网络化控制系统中状态估计问题的研究
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摘要
状态估计不仅是现代决策和控制理论的重要分支,也是保证业务流程安全性和经济性的重要先决条件。21世纪的控制系统是网络、通信与控制相结合的系统。然而,在网络化控制系统(Networked Control Systems,简称NCSs)中,由于网络的介入,控制系统的规模和复杂性显著增加,且引入了各种各样的不确定性因素,从而使得传统的状态估计理论难以适用。因此,网络化控制系统中状态估计策略研究成为自动化领域中的一个前沿课题。
本文针对网络环境下的各类不确定性,包括媒介不确定性和参数不确定性,研究了网络化控制系统中状态估计的若干问题,旨在提出相应的状态估计策略或给出状态估计稳定性条件。
在网络带宽受限情况下,针对观测值被分包传输过程中存在部分或全部Markovian丢失的线性离散系统,基于两状态Markovian丢包模型和改进的卡尔曼滤波迭代方程,给出了状态估计稳定性条件。
针对同时存在Markovian延迟与丢包的离散线性系统,通过在估计器端设置适当长度的缓存器,把具有多状态Markovian时延与丢包的离散定常系统建模成数据包到达过程为两状态Markov链模型的离散时变系统。基于设计的限定接收历史估计器(FRHE)模型,在时延有界的情况下,给出了可选增益的最优FRHE设计策略。
在通信受限同时包括量化影响、传输时延和数据丢包情况下,通过把量化影响转化为一类参数不确定性,把时延和丢包转化为随机参数,分别为线性离散系统设计了鲁棒滤波器和方差约束滤波器。
随着无线通信网络快速代替有线通信网络,多丢包问题尤为突出。针对多丢包网络中的不确定性离散系统,通过把多丢包问题建模成系统模型中的随机参数,在允许的不确定性情况下,分别设计了鲁棒滤波器和方差约束滤波器。
最后,我们给出了全文的总结及今后研究工作的方向与展望。
State estimation is not only an important branch of the modern decision-making and control theory, but also the important precondition for guaranteeing the safety and economy of business processes. In the 21st century, control system becomes an integration of network, communications and control systems. However, in Networked Control Systems (NCSs), since the introduction of network, it makes control system become larger, more complex and include various uncertainties, which makes classical state estimation theory difficult to be applicable. Hence, state estimation problems in Networked Control Systems become a forefront topic in automation field.
In the paper, in the network environment where exists various types of uncertainties including intermediate uncertainty and parameter uncertainty, some state estimation problems of Networked Control System are studied aiming to propose appropriate strategies of state estimation and some state estimation stability conditions.
When observations are partitioned into several parts to deliver through network subject to communication limitation, for discrete-time linear systems with partial or entire packet losses described by a two state Markov chain process, based on a two state Markovian packet dropout model and the expanded Kalman filter updates with partial packet, conditions for stabel estimator are given.
For discrete-time linear systems simultaneously with Markovian delay and packet loss, through setting a buffer with appropriate length at estimator site, a discrete time-invariant system with multiple-state Markovian delay and packet loss is modeled as a time-variant system whose data reception process is described by a two-state Markov chain. Based on the proposed Finite Reception History Estimator (FRHE), the optimal FRHE design strategy is proposed under a known maximum delay.
For linear discrete time-varying systems subject to limited communication capacity which includes measurement quantization, randomly transmission delay and data-packet dropouts, by transforming quantization effects into norm-bounded uncertainties and absorbing time-delay and packet loss variables into the stochastic matrices of the system's representation, robust filtering and variance-constraint filtering, respectively, are proposed.
As wired communication network is replaced by wireless communications network rapidly, multi-packet loss problem is particularly prominent. For discrete time-varying uncertainty system with multiple packet dropouts, based on transforming the consecutive packet losses rate into a stochastic parameter in the system's representation, robust filtering and variance-constraint filtering, respectively, are proposed.
本文针对网络环境下的各类不确定性,包括媒介不确定性和参数不确定性,研究了网络化控制系统中状态估计的若干问题,旨在提出相应的状态估计策略或给出状态估计稳定性条件。
在网络带宽受限情况下,针对观测值被分包传输过程中存在部分或全部Markovian丢失的线性离散系统,基于两状态Markovian丢包模型和改进的卡尔曼滤波迭代方程,给出了状态估计稳定性条件。
针对同时存在Markovian延迟与丢包的离散线性系统,通过在估计器端设置适当长度的缓存器,把具有多状态Markovian时延与丢包的离散定常系统建模成数据包到达过程为两状态Markov链模型的离散时变系统。基于设计的限定接收历史估计器(FRHE)模型,在时延有界的情况下,给出了可选增益的最优FRHE设计策略。
在通信受限同时包括量化影响、传输时延和数据丢包情况下,通过把量化影响转化为一类参数不确定性,把时延和丢包转化为随机参数,分别为线性离散系统设计了鲁棒滤波器和方差约束滤波器。
随着无线通信网络快速代替有线通信网络,多丢包问题尤为突出。针对多丢包网络中的不确定性离散系统,通过把多丢包问题建模成系统模型中的随机参数,在允许的不确定性情况下,分别设计了鲁棒滤波器和方差约束滤波器。
最后,我们给出了全文的总结及今后研究工作的方向与展望。
State estimation is not only an important branch of the modern decision-making and control theory, but also the important precondition for guaranteeing the safety and economy of business processes. In the 21st century, control system becomes an integration of network, communications and control systems. However, in Networked Control Systems (NCSs), since the introduction of network, it makes control system become larger, more complex and include various uncertainties, which makes classical state estimation theory difficult to be applicable. Hence, state estimation problems in Networked Control Systems become a forefront topic in automation field.
