不确定结构非线性随机最优控制的鲁棒性

英文篇名：Robustness of nonlinear stochastic optimal control for uncertain structures
中文刊名：浙江大学学报(工学版)
英文刊名：Journal of Zhejiang University(Engineering Science)
作者：茅僰 ; 应祖光 ; 朱位秋
英文作者：MAO Bo ; YING Zu-guang ; ZHU Wei-qiu(State Key Lab of Fluid Power Transmission and Control ; Institute of Applied Mechanics ; Zhejiang University ; Hangzhou 310027 ; China)
中文关键词：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
英文关键词：uncertain structure ; random excitation ; stochastic averaging method ; stochastic dynamical programming ; optimal control ; robustness
出版日期：2008-07-15
机构：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;
年：2008
期：07
出版单位：浙江大学学报(工学版)

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 shear-type 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.

引文

[1]YONG Jiong-min,ZHOU Xun-yu.Stochastic controls:Hamiltonian systems and HJB equations[M].NewYork:Springer Verlag,1999.
    [2]ZHU Wei-qiu,YING Zu-guang.Optimal nonlinear feed-back control of quasi-Hamiltonian systems[J].Sciencein China,1999,Series A,42(11):1213-1219.
    [3]ZHU Wei-qiu,YING Zu-guang,SOONG T T.An opti-mal nonlinear feedback control strategy for randomly ex-cited structural systems[J].Nonlinear Dynamics,2001,24(1):31-51.
    [4]ZHU Wei-qiu,YING Zu-guang.Nonlinear stochasticoptimal control of partially observable linear structures[J].Engineering Structures,2002,24(3):333-342.
    [5]ZHU Wei-qiu,YING Zu-guang.On Stochastic optimalcontrol of partially observable nonlinear quasi Hamilto-nian systems[J].Journal of Zhejiang University:Sci-ence,2004,5(11):1313-1317.
    [6]ZHU Wei-qiu,DENG Mao-lin.Optimal bounded con-trol for minimizing the response of quasi integrableHamiltonian systems[J].International Journal of Non-Linear Mechanics,2004,39(9):1535-1546.
    [7]YING Zu-guang,ZHU Wei-qiu.A stochastically aver-aged optimal control strategy for quasi-Hamiltonian sys-tems with actuator saturation[J].Automatica,2006,42(9):1577-1582.
    [8]YING Zu-guang,ZHU Wei-qiu,SOONG T T.A sto-chastic optimal semi-active control strategy for ER/MRdampers[J].Journal of Sound and Vibration,2003,259(1):45-62.
    [9]DONG Lei,YING Zu-guang,ZHU Wei-qiu.Stochasticoptimal semi-active control of nonlinear systems usingMR damper[J].Advances in Structural Engineering,2004,7(6):485-494.
    [10]CHENG Hui,ZHU Wei-qiu,YING Zu-guang.Stochasticoptimal semi-active control of hysteretic systems by using amagneto-rheological damper[J].Smart Materials andStructures,2006,15(3):711-718.
    [11]SPENCER B F,DYKE S J,DEOSKAR H S.Bench-mark problems in structural control:Part I-activemass driver system[J].Earthquake Engineering andStructural Dynamics,1998,27(11):1127-1139.