Optimal linear estimator for discrete-time systems with random delays  

作　　者：Chunyan HAN Huanshui ZHANG Gang FENG 

机构地区：[1]School of Control Science and Engineering, University of Jinan, Jinan Shandong 250022, China [2]School of Control Science and Engineering, Shandong University, Jinan Shandong 250061, China [3]Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China

出　　处：《控制理论与应用（英文版）》2012年第1期19-27,共9页

基　　金：supported by the Natural Science Foundation of Shandong Province (No. ZR2011FQ020);the National Natural Science Foundation for Distinguished YoungScholars of China (No. 60825304);the National Natural Science Foundation of China (Nos. 61104050, 61074021)

摘　　要：In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into the one with both multiplicative noises and constant delays. Then, an estimator which includes the cases of smoothing and filter- ing, is derived via the projection formula, and the solution is given in terms of a partial difference Riccati equation with boundary conditions. A predictor for such systems is also presented based on the proposed filter and smoother. The ob- tained estimators have the same dimension as the original state. Conditions for existence, uniqueness, and stability of the steady-state optimal estimators are studied for time-invariant cases. In this case, the obtained estimators are very easy to implement and all calculations can be performed off line, leading to a linear time-invariant estimator.In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into the one with both multiplicative noises and constant delays. Then, an estimator which includes the cases of smoothing and filter- ing, is derived via the projection formula, and the solution is given in terms of a partial difference Riccati equation with boundary conditions. A predictor for such systems is also presented based on the proposed filter and smoother. The ob- tained estimators have the same dimension as the original state. Conditions for existence, uniqueness, and stability of the steady-state optimal estimators are studied for time-invariant cases. In this case, the obtained estimators are very easy to implement and all calculations can be performed off line, leading to a linear time-invariant estimator.

关 键 词：Optimal estimator Random delay Projection formula Partial difference equations Asymptotic stability 

分 类 号：TP271.8[自动化与计算机技术—检测技术与自动化装置] O212.1[自动化与计算机技术—控制科学与工程]