In the paper, in the network environment where exists various types of uncertainties including intermediate uncertainty and parameter uncertainty, some state estimation problems of Networked Control System are studied aiming to propose appropriate strategies of state estimation and some state estimation stability conditions.
When observations are partitioned into several parts to deliver through network subject to communication limitation, for discrete-time linear systems with partial or entire packet losses described by a two state Markov chain process, based on a two state Markovian packet dropout model and the expanded Kalman filter updates with partial packet, conditions for stabel estimator are given.
For discrete-time linear systems simultaneously with Markovian delay and packet loss, through setting a buffer with appropriate length at estimator site, a discrete time-invariant system with multiple-state Markovian delay and packet loss is modeled as a time-variant system whose data reception process is described by a two-state Markov chain. Based on the proposed Finite Reception History Estimator (FRHE), the optimal FRHE design strategy is proposed under a known maximum delay.
For linear discrete time-varying systems subject to limited communication capacity which includes measurement quantization, randomly transmission delay and data-packet dropouts, by transforming quantization effects into norm-bounded uncertainties and absorbing time-delay and packet loss variables into the stochastic matrices of the system's representation, robust filtering and variance-constraint filtering, respectively, are proposed.
As wired communication network is replaced by wireless communications network rapidly, multi-packet loss problem is particularly prominent. For discrete time-varying uncertainty system with multiple packet dropouts, based on transforming the consecutive packet losses rate into a stochastic parameter in the system's representation, robust filtering and variance-constraint filtering, respectively, are proposed.
引文
[1]Walsh G C, Ye H, Bushnell L. Stability analysis of networked control systems. Proc.Amer. Control Conf,1999:2876-2880.
[2]Walsh G C, Ye H, Bushnell L. Stability of networked control systems. IEEE Transactions on Control System Technology,2003,10 (3):438-446.
[3]Zhang W, Branicky M S. Stability of networked control systems. IEEE Contr. Syst. Mag, 2001,2 (1):84-99.
[4]Lian F L, Moyne J R, Tilbury D M. Performance evaluation of control networks:Ethernet, ControlNet and DeviceNet. IEEE Contr. Syst. Mag,2001,2 (1):66-83.
[5]Walsh G C, Beldiman O, Bushnell L. Asymptiotic behavior of etworked control systems. Proc.IEEE Int. Conf. on Control Applications,1999:1448-1453.
[6]Astrom K J, Wittenmark B. Computer-controlled cystems:theory and design. Upper Saddle River:Prentice Hall,1997, Third Edition.
[7]Halevi Y, Ray A. Integrated communication and control systems:Part I-Analysis. ASME Journal of Dynamic Systems, Measurement and Control,1988,110:367-373.
[8]Ray A, Liou L W, Shen J H. State estimation using randomly delayed measurements. ASME Journal of Dynamic Systems, Measurement and Control,1993,115:19-26.
[9]Chan H, Ozguner U. Closed-loop control of systems over a communications network with queues. Int. Journal of Control,1995,62 (3):493-510.
[10]于之训,陈堂辉,王月娟.时延网络控制系统均方指数稳定的研究.控制与决策,2000,15(3)：278-281.
[11]王飞跃,王成红.基于网络控制的若干基本问题的思考和分析.自动化学报,2002,28：171-176.
[12]朱其新,胡寿松,侯霞.长时滞网络控制系统的随机稳定性研究.东南大学学报,2003,33(3)：368-371.
[13]谢林柏.网络化控制系统中若干问题的研究：(博士学位论文).武汉：华中科技大学,2004.
[14]Imer O C, Basar T. Optimal estimation with limited measurements. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain:IEEE Press,2005:1029-1034.
[15]Wiener N. Extrapolation, and interpolation, and smoothing of stationary time series, with engineering applications. MIT Press, Cambridge, Mass,1949.
[16]Kalman R. E. A new approach to linear filtering and prediction problems, Trans, ASME J.Basic Eng.,1960,82:35-45.
[17]解学书，钟宜生著.H∞控制理论.北京：清华大学出版社,1994年9月.
[18]中铁龙著.H∞控制理论与应用.北京：清华大学出版社,1996年11月.
[19]Xie L H, Soh Y C, de Souza C E. Robust Kalman filtering for uncertain systems. IEEE Transactions on Automatic Control,1994,39 (6):1310-1314.
[20]Shaked U, de Souza C E. Robust minimum variance filtering. IEEE Transactions on Signal Processing,1995,43 (11):2474-2483.
[21]Theodor Y, Shaked U. Robust discrete-time minimum-variance filtering. IEEE Transactions on Signal Processing,1996,44 (2):181-189.
[22]Shaked U, Xie L H, Soh Y C. New approaches to robust minimum variance filter design. IEEE Transactions on Signal Processing,2001,49 (11):2620-2629.
[23]Zhu X, Soh Y C, Xie L H. Design and analysis of discrete-time robust Kalman filters. Automatica,2002,38:1069-1077.
[24]Bolzern P, Colaneri P, De Nicolao G. Optimal design of robust predictors for linear discrete-time systems. Systems & Control Letters,1995,26:25-31.
[25]Wang Z D, Huang B. Robust H2/H∞ filtering for linear systems with error variance constraints. IEEE Tranctions on Signal Processing,2000,48 (8):2463-2467.
[26]Fialho I J, Georgiou T T. On the L1 norm uncertain linear systems. Proceedings of the 1995 American Control Conference, Seattle, WA, USA,1995:939-943.
