随机激励滞回系统的非线性最优控制

Nonlinear Optimal Control of Random Excited Hysteretic Systems

基于最优多项式控制框架,将物理随机最优控制方法推广到一般非线性随机动力系统的最优控制中,发展了适用于随机激励滞回系统的非线性最优控制策略,并以随机地震动作用下Bouc-Wen系统最优控制为例进行了分析。数值算例表明,采用能量均衡的超越概率准则,1阶线性控制器可以覆盖高阶非线性控制器的控制效果,从而可以避免高阶控制器因时滞影响造成反馈误差放大、导致系统不稳定的情况。同时,滞回系统反应得到了一定程度地控制,滞回性态和耗能特性也得到了明显改善。结果表明,发展的非线性随机最优控制策略可以对一般随机激励滞回系统实施有效地控制,从而能够获得所期望的系统目标性态。

The physical stochastic optimal control strategy is extended,and a novel nonlinear optimal control method for randomly excited hysteretic systems is developed,referring to the optimal polynomial control scheme.For an illustrative purpose,the nonlinear stochastic optimal control of an earthquake-excited multi-degree-of-freedom hysteretic structure described by Bouc-Wen differential model is carried out.Numerical results reveal that the linear control with the 1st-order controller suffices even for the hysteretic systems when an exceedance probability based control criterion for designing the optimal weighting matrices is employed.This is practically meaningful since it bypasses the need to utilize nonlinear controllers which may be associated with dynamical instabilities due to time delay and computational dynamics.It is remarkable,meanwhile,that the structural response,hysteretic behavior and energy dissipation of the controlled system can be improved to a desirable performance,which elucidates the validity and applicability of the developed nonlinear stochastic optimal control methodology.