宽带激励下非线性振动系统响应的最小化控制

将一种基于广义谐和函数的随机平均法和随机动态规划原理相结合，提出了一种非线性随机最优控制方法，可以为受宽带激励的单自由度强非线性振动系统设计最优控制规律，以使得系统的稳态响应最小化。方法中的随机平均法用来得到受控系统位移幅值的Ito随机微分方程；用随机动态规划原理为系统稳态响应最小化建立动态规划方程；在控制力为有界的条件下，从动态规划方程中可以导出最优控制规律；通过求解FPK方程得到受控系统的响应。本文用一个具体的例子阐述了这一控制方法的实施过程。

Control for Minimizing the Response of Non-Linear System under Wide-Band Excitation

In this paper, a nonlinear stochastic optimal control method is proposed based on the stochastic dynamical programming principle and an averaging method which is based on generalized harmonic function. The proposed method can be used to design optimal control law to minimize the response of SDOF strongly non-linear vibration systems under wide-band excitation. The It stochastic differential equation of displacement magnitude is obtained by using the averaging method. The dynamical programming equation for minimizing the response of the system is formulated by using the stochastic dynamical programming principle. The optimal control law is derived from dynamical programming equation and the bounded control constraints condition. The response of the controlled system is obtained by solving FPK equation. An example is given in details to illustrate the proposed control method.