[27]高会军,王常虹,李艳辉.时滞不确定离散系统的鲁棒l2-l∞滤波.自动化学报,2003,29(5)：666-672.
[28]高会军,干常虹.不确定连续系统的鲁棒l2-l∞滤波新方法.自动化学报,2009,29(6)：46-53.
[29]Yaz E, Skelton R E. Continuous and discrete state estimation with error covariance assignment. Proceeding of IEEE Conference of Decision & Control, Brighton, U.K.,1991, pp:3091-3092.
[30]Wang Z D, Huang B, Huo P. Sampled-data filtering with error covariance assignment. IEEE Transaction on Signal Processing,2001,49 (3):666-670.
[3l]Yaz E, Ray A. Linear unbiased state estimation under randomly varying bounded sensor delay. Application Mathematical Letter,1998,11 (4):27-32.
[32]Evans J S, Krishnamurthy V. Hidden Markov model state estimation with randomly delayed observations. IEEE Transactions on Signal Processing,1999,47(8):2157-2166.
[33]Shu Z, Lam J, Xu S Y. Robust stabilization of Markovian delay systems with delay-dependent exponential estimates. Automatica,2006,42:2001-2008.
[34]Zhang H S, Lu X, Cheng D Z. Optimal estimation for continuous-time systems with delayed measurements. IEEE Transaction on Automatic Control,2006,51(5):823-827.
[35]Fridman E, Shaked U, Xie L. Robust H(?) filtering of linear systems with time delays. International Journal of Robust and Nonlinear Control,2003,13:983-1010.
[36]Michael B, Jesus R G, Rodolfo M Z. Optimal filtering for linear state delay systems. IEEE Transactions on Automatic Control,2005,50 (5):684-690.
[37]Michael B, Aracelia A G, Jesus R G. Optimal filtering for linear systems with state and observation delays.2005 American Control Conference, Portland, OR, USA:IEEE Press, 2005:4039-4044.
[38]Wang Z D, Yang F W, Daniel W C et al. Robust H∞ filtering for stochastic time- delay systems with missing measurements. IEEE Transactions on Signal Processing,2006,54 (7):2579-2587.
[39]Lu X, Xie L H, Zhang H S et al. Robust Kalman filtering for discrete-time systems with measurement delay. IEEE Transactions on Circuits and Systems-Ⅱ:Express Briefs,2007, 54 (6):522-526.
[40]Wang Z D, Daniel W C, Liu X H. Robust filtering under randomly varying sensor delay with variance constraints. IEEE Transactions on Circuits and Systems-II:Express Briefs, 2004,51 (6):320-326.
[41]He X, Wang Z D, Zhou D. Robust H∞ filtering for networked systems with multiple state delays. International Journal of Control,2007,80 (8):1217-1232.
[42]Wen C B, Zhen Z L, Gao H J. H∞. estimation for uncertain systems with multiple state delays. The 1st International Symposium on Systems and Control in Astronautics,2006.
[43]Schenato L. Optimal estimation in networked control systems subject to random delay and packet loss. Proceedings of the 45th Conference on Decision & Control. United States: IEEE Press,2006:5615-5620.
[44]Schenato L. Kalman filtering for networked control systems with random delay and packet loss. The 17th International Symposium on Mathematical Theory of Networks and Systems. Japan: IEEE Press,2006:1509-1517.
[45]Jin Z P, Gupta V, Hassibi B. State estimation utilizing multiple description coding over lossy networks. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain:IEEE Press,2005:872-878.
[46]Wang Z D, Ho W C, Liu X H. Variance-constrained filtering for uncertain stochastic systems with missing measurements. IEEE Transactions on Automatic Control,2003,48 (7):1254-1258.
[47]Wang Z D, Yang F W, Daniel W C et al. Robust finite-horizon filtering for stochastic system with missing measurements, IEEE Signal Processing Letters,2005,12 (6):437-440.
[48]Wang W, Yang F W. H∞ filtering design for discrete-time systems with missing measurements. Acta Automatica Sinica,2006,32(1):107-111.
[49]Sinopoli B, Schenato L, Franceschetti M et al. Kalman filtering with intermittent observations. IEEE Transactions on Automatic Control,2004,49(9):1453-1464.
[50]Liu X H, Goldsmith A. Kalman filtering with partial observation losses. The 43rd IEEE Conference on Decision & Control, Atlantis, Bahamas:IEEE Press,2004, pp:4180-4186.
[51]Huang M Y, Dey S. Kalman filtering with Markovian packet losses and stability criteria. Proceeding of the 45"'IEEE Conference on Decision & Control, San Diego, CA, USA:IEEE Press, 2006:5621-5626.
[52]Huang M Y, Dey S. Stability of Kalman filtering with Markovian packet losses. Automatica, 2007,43 (4):598-607.
[53]Smith S C, Seiler P. Estimation with lossy measurements:jump estimators for jump systems. IEEE Transactions on Automatic Control,2003,48(12):2163-2171.
[54]Plarre K, Bullo F. On Kalman filtering for detectable systems with intermittent observations. IEEE Transactions on Automatic Control,2009,54 (2):386-390.
[55]Shi L, Epstein M, Tiwari A et al. Estimation with information loss:asymptotic analysis and error bounds. Proceedings of the 44"'IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain:IEEE Press,2005:1215-1221.
[56]Sun S L, Xie L H, Xiao W D et al. Optimal linear estimation for systems with multiple packet dropouts. Automatica,2008,44:1333-1342.
