Linear Optimal Estimation of Discrete-time Systems with Multiple Measurement Delays
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- 英文论文题名：Linear Optimal Estimation of Discrete-time Systems with Multiple Measurement Delays
- 论文作者：Shuai Liu ; Lihua Xie
- 英文论文作者：Shuai Liu ; Lihua Xie ; School of Control Science and Engineering ; Shandong University ; School of Electrical and Electronic Engineering ; Nanyang Technological University
- 年：2017
- 作者机构：School of Control Science and Engineering,Shandong University;School of Electrical and Electronic Engineering,Nanyang Technological University;
- 英文论文关键词：Riccati Equation ; Delay Systems ; Optimal Estimation
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O21
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：246k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we consider an optimal estimation problem in the sense of least mean square error for linear discrete-time systems with multiple state delays in the measurement output. Since computation complexity is high for augmentation approach,a lot of researches have been dedicated to finding alternative ways for the optimal estimation design. In existing studies, two dimensional Riccati iteration is unavoidable for calculating the optimal gain. Meanwhile, in the continuous-time setting, the counterpart of the two dimensional Riccati equation is partial differential equation which is difficult to solve. We shall provide a new result that the gain of the optimal estimation is obtained in terms of the solution of a Retarded Riccati-like equation instead of two dimensional Riccati equation. Furthermore, by applying the result to single delay case, we have found a relationship between optimal estimation of systems with multiple delays and optimal prediction.
In this paper, we consider an optimal estimation problem in the sense of least mean square error for linear discrete-time systems with multiple state delays in the measurement output. Since computation complexity is high for augmentation approach,a lot of researches have been dedicated to finding alternative ways for the optimal estimation design. In existing studies, two dimensional Riccati iteration is unavoidable for calculating the optimal gain. Meanwhile, in the continuous-time setting, the counterpart of the two dimensional Riccati equation is partial differential equation which is difficult to solve. We shall provide a new result that the gain of the optimal estimation is obtained in terms of the solution of a Retarded Riccati-like equation instead of two dimensional Riccati equation. Furthermore, by applying the result to single delay case, we have found a relationship between optimal estimation of systems with multiple delays and optimal prediction.
In this paper, we consider an optimal estimation problem in the sense of least mean square error for linear discrete-time systems with multiple state delays in the measurement output. Since computation complexity is high for augmentation approach,a lot of researches have been dedicated to finding alternative ways for the optimal estimation design. In existing studies, two dimensional Riccati iteration is unavoidable for calculating the optimal gain. Meanwhile, in the continuous-time setting, the counterpart of the two dimensional Riccati equation is partial differential equation which is difficult to solve. We shall provide a new result that the gain of the optimal estimation is obtained in terms of the solution of a Retarded Riccati-like equation instead of two dimensional Riccati equation. Furthermore, by applying the result to single delay case, we have found a relationship between optimal estimation of systems with multiple delays and optimal prediction.
引文
[1]H.Kwakernaak,“Optimal filtering in linear systems with time delays,”IEEE Transactions on Automatic Control,vol.12,no.2,pp.169–173,1967.
[2]V.Shukla and M.D.Srinath,“Optimal filtering in linear distributed parameter systems with multiple time delays,”International Journal of Control,vol.16,no.4,pp.673–687,1972.
[3]J.Mishra and V.Rajamani,“Least-squares state estimation in time-delay systems with colored observation noise:An innovations approach,”IEEE Transactions on Automatic Control,vol.20,no.1,pp.140–142,1975.
[4]E.Fridman,U.Shaked,and L.Xie,“Robust h∞filtering of linear systems with time-varying delay,”IEEE Transactions on Automatic Control,vol.48,no.1,pp.159–165,2003.
[5]M.Basin and R.Martinez-Zuniga,“Optimal linear filtering over observations with multiple delays,”International Journal of Robust and Nonlinear Control,vol.14,no.8,pp.685–696,2004.
[6]I.Y.Song,D.Y.Kim,V.Shin,and M.Jeon,“Receding horizon filtering for discrete-time linear systems with state and observation delays,”IET Radar,Sonar&Navigation,vol.6,no.4,pp.263–271,2012.
[7]S.Kong,M.Saif,and H.Zhang,“Optimal filtering for ito?-stochastic continuous-time systems with multiple delayed measurements,”IEEE Transactions on Automatic Control,vol.58,no.7,pp.1872–1877,2013.
