×

Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts. (English) Zbl 1301.93159

Summary: This paper is concerned with the distributed \(H_\infty\) filtering problem for a class of nonlinear systems with Randomly Occurring Sensor Saturations (ROSS) and successive packet dropouts in sensor networks. The issue of ROSS is brought up to account for the random nature of sensor saturations in a networked environment of sensors, and accordingly, a novel sensor model is proposed to describe both the ROSS and successive packet dropouts within a unified framework. Two sets of Bernoulli distributed white sequences are introduced to govern the random occurrences of the sensor saturations and successive packet dropouts. Through available output measurements from not only the individual sensor but also its neighboring sensors, a sufficient condition is established for the desired distributed filter to ensure that the filtering dynamics is exponentially mean-square stable and the prescribed \(H_\infty\) performance constraint is satisfied. The solution of the distributed filter gains is characterized by solving an auxiliary convex optimization problem. Finally, a simulation example is provided to show the effectiveness of the proposed filtering scheme.

MSC:

93E11 Filtering in stochastic control theory
93E10 Estimation and detection in stochastic control theory
90B15 Stochastic network models in operations research
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bertrand, Distributed adaptive node-specific signal estimation in fully connected sensor networks - part I: sequential node updating, IEEE Transactions on Signal Processing 58 (10) pp 5277– (2010) · Zbl 1392.94100 · doi:10.1109/TSP.2010.2052612
[2] Bertrand, Distributed adaptive node-specific signal estimation in fully connected sensor networks - part II: simultaneous and asynchronous node updating, IEEE Transactions on Signal Processing 58 (10) pp 5292– (2010) · Zbl 1392.94101 · doi:10.1109/TSP.2010.2052613
[3] Bianchi, Linear precoders for the detection of a Gaussian process in wireless sensors networks, IEEE Transactions on Signal Processing 59 (3) pp 882– (2011) · Zbl 1392.94602 · doi:10.1109/TSP.2010.2092771
[4] Kokiopoulou, Distributed classification of multiple observation sets by consensus, IEEE Transactions on Signal Processing 59 (1) pp 104– (2011) · Zbl 1391.62118 · doi:10.1109/TSP.2010.2086450
[5] Kokiopoulou, Polynomial filtering for fast convergence in distributed consensus, IEEE Transactions on Signal Processing 57 (1) pp 342– (2009) · Zbl 1391.94898 · doi:10.1109/TSP.2008.2006147
[6] Mostofi, Binary consensus over fading channels, IEEE Transactions on Signal Processing 58 (12) pp 6340– (2010) · Zbl 1392.94348 · doi:10.1109/TSP.2010.2070498
[7] Sundaresan, Location estimation of a random signal source based on correlated sensor observations, IEEE Transactions on Signal Processing 59 (2) pp 787– (2011) · Zbl 1392.94473 · doi:10.1109/TSP.2010.2084084
[8] Cattivelli FS Sayed AH Diffusion strategies for distributed Kalman filtering: formulation and performance analysis Proceedings of the Cognitive Information Processing 2008 36 41
[9] Cattivelli, Diffusion strategies for distributed Kalman filtering and smoothing, IEEE Transactions on Automatic Control 55 (9) pp 1520– (2010) · Zbl 1368.93706 · doi:10.1109/TAC.2010.2042987
[10] Chai L Hu B Jiang P Distributed State Estimation based on Quantized Observations in a Bandwidth Constrained Sensor Network Proceedings of the 7th World Congress on Intelligent Control and Automation 2008 2411 2415
[11] Farina M Ferrari-Trecate G Scattolini R Distributed moving horizon estimation for sensor networks Proceedings 1st IFAC Workshop on Estimation and Control of Networked Systems 2009 126 131
[12] Dong, Distributed filtering for a class of time varying systems over sensor networks with quantization errors and successive packet dropouts, IEEE Transactions on Signal Processing 60 (6) pp 3164– (2012) · Zbl 1391.93232 · doi:10.1109/TSP.2012.2190599
[13] Speranzon, A distributed minimum variance estimator for sensor networks, IEEE Journal on Selected Areas in Communications 26 (4) pp 609– (2008) · doi:10.1109/JSAC.2008.080504
[14] Teng, Decentralized variational filtering for target tracking in binary sensor networks, IEEE Transactions on Mobile Computing 9 (10) pp 1465– (2010) · doi:10.1109/TMC.2010.117
[15] Cattivelli FS Sayed AH Diffusion mechanisms for fixed-point distributed Kalman smoothing Proceedings of the 16th European Signal Processing Conference 2008
[16] Shen, Distributed H filtering for polynomial nonlinear stochastic systems in sensor networks, IEEE Transactions on Industrial Electronics 58 (5) pp 1971– (2011) · doi:10.1109/TIE.2010.2053339
[17] Olfati-Saber R Distributed Kalman filtering for sensor networks Proceedings of the 46th IEEE Conference on Decision and Control 2007 5492 5498
[18] Olfati-Saber R Shamma JS Consensus filters for sensor networks and distributed sensor fusion Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 6698 6703
