线性广义系统的最优和鲁棒满阶平滑器  

Optimal and robust full-order smoothers for linear descriptor systems

作　　者：窦寅丰[1] 孙书利[1] 冉陈键[1] DOU Yin-feng;SUN Shu-li;RAN Chen-jian(Electronic Engineering College, Heilongjiang University, Harbin Heilongjiang 150080, China)

机构地区：[1]黑龙江大学电子工程学院,黑龙江哈尔滨150080

出　　处：《控制理论与应用》2018年第2期207-214,共8页Control Theory & Applications

基　　金：国家自然科学基金项目(61573132;61203121);黑龙江省普通高等学校电子工程重点实验室(黑龙江大学)开放课题(DZGC201605);2017年度黑龙江省省属高等学校基本科研业务费科研项目资助~~

摘　　要：对于线性离散随机广义系统,利用增广状态方法将平滑器问题转化为增广状态的滤波器问题.基于极大似然线性估计准则,提出了最优的满阶平滑器,其中增广状态滤波器的误差方差阵满足广义Riccati方程.当线性离散广义系统的过程噪声和观测噪声的方差不确定时,基于极大极小鲁棒设计原理和最优满阶平滑算法,得到了鲁棒满阶平滑器.应用动态误差方差分析方法证明了其鲁棒性,即鲁棒平滑误差方差阵存在一个上界方差矩阵.数值仿真例子验证了其有效性和正确性.For the linear discrete stochastic descriptor systems,the smoothing problem has been transformed to the filtering problem of one augmented state.Based on the maxinum likelihood(ML)linear estimation criterion,the optimal full-order smoothers are presented,where the filtering error variance of the augmented state is presented based on the descriptor Riccati equation.When the variances of the process noise and the measurement noise of the descriptor systems are uncertain,robust full-order smoothers are obtained based on the max-min robust design theory and the optimal fullorder smoothing algorithm.Applying the dynamic error variance analysis(DEVA)method,the robustness is proved,i.e.,the variance matrices of the robust smoothers have upper bound variance matrices.Simulation example verifies the effectiveness.

关 键 词：广义系统 最优满阶平滑器 鲁棒满阶平滑器 鲁棒性 动态误差方差分析方法 

分 类 号：O211.64[理学—概率论与数理统计]