[8]H.Zhang,L.Xie,D.Zhang,and Y.C.Soh,“A reorganized innovation approach to linear estimation,”IEEE Transactions on Automatic Control,vol.49,no.10,pp.1810–1814,2004.
[9]X.Lu,H.Zhang,W.Wang,and K.-L.Teo,“Kalman filtering for multiple time-delay systems,”Automatica,vol.41,no.8,pp.1455–1461,2005.
[10]H.Zhang,X.Lu,and D.Cheng,“Optimal estimation for continuous-time systems with delayed measurements,”IEEE Transactions on Automatic Control,vol.51,no.5,pp.823–827,2006.
[11]H.Zhang,G.Feng,G.Duan,and X.Lu,“H∞filtering for multiple-time-delay measurements,”IEEE Transactions on Signal Processing,vol.54,no.5,pp.1681–1688,2006.
[12]H.Zhang,L.Xie,and W.Wang,“Optimal estimation for systems with time-varying delay,”pp.1391–1398,2010.
[13]S.Sun,L.Xie,W.Xiao,and Y.C.Soh,“Optimal linear estimation for systems with multiple packet dropouts,”Automatica,vol.44,no.5,pp.1333–1342,2008.
[14]C.Han and H.Zhang,“Linear optimal filtering for discretetime systems with random jump delays,”Signal Processing,vol.89,no.6,pp.1121–1128,2009.
[15]C.Han,H.Zhang,and M.Fu,“Optimal filtering for networked systems with markovian communication delays,”Automatica,vol.49,no.10,pp.3097–3104,2013.
[2]V.Shukla and M.D.Srinath,“Optimal filtering in linear distributed parameter systems with multiple time delays,”International Journal of Control,vol.16,no.4,pp.673–687,1972.
[3]J.Mishra and V.Rajamani,“Least-squares state estimation in time-delay systems with colored observation noise:An innovations approach,”IEEE Transactions on Automatic Control,vol.20,no.1,pp.140–142,1975.
[4]E.Fridman,U.Shaked,and L.Xie,“Robust h∞filtering of linear systems with time-varying delay,”IEEE Transactions on Automatic Control,vol.48,no.1,pp.159–165,2003.
[5]M.Basin and R.Martinez-Zuniga,“Optimal linear filtering over observations with multiple delays,”International Journal of Robust and Nonlinear Control,vol.14,no.8,pp.685–696,2004.
[6]I.Y.Song,D.Y.Kim,V.Shin,and M.Jeon,“Receding horizon filtering for discrete-time linear systems with state and observation delays,”IET Radar,Sonar&Navigation,vol.6,no.4,pp.263–271,2012.
[7]S.Kong,M.Saif,and H.Zhang,“Optimal filtering for ito?-stochastic continuous-time systems with multiple delayed measurements,”IEEE Transactions on Automatic Control,vol.58,no.7,pp.1872–1877,2013.
[8]H.Zhang,L.Xie,D.Zhang,and Y.C.Soh,“A reorganized innovation approach to linear estimation,”IEEE Transactions on Automatic Control,vol.49,no.10,pp.1810–1814,2004.
[9]X.Lu,H.Zhang,W.Wang,and K.-L.Teo,“Kalman filtering for multiple time-delay systems,”Automatica,vol.41,no.8,pp.1455–1461,2005.
[10]H.Zhang,X.Lu,and D.Cheng,“Optimal estimation for continuous-time systems with delayed measurements,”IEEE Transactions on Automatic Control,vol.51,no.5,pp.823–827,2006.
[11]H.Zhang,G.Feng,G.Duan,and X.Lu,“H∞filtering for multiple-time-delay measurements,”IEEE Transactions on Signal Processing,vol.54,no.5,pp.1681–1688,2006.
[12]H.Zhang,L.Xie,and W.Wang,“Optimal estimation for systems with time-varying delay,”pp.1391–1398,2010.
[13]S.Sun,L.Xie,W.Xiao,and Y.C.Soh,“Optimal linear estimation for systems with multiple packet dropouts,”Automatica,vol.44,no.5,pp.1333–1342,2008.
[14]C.Han and H.Zhang,“Linear optimal filtering for discretetime systems with random jump delays,”Signal Processing,vol.89,no.6,pp.1121–1128,2009.
[15]C.Han,H.Zhang,and M.Fu,“Optimal filtering for networked systems with markovian communication delays,”Automatica,vol.49,no.10,pp.3097–3104,2013.