作用下，随机结构位移闭环响应的均值和方差的计算表达式。通过算例考察了结构各个参数的随机性对闭环响应的影响，经与Monte Carlo数值模拟法结果比较，验证了文中理论分析和计算方法的正确性。

Abstract: Based on mode coordinate, the optimal vibration control of truss structure is designed. Using the approximately discrete method, the approximate solutions of structure closed-loop response are obtained. The approximate solutions can substitute for the exact solutions. The randomness of physical and geometric dimensions parameters of truss structure was considered and represented in the form of random factor. And then, the computational expressions of the mean value and the variance of the stochastic parameters structure closed-loop response under the optimal vibration control were derived by means of the random variable’s functional moment method. Finally, the influence of the randomness of structural physical and geometric dimensions parameters on the structure closed-loop response is analyzed by example with the method of this paper and the Monte Carlo method, validating the feasibility of this method discussed by this paper.