非线性系统随机振动响应限界极大极小控制

Optimal Bounded Control of Large Random Vibration Responses in Nonlinear Systems

研究非线性系统随机振动的限界极大极小最优控制。引入调控变量放大振动峰响应,用高阶多项式作为性能指标函数,提高其中峰值占比,建立非线性随机振动峰响应的极小化最优控制问题方程;应用随机动态规划原理建立HJB方程,考虑控制作用的有界性,确定半连续与跳变型极大极小最优控制律;最后通过数值结果,说明该最优控制能够有效地抑制非线性随机振动,并调控变量、控制界限、跳变型控制等对于控制效果的影响。

The optimal bounded minimum-maximum control for random vibration of nonlinear systems was studied. A variable was employed for rescaling system responses and a high-order power polynomial was used as the cost function of performance index for magnifying large vibration responses. The optimal bounded minimum-maximum control problem for nonlinear random vibration was expressed by a transformed differential equation and a performance index of the system. Then, the HJB equation was derived based on the random dynamical programming principle. The optimal bounded semi-continuous and switching control laws were obtained by solving the equation with the consideration of the control bound. The control effects for different variable values, control bounds, semi-continuous control and switching control were compared one-another. Numerical results show that the proposed control can effectively suppress the nonlinear random vibration.