[57]Sahebsara M. Optimal filtering in multiple channels networked control systems with multiple packet dropouts. Proceeding of the 47th IEEE Conference on Decision and Control. Cancun, Mexico:IEEE Press,2008:3366-3371.
[58]Sahebsara M, Chen T W, Shah S L. Optimal H(?) filtering in networked control systems with multiple packet dropouts. IEEE Transactions on Automatic Control,2007,52 (8):1508-1513.
[59]Sun S L, Xie L H, Xiao W D et al. Optimal full-order and reduced-order estimators for discrete-time systems with multiple packet dropouts. IEEE Transactions on Signal Processing,2008,56(8):4031-4038
[60]Sun S L, Xie L H, Xiao W D et al. Optimal filtering for systems with multiple packet dropouts. IEEE Transactions on Circuits and Systems-Ⅱ:Express Briefs,2008,55 (7): 695-699.
[61]Sun S L. Linear minimum variance estimators for systems with bounded random measurement delays and packet dropouts. Signal Processing,2009,89:1457-1466.
[62]Sahebsara M, Chen T W, Shah S L. Optimal H∞ filtering in networked control systems with multiple packet dropouts. Systems & Control Letters,2008,57:696-702.
[63]Sahebsara M, Chen T W, Shah S L. Optimal H(?) filtering with random sensor delay, multiple packet dropout and uncertain observations. International Journal of Control,2007,80(2): 292-301.
[64]Nair G N, Evans R J. State estimation via a capacity-limited communication channel. Proceedings of the 36th Conference on Decision & Control, Dec.1997,1:866-871.
[65]Nair G N, Evans R J. State estimation under bit-rate constraints. Proceedings of the 37th Conference on Decision & Control, De.1998,1:251-256.
[66]Nair G N, Evans R J. A finite-dimensional coder-estimator for the rate constrained state estimation. In Proceeding of the 14th IFAC World Congress,1999,1:19-24.
[67]Nair G N, Evans R J. Structural results for finite bit-rate state estimation. Proceedings of Information, Decision and Control, Feb.1999, pp:47-52.
[68]Dokuchaev N G, Savkin A V. Recursive state estimation via limited capacity communication channels. Proceedings of the 38th IEEE Conference on Decision and Control, Dec,1999, 5:4929-4932.
[69]Savkin A V, Petersen I R. Set-valued state estimation via a limited capacity communication channel. Proceedings of the 41st IEEE Conference on Decision and Control, December 2002,4:4042-4046.
[70]Malyavej V. Robust control and state estimation via limited capacity communication networks. Australia:The University of New South Wales School of Electrical Engineering and Telecommunications Sydney,2005.
[71]Li X, Wong W S. State estimation with communication constraints. System & Control Letters,1996,28:49-54.
[72]Li X, Wong W S. Constrained State Estimation for Systems with Finite Communication Bandwidth. Proceedings of the 37th IEEE Conference on Decision & Control, Dec 1998:1400-1406.
[73]Yuksel S, Basar T. Quantization for LTI Systems with noiseless channels. Proc. IEEE CCA,2003:423-429.
[74]Yuksel S, Basar T. State estimation and control for linear systems over communication networks, Proc. IEEE CCA,2003:409-414.
[75]Dong Z, You Z. Finite-horizon robust Kalman filtering for uncertain discrete time-varying systems with uncertain-convariance white noise. IEEE Signal Processing Letters,2006,13 (8):493-496.
[76]张勇,史忠科,戴冠中.离散系统的鲁棒最小方差滤波新算法及分析.自动化学报,2000,26(6)：782-787
[77]Oliveira R C L F, Peres P L D, LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions. System Control Letter,2006,55 (1):52-61
[78]Petersen I R, McFarlane D C. Robust state estimation for uncertain systems. Proceedings of the 30th Conference on Decision and Control, Brighton, England:IEEE Press, 1991:2630-2631.
[79]Petersen I R, McFarlane D C. Optimal guaranteed cost filtering for uncertain discrete-time linear systems. International Journal of Robust and Nonlinear Control,1996, 6(4):267-280.
[80]Xie L H, Soh Y C, Souza C E. Robust Kalman filtering for uncertain systems. IEEE Transactions on Automatic Control,1994,39(6):1310-1314.
[8l]Wang Z D, Guo Z, Unbehauen H. Robust H2/H∞ -state estimation for discrete-time systems with error variance constraints. IEEE Tranctions on Automatic Control,1997,42 (10):1431-1435.
[82]Hung Y S, Yang F W. Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty. Automatica,2003,39:1185-1194.
[83]Wang Z D, Fan J A. Robust H∞ filter design with variance constraints and parabolic pole assignment. IEEE Signal Processing Letters,2006,13 (3):137-140.
[84]Wang Z D, Qiao H. Robust filtering for bilinear uncertain stochastic discrete-time systems. IEEE Transaction on Signal Processing,2002,50:560-567.
[85]Yang F W, Wang Z D, Hung Y S. Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noise. IEEE Transactions on Automatic Control,2002,47 (7):1179-1183.
[86]Wang F, Balakrishnan V. Robust steady-state filtering for systems with deterministic and stochastic uncertainties. IEEE Transactions on Signal Processing,2003,51(10): 2550-2558.
[87]吴淮宁,费元春.不确定离散系统的最优鲁棒滤波.控制理论与应用,1999,16(2)：292-296.
[88]Wu A G, Duan G R. Robust H∞ estimation for uncertain contimuous-time systems. Proceedings of the 4th International Conference on Machine Learning and Cybernetics, Guangzhou, China:IEEE Press,2005:448-453.
