State estimation over non-acknowledgment networks with Markovian packet dropouts

Abstract In this paper, we investigate state estimation for systems with packet dropouts. According to whether there are acknowledgment (ACK) signals sent by the actuator to the estimator indicating the status of control packet dropouts or not, the systems are classified into two types: ACK systems, those with ACK signals, and non-ACK (NACK) systems, those without. We first obtain the optimal estimator (OE) for NACK systems with Markovian packet dropouts. However, the number of the components in the OE grows exponentially, making its stability analysis complicated and its computation time-consuming. Therefore, we proceed to design a computationally efficient approximate optimal estimator (AOE) using a relative-entropy-based approach. We prove that the proposed AOE has the same stability as the OE. We show that, even the separation principle does not hold for NACK systems, the stability of the OE can also be investigated separately; and discover that the OE for an NACK system has the same stability as the OE for the corresponding ACK system, even their structures are quite different. Finally, for strongly observable NACK systems, we establish a necessary and sufficient condition for the stability of the OE and the AOE.

[1]  Xingde Wang.  Recursive algorithms for linear LMSE estimators under uncertain observations , 1984 .

[2]  Minyue Fu,et al.  Kalman Filtering With Intermittent Observations: On the Boundedness of the Expected Error Covariance , 2014, IEEE Transactions on Automatic Control.

[3]  Hongli Dong,et al.  Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts , 2014 .

[4]  Daniel E. Quevedo,et al.  Kalman Filtering With Relays Over Wireless Fading Channels , 2015, IEEE Transactions on Automatic Control.

[5]  Nitish V. Thakor,et al.  Describing the Nonstationarity Level of Neurological Signals Based on Quantifications of Time–Frequency Representation , 2007, IEEE Transactions on Biomedical Engineering.

[6]  John R. Hershey,et al.  Approximating the Kullback Leibler Divergence Between Gaussian Mixture Models , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[7]  Wei Xing Zheng,et al.  Distributed ℋ∞ Filtering for a Class of Discrete-Time Markov Jump Lur'e Systems With Redundant Channels , 2016, IEEE Trans. Ind. Electron..

[8]  Yan Song,et al.  Robust model predictive control under redundant channel transmission with applications in networked DC motor systems , 2016 .

[9]  Hong Lin,et al.  On stability and convergence of optimal estimation for networked control systems with dual packet losses without acknowledgment , 2018, Autom..

[10]  Renquan Lu,et al.  Estimation and LQG Control Over Unreliable Network With Acknowledgment Randomly Lost , 2017, IEEE Transactions on Cybernetics.

[11]  Donghua Zhou,et al.  Event-Based Recursive Distributed Filtering Over Wireless Sensor Networks , 2015, IEEE Transactions on Automatic Control.

[12]  Bruno Sinopoli,et al.  Kalman Filtering With Intermittent Observations: Tail Distribution and Critical Value , 2012, IEEE Transactions on Automatic Control.

[13]  Wei Liu,et al.  State estimation for networked systems with Markovian communication constraints and multiple packet dropouts , 2017, J. Frankl. Inst..

[14]  Lihua Xie,et al.  Mean square stability for Kalman filtering with Markovian packet losses , 2011, Autom..

[15]  Fuad E. Alsaadi,et al.  Recent advances on filtering and control for cyber-physical systems under security and resource constraints , 2016, J. Frankl. Inst..

[16]  Pramod K. Varshney,et al.  Autonomous Fall Detection With Wearable Cameras by Using Relative Entropy Distance Measure , 2017, IEEE Transactions on Human-Machine Systems.

[17]  Mohamed T. Hadidi,et al.  Linear recursive state estimators under uncertain observations , 1978 .

[18]  Xiaoqing Frank Liu,et al.  Cyber-physical manufacturing cloud: Architecture, virtualization, communication, and testbed , 2017 .

[19]  Federica Pascucci,et al.  Monitoring system reaction in cyber-physical testbed under cyber-attacks , 2017, Comput. Electr. Eng..

[20]  Bruno Sinopoli,et al.  Kalman filtering with intermittent observations , 2004, IEEE Transactions on Automatic Control.

[21]  Wei Xing Zheng,et al.  State Estimation of Discrete-Time Switched Neural Networks With Multiple Communication Channels , 2017, IEEE Transactions on Cybernetics.

[22]  Hong Lin,et al.  Optimal Estimation and Control for Lossy Network: Stability, Convergence, and Performance , 2017, IEEE Transactions on Automatic Control.

[23]  Hongye Su,et al.  Optimal Estimation in UDP-Like Networked Control Systems With Intermittent Inputs: Stability Analysis and Suboptimal Filter Design , 2016, IEEE Transactions on Automatic Control.

[24]  Peter C. Mignerey,et al.  Evaluation of Relative Entropy for Distributed Passive Detection of Weak Acoustic Signals , 2017, IEEE Journal of Oceanic Engineering.

[25]  Yuanqing Xia,et al.  Secure filtering for stochastic non-linear systems under multiple missing measurements and deception attacks , 2017 .

[26]  Bruno Sinopoli,et al.  Foundations of Control and Estimation Over Lossy Networks , 2007, Proceedings of the IEEE.

[27]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[28]  Jun Tang,et al.  Relative Entropy-Based Waveform Design for MIMO Radar Detection in the Presence of Clutter and Interference , 2015, IEEE Transactions on Signal Processing.

[29]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[30]  O. Costa.  Linear minimum mean square error estimation for discrete-time Markovian jump linear systems , 1994, IEEE Trans. Autom. Control..

[31]  James Lam,et al.  Interacting Multiple Model Estimator for Networked Control Systems: Stability, Convergence, and Performance , 2019, IEEE Transactions on Automatic Control.

[32]  A.G. Alleyne,et al.  Closed-loop control over wireless networks , 2004, IEEE Control Systems.

[33]  Jason L. Speyer,et al.  Stochastic Processes, Estimation, and Control , 2008, Advances in design and control.

[34]  Subhrakanti Dey,et al.  Stability of Kalman filtering with Markovian packet losses , 2007, Autom..

[35]  Daniel W. C. Ho,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009, Autom..

[36]  Behrouz A. Forouzan.  TCP/IP Protocol Suite , 1999 .

[37]  Frank Allgöwer,et al.  Estimating the fates of the control packets for Networked Control Systems with loss of control and measurement packets , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[38]  Shaoying Wang,et al.  Distributed state estimation for stochastic non-linear systems with random delays and packet dropouts , 2015 .