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

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.