[89]孙平,井元伟.基于采样测量值的不确定系统鲁棒H∞滤波.控制与决策,2006,21(6)：697-704
[90]陈莉,钟麦英.不确定奇异时滞系统的鲁棒H∞故障诊断滤波器设计.自动化学报,2008,34(8)：943-949
[91]Theodor Y, Shaked U. Robust discrete-time minimum-variance filtering. IEEE Transactions on Signal Processing,1996,44 (2):181-189.
[92]王武,杨富文,詹耀清.测量数据丢失的随机不确定离散系统的鲁棒H2状态估计.控制理论与应用,2008,25(3)：439-445.
[93]关新平,张群亮.不确定离散时滞系统的鲁棒H∞滤波与仿真.系统仿真学报,2002,14(8)：1078-1111.
[94]Gao H J, Chen T W. H∞ estimation for uncertain systems with limited communication capacity. IEEE Transactions on Automatic Control,2007,52(11):1310-1314.
[95]Ben-Israel A, Greville T N E. Generalized Inverses:Theory and Applications. New York: Wiley,1974.
[96]Wang Y, Xie L, de Souza C E. Robust control of a class of uncertain nonlinear systems. System Control Letter,1992,19:139-149.
[97]Matveev A, Savkin A. The problem of state estimation via asynchronous communication channels with irregular transmission times. IEEE Trans Autom Contr,2003,48 (4):670-676.
[98]Zhang H S, Xie L H, Zhang G D et al. A reorganized innovation approach to linear estimation. IEEE Trans Autom Contr,2004,49 (10):1810—1814.
[99]Gao Y, Duan G R, Meng X Y. Robust H∞ Filter design for 2D discrete systems in roesser model. International Journal of Automation and Computing,2008,4 (5):413-418.
[100]Yang L, Guan X P, Long C N et al. Feedback stabilization over wireless network using adaptive coded modulation. International Journal of Automation and Computing,2008,4 (5):381-388.
[101]Gajic Z, Qureshi M. Lyapunov matrix equation in system stability and control. Dover Publications,1995.
[102]Fu M, Xie L. The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control,2005,50(11):1698-1711.
[103]Yang F W, Wang Z D, Feng G et al. Robust filtering with randomly varying sensor delay:the finite-horizon case. IEEE Transactions on Circuits and Systems-Ⅰ:Regular papers, 2009,56(3):664-672.
[104]Elia N, Mitter S K. Stabilization of linear systems with limited information. IEEE Trans. Autom. Control,2001,46(9):1384-1400.
[105]Su C L, Lu C N. Interconnected network state estimation using randomly delayed measurements. IEEE Transactions on Power Systems,2001,16 (4):870-878.
[106]Nahi N. Optimal recursive estimation with uncertain observation. IEEE Trans. Inf. Theory,1969, IT-15(4):457-462.
[107]Hadjicostis C N, Touri R. Feedback control utilizing packet dropping network links. Proceedings of the IEEE Conference on Decision and Control,2002,2:1205-1210.
[108]Ling Q, Lemmon M. Optimal dropout compensation in networked control systems. IEEE Conference on Decision and Control,2003.1:670-675.
[109]Giorgiev D, Tilbury D. Packet-based control. Proceedings of the America Control Conference,2004:329-336.
[110]Stengel R F. Stochastic optimal control:theory and application. New York:Wiley, 1986.
[111]Beran E, Grigoriadis K. A combined alternating projections and semidefinite programming algorithm for low-order control design. Processing of the World congress of IFAC, San Francisco, CA,1996, C:85-90.
[112]Saberi A, Sannuti P, Chen B M. H2 optimal control. Series in Systems and Control Engineering, London, U.K.:rentice-Hall,1995.
[2]Walsh G C, Ye H, Bushnell L. Stability of networked control systems. IEEE Transactions on Control System Technology,2003,10 (3):438-446.
[3]Zhang W, Branicky M S. Stability of networked control systems. IEEE Contr. Syst. Mag, 2001,2 (1):84-99.
[4]Lian F L, Moyne J R, Tilbury D M. Performance evaluation of control networks:Ethernet, ControlNet and DeviceNet. IEEE Contr. Syst. Mag,2001,2 (1):66-83.
[5]Walsh G C, Beldiman O, Bushnell L. Asymptiotic behavior of etworked control systems. Proc.IEEE Int. Conf. on Control Applications,1999:1448-1453.
[6]Astrom K J, Wittenmark B. Computer-controlled cystems:theory and design. Upper Saddle River:Prentice Hall,1997, Third Edition.
[7]Halevi Y, Ray A. Integrated communication and control systems:Part I-Analysis. ASME Journal of Dynamic Systems, Measurement and Control,1988,110:367-373.
[8]Ray A, Liou L W, Shen J H. State estimation using randomly delayed measurements. ASME Journal of Dynamic Systems, Measurement and Control,1993,115:19-26.
[9]Chan H, Ozguner U. Closed-loop control of systems over a communications network with queues. Int. Journal of Control,1995,62 (3):493-510.
[10]于之训,陈堂辉,王月娟.时延网络控制系统均方指数稳定的研究.控制与决策,2000,15(3)：278-281.
[11]王飞跃,王成红.基于网络控制的若干基本问题的思考和分析.自动化学报,2002,28：171-176.
[12]朱其新,胡寿松,侯霞.长时滞网络控制系统的随机稳定性研究.东南大学学报,2003,33(3)：368-371.
[13]谢林柏.网络化控制系统中若干问题的研究：(博士学位论文).武汉：华中科技大学,2004.