[19] Olfati-Saber R Kalman-consensus filter optimality stability and performance Proceedings of the 48th IEEE Conference on Decision and Control 2009 7036 7042
[20] Shen, Distributed H- filtering in sensor networks with multiple missing measurements: the finite-horizon case, Automatica 46 (10) pp 1682– (2010) · Zbl 1204.93122 · doi:10.1016/j.automatica.2010.06.025
[21] Yu, Distributed consensus filtering in sensor networks, IEEE Transactions on Systems Man and Cybernetics-Part B 39 (6) pp 1568– (2009) · doi:10.1109/TSMCB.2009.2021254
[22] Dong, H fuzzy control for systems with repeated scalar nonlinearities and random packet losses, IEEE Transactions on Fuzzy Systems 17 (2) pp 440– (2009) · doi:10.1109/TFUZZ.2009.2014223
[23] Gao, H estimation for uncertain systems with limited communication capacity, IEEE Transactions on Automatic Control 52 (11) pp 2070– (2007) · Zbl 1366.93155 · doi:10.1109/TAC.2007.908316
[24] Wang, Robust H filtering for stochastic time-delay systems with missing measurements, IEEE Transactions on Signal Processing 54 (7) pp 2579– (2006) · Zbl 1373.94729 · doi:10.1109/TSP.2006.874370
[25] Wang, Quantized H control for nonlinear stochastic time-delay systems with missing measurements, IEEE Transactions on Automatic Control 57 (6) pp 1431– (2012) · Zbl 1369.93583 · doi:10.1109/TAC.2011.2176362
[26] Wang, H filtering with randomly occurring sensor saturations and missing measurements, Automatica 48 (3) pp 556– (2012) · Zbl 1244.93162 · doi:10.1016/j.automatica.2012.01.008
[27] Shu, Non-fragile exponential stability assignment of discrete-time linear systems with missing data in Actuators, IEEE Transactions on Automatic Control 54 (3) pp 625– (2009) · Zbl 1367.93481 · doi:10.1109/TAC.2008.2009598
[28] Xiong, Stabilization of linear systems over networks with bounded packet loss, Automatica 43 (1) pp 80– (2007) · Zbl 1140.93383 · doi:10.1016/j.automatica.2006.07.017
[29] Dong, Fuzzy-model-based robust fault detection with stochastic mixed time-delays and successive packet dropouts, IEEE Transactions on Systems, Man, and Cybernetics-Part B 42 (2) pp 365– (2012) · doi:10.1109/TSMCB.2011.2163797
[30] Sahebsara, Optimal H2 filtering with random sensor delay, multiple packet dropout and uncertain observations, International Journal of Control 80 (2) pp 292– (2007) · Zbl 1140.93486 · doi:10.1080/00207170601019500
[31] Chen B-S Wang S-S The design of feedback controller with nonlinear saturating actuator: time domain approach Proceedings of the 25th Conference on Decision and Control 1986 2048 2053
[32] Du, Energy-to-peak performance controller design for building via static output feedback under consideration of actuator saturation, Computers and Structures 84 (31-32) pp 2277– (2006) · doi:10.1016/j.compstruc.2006.08.032
[33] Haidar, Exponential stability and static output feedback stabilization of singular time-delay systems with saturating actuators, International Journal of Robust and Nonlinear Control 3 (9) pp 1293– (2009)
[34] Hu, An analysis and design method for linear systems subject to actuator saturation and disturbance, Automatica 38 (2) pp 351– (2002) · Zbl 0991.93044 · doi:10.1016/S0005-1098(01)00209-6
[35] Krikelis, Design of tracking systems subject to actuator saturation and integrator wind-up, International Journal of Control 39 (4) pp 667– (1984) · Zbl 0532.93023 · doi:10.1080/00207178408933196
[36] Lv, Analysis and design of singular linear systems under actuator saturation and L2/L disturbances, Systems & Control Letters 57 (11) pp 904– (2008) · Zbl 1149.93030 · doi:10.1016/j.sysconle.2008.04.004
[37] Zhou, An ARE approach to semi-global stabilization of discrete-time descriptor linear systems with input saturation, Systems and Control Letters 58 (8) pp 609– (2009) · Zbl 1166.93021 · doi:10.1016/j.sysconle.2009.03.009
[38] Zuo, Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation, Automatica 46 (3) pp 569– (2010) · Zbl 1194.93093 · doi:10.1016/j.automatica.2010.01.024
[39] Wang, Robust H finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations, IEEE Transactions on Automatic Control 55 (7) pp 1716– (2010) · Zbl 1368.93668 · doi:10.1109/TAC.2010.2047033
[40] Xiao, Robust filtering for discrete-time systems with saturation and its application to transmultiplexers, IEEE Transactions on Signal Processing 52 (5) pp 1266– (2004) · Zbl 1370.93291 · doi:10.1109/TSP.2004.826180
[41] Yang, Set-membership filtering for systems with sensor saturation, Automatica 45 (8) pp 1896– (2009) · Zbl 1185.93049 · doi:10.1016/j.automatica.2009.04.011
[42] Zuo, Output feedback H controller design for linear discrete-time systems with sensor nonlinearities, IEE Proceedings - Control Theory and Applications 152 (1) pp 19– (2005) · doi:10.1049/ip-cta:20051011
[43] Khalil, Nonlinear Systems (1996)
[44] Boyd, Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004 · doi:10.1137/1.9781611970777
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.