不确定结构非线性随机最优控制的鲁棒性  

Robustness of nonlinear stochastic optimal control for uncertain structures

作　　者：茅僰[1] 应祖光[1] 朱位秋[1] 

机构地区：[1]浙江大学应用力学研究所流体传动及控制国家重点实验室,浙江杭州310027

出　　处：《浙江大学学报（工学版）》2008年第7期1101-1105,1157,共6页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金重点资助项目(10332030);国家自然科学基金资助项目(10772159)

摘　　要：对地震地面运动引起的不确定剪切结构振动的非线性随机最优控制的鲁棒性进行了研究.基于系统参数不确定性与激励随机性的独立性假定,将具平均参数的名义结构进行模态变换解耦,运用拟可积哈密顿系统随机平均法与随机动态规划原理得到非线性随机最优控制力;利用随机平均法与概率分析估算受控的具有不确定参数结构的均方根响应、控制效果与控制效率的均值和标准差;以受控结构均方根响应、控制效果与控制效率的变差系数对不确定参数变差系数的敏感度作为鲁棒性评价指标,对非线性随机最优控制进行评价.通过对一个承受宽带随机基础激励的含不确定参数的三层剪切结构的数值计算与分析表明,该非线性随机最优控制策略对不确定参数具有很好的鲁棒性.The robustness of the nonlinear stochastic optimal control for the vibration of uncertain sheartype structure due to ground motion induced by earthquake was studied. Based on the independence between parameter uncertainty and randomness of excitation, the nominal system with average parameters was decoupled by using modal transformation and the optimal control forces were obtained by applying the stochastic averaging method for quasi integrable Hamilton systems and dynamical programming principle. The mean and standard deviation of root-mean-square response, control effectiveness and efficiency for controlled uncertain structure were predicted by using the stochastic averaging method and probabilistic analysis. The robustness of the nonlinear stochastic optimal control was evaluated in terms of the sensitivities of the variation coefficients of root-mean-square response, control effectiveness and control efficiency to those of uncertain parameters. The numerical results for an example of an uncertain three-story structure subject to wide-band random ground excitation show that the nonlinear stochastic optimal control is quite robust to the uncertain parameters.

关 键 词：不确定性结构 随机激励 随机平均法 随机动态规划 最优控制 鲁棒性 

分 类 号：O324[理学—一般力学与力学基础] O328[理学—力学]