[14]Imer O C, Basar T. Optimal estimation with limited measurements. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain:IEEE Press,2005:1029-1034.
[15]Wiener N. Extrapolation, and interpolation, and smoothing of stationary time series, with engineering applications. MIT Press, Cambridge, Mass,1949.
[16]Kalman R. E. A new approach to linear filtering and prediction problems, Trans, ASME J.Basic Eng.,1960,82:35-45.
[17]解学书，钟宜生著.H∞控制理论.北京：清华大学出版社,1994年9月.
[18]中铁龙著.H∞控制理论与应用.北京：清华大学出版社,1996年11月.
[19]Xie L H, Soh Y C, de Souza C E. Robust Kalman filtering for uncertain systems. IEEE Transactions on Automatic Control,1994,39 (6):1310-1314.
[20]Shaked U, de Souza C E. Robust minimum variance filtering. IEEE Transactions on Signal Processing,1995,43 (11):2474-2483.
[21]Theodor Y, Shaked U. Robust discrete-time minimum-variance filtering. IEEE Transactions on Signal Processing,1996,44 (2):181-189.
[22]Shaked U, Xie L H, Soh Y C. New approaches to robust minimum variance filter design. IEEE Transactions on Signal Processing,2001,49 (11):2620-2629.
[23]Zhu X, Soh Y C, Xie L H. Design and analysis of discrete-time robust Kalman filters. Automatica,2002,38:1069-1077.
[24]Bolzern P, Colaneri P, De Nicolao G. Optimal design of robust predictors for linear discrete-time systems. Systems & Control Letters,1995,26:25-31.
[25]Wang Z D, Huang B. Robust H2/H∞ filtering for linear systems with error variance constraints. IEEE Tranctions on Signal Processing,2000,48 (8):2463-2467.
[26]Fialho I J, Georgiou T T. On the L1 norm uncertain linear systems. Proceedings of the 1995 American Control Conference, Seattle, WA, USA,1995:939-943.
[27]高会军,王常虹,李艳辉.时滞不确定离散系统的鲁棒l2-l∞滤波.自动化学报,2003,29(5)：666-672.
[28]高会军,干常虹.不确定连续系统的鲁棒l2-l∞滤波新方法.自动化学报,2009,29(6)：46-53.
[29]Yaz E, Skelton R E. Continuous and discrete state estimation with error covariance assignment. Proceeding of IEEE Conference of Decision & Control, Brighton, U.K.,1991, pp:3091-3092.
[30]Wang Z D, Huang B, Huo P. Sampled-data filtering with error covariance assignment. IEEE Transaction on Signal Processing,2001,49 (3):666-670.
[3l]Yaz E, Ray A. Linear unbiased state estimation under randomly varying bounded sensor delay. Application Mathematical Letter,1998,11 (4):27-32.
[32]Evans J S, Krishnamurthy V. Hidden Markov model state estimation with randomly delayed observations. IEEE Transactions on Signal Processing,1999,47(8):2157-2166.
[33]Shu Z, Lam J, Xu S Y. Robust stabilization of Markovian delay systems with delay-dependent exponential estimates. Automatica,2006,42:2001-2008.
[34]Zhang H S, Lu X, Cheng D Z. Optimal estimation for continuous-time systems with delayed measurements. IEEE Transaction on Automatic Control,2006,51(5):823-827.
[35]Fridman E, Shaked U, Xie L. Robust H(?) filtering of linear systems with time delays. International Journal of Robust and Nonlinear Control,2003,13:983-1010.
[36]Michael B, Jesus R G, Rodolfo M Z. Optimal filtering for linear state delay systems. IEEE Transactions on Automatic Control,2005,50 (5):684-690.
[37]Michael B, Aracelia A G, Jesus R G. Optimal filtering for linear systems with state and observation delays.2005 American Control Conference, Portland, OR, USA:IEEE Press, 2005:4039-4044.
[38]Wang Z D, Yang F W, Daniel W C et al. Robust H∞ filtering for stochastic time- delay systems with missing measurements. IEEE Transactions on Signal Processing,2006,54 (7):2579-2587.
[39]Lu X, Xie L H, Zhang H S et al. Robust Kalman filtering for discrete-time systems with measurement delay. IEEE Transactions on Circuits and Systems-Ⅱ:Express Briefs,2007, 54 (6):522-526.
[40]Wang Z D, Daniel W C, Liu X H. Robust filtering under randomly varying sensor delay with variance constraints. IEEE Transactions on Circuits and Systems-II:Express Briefs, 2004,51 (6):320-326.
[41]He X, Wang Z D, Zhou D. Robust H∞ filtering for networked systems with multiple state delays. International Journal of Control,2007,80 (8):1217-1232.
[42]Wen C B, Zhen Z L, Gao H J. H∞. estimation for uncertain systems with multiple state delays. The 1st International Symposium on Systems and Control in Astronautics,2006.
[43]Schenato L. Optimal estimation in networked control systems subject to random delay and packet loss. Proceedings of the 45th Conference on Decision & Control. United States: IEEE Press,2006:5615-5620.
[44]Schenato L. Kalman filtering for networked control systems with random delay and packet loss. The 17th International Symposium on Mathematical Theory of Networks and Systems. Japan: IEEE Press,2006:1509-1517.
[45]Jin Z P, Gupta V, Hassibi B. State estimation utilizing multiple description coding over lossy networks. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain:IEEE Press,2005:872-878.
[46]Wang Z D, Ho W C, Liu X H. Variance-constrained filtering for uncertain stochastic systems with missing measurements. IEEE Transactions on Automatic Control,2003,48 (7):1254-1258.
