带丢包不确定广义系统鲁棒Kalman预报器  

Robust Kalman Predictor for Uncertain Descriptor System with Packet Dropouts

作　　者：陶贵丽 刘文强 张兴华 牛晓霞 TAO Guili;LIU Wenqiang;ZHANG Xinghua;NIU Xiaoxia(College of Media Engineering,Communication University of Zhejiang,Hangzhou 310018;School of Information and Electronic Engineering,Zhejiang Gongshang University,Hangzhou 310018;Computer and Information Engineering College,Heilongjiang University of Science and Technology,Harbin 150001)

机构地区：[1]浙江传媒学院媒体工程学院,杭州310018 [2]浙江工商大学信息与电子工程学院,杭州310018 [3]黑龙江科技大学计算机与信息工程学院,哈尔滨150001

出　　处：《系统科学与数学》2021年第5期1215-1232,共18页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61803148);黑龙江省自然科学基金(LH2019F035);浙江传媒学院青年教师科研提升计划项目(ZC19XJ035);浙江传媒学院科研启动费项目(Z301B19539)资助课题。

摘　　要：针对一类带丢包和不确定噪声方差的广义系统,设计了鲁棒时变Kalman预报器.利用矩阵的非奇异线性变换,通过增广状态方法和虚拟噪声技术,将原系统转化为两个仅带有不确定噪声方差的降阶非广义子系统.根据极大极小鲁棒估计原理,基于带噪声方差保守上界的最坏情形子系统,得到子系统的鲁棒时变Kalman预报器.根据降阶子系统和原广义系统之间的关系,给出原系统的鲁棒时变Kalman预报器和预报误差方差阵.应用Lyapunov方程方法证明其鲁棒性,使得对于所有容许的不确定性,它的实际预报误差方差阵被保证有相应的最小上界.仿真例子验证了所提算法的有效性和正确性.This paper addresses the design of robust time-varying Kalman predictor for a class of descriptor system with packet dropouts and uncertain noise variances.Using nonsingular linear transformation of matrix,by augmented state method and fictitious noise technique,the original system is transformed into two reduced-order non-descriptor subsystems with only uncertain noise variances.According to the minimax robust estimation principle,based on the worst-case subsystems with the conservative upper bounds of the noise variances,the robust time-varying Kalman predictors are presented for the subsystems.According to the relationship between the reduced-order subsystems and the original descriptor system,the robust timevarying Kalman predictor and prediction error variance matrix of the original system are presented.Its robustness is proved by using Lyapunov equation approach,such that its actual prediction error variance is guaranteed to have the corresponding minimal upper bound for all admissible uncertainties.A simulation example shows the effectiveness and correctness of the proposed results.

关 键 词：广义系统 鲁棒预报器 丢包 不确定噪声方差 Lyapunov方程方法 

分 类 号：O211.6[理学—概率论与数理统计]