[47]Wang Z D, Yang F W, Daniel W C et al. Robust finite-horizon filtering for stochastic system with missing measurements, IEEE Signal Processing Letters,2005,12 (6):437-440.
[48]Wang W, Yang F W. H∞ filtering design for discrete-time systems with missing measurements. Acta Automatica Sinica,2006,32(1):107-111.
[49]Sinopoli B, Schenato L, Franceschetti M et al. Kalman filtering with intermittent observations. IEEE Transactions on Automatic Control,2004,49(9):1453-1464.
[50]Liu X H, Goldsmith A. Kalman filtering with partial observation losses. The 43rd IEEE Conference on Decision & Control, Atlantis, Bahamas:IEEE Press,2004, pp:4180-4186.
[51]Huang M Y, Dey S. Kalman filtering with Markovian packet losses and stability criteria. Proceeding of the 45"'IEEE Conference on Decision & Control, San Diego, CA, USA:IEEE Press, 2006:5621-5626.
[52]Huang M Y, Dey S. Stability of Kalman filtering with Markovian packet losses. Automatica, 2007,43 (4):598-607.
[53]Smith S C, Seiler P. Estimation with lossy measurements:jump estimators for jump systems. IEEE Transactions on Automatic Control,2003,48(12):2163-2171.
[54]Plarre K, Bullo F. On Kalman filtering for detectable systems with intermittent observations. IEEE Transactions on Automatic Control,2009,54 (2):386-390.
[55]Shi L, Epstein M, Tiwari A et al. Estimation with information loss:asymptotic analysis and error bounds. Proceedings of the 44"'IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain:IEEE Press,2005:1215-1221.
[56]Sun S L, Xie L H, Xiao W D et al. Optimal linear estimation for systems with multiple packet dropouts. Automatica,2008,44:1333-1342.
[57]Sahebsara M. Optimal filtering in multiple channels networked control systems with multiple packet dropouts. Proceeding of the 47th IEEE Conference on Decision and Control. Cancun, Mexico:IEEE Press,2008:3366-3371.
[58]Sahebsara M, Chen T W, Shah S L. Optimal H(?) filtering in networked control systems with multiple packet dropouts. IEEE Transactions on Automatic Control,2007,52 (8):1508-1513.
[59]Sun S L, Xie L H, Xiao W D et al. Optimal full-order and reduced-order estimators for discrete-time systems with multiple packet dropouts. IEEE Transactions on Signal Processing,2008,56(8):4031-4038
[60]Sun S L, Xie L H, Xiao W D et al. Optimal filtering for systems with multiple packet dropouts. IEEE Transactions on Circuits and Systems-Ⅱ:Express Briefs,2008,55 (7): 695-699.
[61]Sun S L. Linear minimum variance estimators for systems with bounded random measurement delays and packet dropouts. Signal Processing,2009,89:1457-1466.
[62]Sahebsara M, Chen T W, Shah S L. Optimal H∞ filtering in networked control systems with multiple packet dropouts. Systems & Control Letters,2008,57:696-702.
[63]Sahebsara M, Chen T W, Shah S L. Optimal H(?) filtering with random sensor delay, multiple packet dropout and uncertain observations. International Journal of Control,2007,80(2): 292-301.
[64]Nair G N, Evans R J. State estimation via a capacity-limited communication channel. Proceedings of the 36th Conference on Decision & Control, Dec.1997,1:866-871.
[65]Nair G N, Evans R J. State estimation under bit-rate constraints. Proceedings of the 37th Conference on Decision & Control, De.1998,1:251-256.
[66]Nair G N, Evans R J. A finite-dimensional coder-estimator for the rate constrained state estimation. In Proceeding of the 14th IFAC World Congress,1999,1:19-24.
[67]Nair G N, Evans R J. Structural results for finite bit-rate state estimation. Proceedings of Information, Decision and Control, Feb.1999, pp:47-52.
[68]Dokuchaev N G, Savkin A V. Recursive state estimation via limited capacity communication channels. Proceedings of the 38th IEEE Conference on Decision and Control, Dec,1999, 5:4929-4932.
[69]Savkin A V, Petersen I R. Set-valued state estimation via a limited capacity communication channel. Proceedings of the 41st IEEE Conference on Decision and Control, December 2002,4:4042-4046.
[70]Malyavej V. Robust control and state estimation via limited capacity communication networks. Australia:The University of New South Wales School of Electrical Engineering and Telecommunications Sydney,2005.
[71]Li X, Wong W S. State estimation with communication constraints. System & Control Letters,1996,28:49-54.
[72]Li X, Wong W S. Constrained State Estimation for Systems with Finite Communication Bandwidth. Proceedings of the 37th IEEE Conference on Decision & Control, Dec 1998:1400-1406.
[73]Yuksel S, Basar T. Quantization for LTI Systems with noiseless channels. Proc. IEEE CCA,2003:423-429.
[74]Yuksel S, Basar T. State estimation and control for linear systems over communication networks, Proc. IEEE CCA,2003:409-414.
[75]Dong Z, You Z. Finite-horizon robust Kalman filtering for uncertain discrete time-varying systems with uncertain-convariance white noise. IEEE Signal Processing Letters,2006,13 (8):493-496.
[76]张勇,史忠科,戴冠中.离散系统的鲁棒最小方差滤波新算法及分析.自动化学报,2000,26(6)：782-787
[77]Oliveira R C L F, Peres P L D, LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions. System Control Letter,2006,55 (1):52-61
[78]Petersen I R, McFarlane D C. Robust state estimation for uncertain systems. Proceedings of the 30th Conference on Decision and Control, Brighton, England:IEEE Press, 1991:2630-2631.
[79]Petersen I R, McFarlane D C. Optimal guaranteed cost filtering for uncertain discrete-time linear systems. International Journal of Robust and Nonlinear Control,1996, 6(4):267-280.
[80]Xie L H, Soh Y C, Souza C E. Robust Kalman filtering for uncertain systems. IEEE Transactions on Automatic Control,1994,39(6):1310-1314.
[8l]Wang Z D, Guo Z, Unbehauen H. Robust H2/H∞ -state estimation for discrete-time systems with error variance constraints. IEEE Tranctions on Automatic Control,1997,42 (10):1431-1435.
[82]Hung Y S, Yang F W. Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty. Automatica,2003,39:1185-1194.
[83]Wang Z D, Fan J A. Robust H∞ filter design with variance constraints and parabolic pole assignment. IEEE Signal Processing Letters,2006,13 (3):137-140.
[84]Wang Z D, Qiao H. Robust filtering for bilinear uncertain stochastic discrete-time systems. IEEE Transaction on Signal Processing,2002,50:560-567.
[85]Yang F W, Wang Z D, Hung Y S. Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noise. IEEE Transactions on Automatic Control,2002,47 (7):1179-1183.
[86]Wang F, Balakrishnan V. Robust steady-state filtering for systems with deterministic and stochastic uncertainties. IEEE Transactions on Signal Processing,2003,51(10): 2550-2558.
[87]吴淮宁,费元春.不确定离散系统的最优鲁棒滤波.控制理论与应用,1999,16(2)：292-296.
[88]Wu A G, Duan G R. Robust H∞ estimation for uncertain contimuous-time systems. Proceedings of the 4th International Conference on Machine Learning and Cybernetics, Guangzhou, China:IEEE Press,2005:448-453.
[89]孙平,井元伟.基于采样测量值的不确定系统鲁棒H∞滤波.控制与决策,2006,21(6)：697-704
[90]陈莉,钟麦英.不确定奇异时滞系统的鲁棒H∞故障诊断滤波器设计.自动化学报,2008,34(8)：943-949
[91]Theodor Y, Shaked U. Robust discrete-time minimum-variance filtering. IEEE Transactions on Signal Processing,1996,44 (2):181-189.
[92]王武,杨富文,詹耀清.测量数据丢失的随机不确定离散系统的鲁棒H2状态估计.控制理论与应用,2008,25(3)：439-445.
[93]关新平,张群亮.不确定离散时滞系统的鲁棒H∞滤波与仿真.系统仿真学报,2002,14(8)：1078-1111.
[94]Gao H J, Chen T W. H∞ estimation for uncertain systems with limited communication capacity. IEEE Transactions on Automatic Control,2007,52(11):1310-1314.
[95]Ben-Israel A, Greville T N E. Generalized Inverses:Theory and Applications. New York: Wiley,1974.
[96]Wang Y, Xie L, de Souza C E. Robust control of a class of uncertain nonlinear systems. System Control Letter,1992,19:139-149.
[97]Matveev A, Savkin A. The problem of state estimation via asynchronous communication channels with irregular transmission times. IEEE Trans Autom Contr,2003,48 (4):670-676.
[98]Zhang H S, Xie L H, Zhang G D et al. A reorganized innovation approach to linear estimation. IEEE Trans Autom Contr,2004,49 (10):1810—1814.
[99]Gao Y, Duan G R, Meng X Y. Robust H∞ Filter design for 2D discrete systems in roesser model. International Journal of Automation and Computing,2008,4 (5):413-418.
[100]Yang L, Guan X P, Long C N et al. Feedback stabilization over wireless network using adaptive coded modulation. International Journal of Automation and Computing,2008,4 (5):381-388.
[101]Gajic Z, Qureshi M. Lyapunov matrix equation in system stability and control. Dover Publications,1995.
[102]Fu M, Xie L. The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control,2005,50(11):1698-1711.
[103]Yang F W, Wang Z D, Feng G et al. Robust filtering with randomly varying sensor delay:the finite-horizon case. IEEE Transactions on Circuits and Systems-Ⅰ:Regular papers, 2009,56(3):664-672.
[104]Elia N, Mitter S K. Stabilization of linear systems with limited information. IEEE Trans. Autom. Control,2001,46(9):1384-1400.
[105]Su C L, Lu C N. Interconnected network state estimation using randomly delayed measurements. IEEE Transactions on Power Systems,2001,16 (4):870-878.
[106]Nahi N. Optimal recursive estimation with uncertain observation. IEEE Trans. Inf. Theory,1969, IT-15(4):457-462.
[107]Hadjicostis C N, Touri R. Feedback control utilizing packet dropping network links. Proceedings of the IEEE Conference on Decision and Control,2002,2:1205-1210.
[108]Ling Q, Lemmon M. Optimal dropout compensation in networked control systems. IEEE Conference on Decision and Control,2003.1:670-675.
[109]Giorgiev D, Tilbury D. Packet-based control. Proceedings of the America Control Conference,2004:329-336.
[110]Stengel R F. Stochastic optimal control:theory and application. New York:Wiley, 1986.
[111]Beran E, Grigoriadis K. A combined alternating projections and semidefinite programming algorithm for low-order control design. Processing of the World congress of IFAC, San Francisco, CA,1996, C:85-90.
[112]Saberi A, Sannuti P, Chen B M. H2 optimal control. Series in Systems and Control Engineering, London, U.K.:rentice-Hall,1995.