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Recursive distributed filtering for two-dimensional shift-varying systems over sensor networks under stochastic communication protocols. (English) Zbl 1436.93140

Summary: This paper is concerned with the distributed filtering problem for a class of two-dimensional shift-varying systems over sensor networks subject to stochastic communication protocol (SCP) over a finite horizon. The communication between the sensor nodes and the filters is implemented through shared channels of limited capacity. To avoid data collisions, the SCP is applied to determine the transmission order of the signals/packets for each sensor. The considered scheduling behavior is characterized by mutually uncorrelated random variables with known probability distributions. Recursive distributed filters are proposed to estimate the system state through available information from both individual and neighboring nodes in the sensor network according to a given topology. Attention is focused on the design of distributed filters in order to ensure the locally minimal upper bound on the error variance of the state estimation. Sufficient conditions are first established, via intensive stochastic analysis and mathematical induction, on the existence of an upper bound of the estimation error variance. Then, by means of a matrix simplification technique, the desired filter gains are designed to optimize the obtained upper bound at each shift step. Finally, a practical example is given to verify the effectiveness of the proposed filter strategy.

MSC:

93E11 Filtering in stochastic control theory
93B70 Networked control
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[1] Ahn, C. K.; Shi, P.; Basin, M. V., Two-dimensional dissipative control and filtering for Roesser model, IEEE Transactions on Automatic Control, 60, 7, 1745-1759 (2015) · Zbl 1360.93488
[2] Ahn, C. K.; Shi, P.; Karimi, H. R., Novel results on generalized dissipativity of two-dimensional digital filters, IEEE Transactions on Circuits and Systems-II: Express Briefs, 63, 9, 893-897 (2016)
[3] Akyildiz, I. F.; Su, W.; Sankarasubramaniam, Y.; Cayirci, E., Wireless sensor networks: A survey, Computer Networks, 38, 4, 393-422 (2002)
[4] Basin, M.; Shi, P.; Calderon-Alvarez, D., Central suboptimal \(\mathcal{H}_\infty\) filter design for linear time-varying systems with state and measurement delays, International Journal of Systems Science, 41, 4, 411-421 (2010) · Zbl 1301.93157
[5] Bose, N. K., Multidimensional systems theory and applications (2003), Kluwer Academic Publisher: Kluwer Academic Publisher The Netherlands · Zbl 1046.93001
[6] Caballero-Águila, R.; Hermoso-Carazo, A.; Linares-Pérez, J., New distributed fusion filtering algorithm based on covariances over sensor networks with random packet dropouts, International Journal of Systems Science, 48, 9, 1805-1817 (2017) · Zbl 1371.93184
[7] Castagnetti, A.; Pegatoquet, A.; Le, T. L.; Auguin, M., A joint duty-cycle and transmission power management for energy harvesting WSN, IEEE Transactions on Industrial Informatics, 10, 2, 928-936 (2014)
[8] Cattivelli, F. S.; Sayed, A. H., Diffusion strategies for distributed Kalman filtering and smoothing, IEEE Transactions on Automatic Control, 55, 9, 2069-2084 (2010) · Zbl 1368.93706
[9] Chen, D.; Nixon, M.; Mok, A., WirelessHART: Real-time mesh network for industrial automation (2010), Springer: Springer Boston, MA
[10] Chen, B.; Zhang, W.; Hu, G.; Yu, L., Networked fusion Kalman filtering with multiple uncertainties, IEEE Transactions on Aerospace and Electronic Systems, 51, 3, 2332-2349 (2015)
[11] de Souza, C. E.; Xie, L.; Coutinho, D. F., Robust filtering for 2-D discrete-time linear systems with convex-bounded parameter uncertainty, Automatica, 46, 4, 673-681 (2010) · Zbl 1193.93178
[12] Dong, H.; Wang, Z.; Gao, H., Distributed \(H_\infty\) filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks, IEEE Transactions on Industrial Electronics, 60, 10, 4665-4672 (2013)
[13] Donkers, M. C.F.; Heemels, W. P.M. H.; Bernardini, D.; Bemporad, A.; Shneer, V., Stability analysis of stochastic networked control systems, Automatica, 48, 4, 917-925 (2012) · Zbl 1246.93120
[14] Du, C.; Xie, L.; Soh, Y. C., \( H_\infty\) filtering of 2-D discrete systems, IEEE Transactions on Signal Processing, 48, 6, 1760-1768 (2000) · Zbl 0996.93089
[15] Ge, X.; Han, Q.-L., Distributed sampled-data asynchronous \(H_\infty\) filtering of Markovian jump linear systems over sensor networks, Signal Processing, 127, 86-99 (2016)
[16] Geng, H.; Liang, Y.; Yang, F.; Xu, L.; Pan, Q., The joint optimal filtering and fault detection for multi-rate sensor fusion under unknown inputs, Information Fusion, 29, 57-67 (2016)
[17] Gungor, V. C.; Hancke, G. P., Industrial wireless sensor networks: Challenges, design principles, and technical approaches, IEEE Transactions on Industrial Electronics, 56, 10, 4258-4265 (2009)
[18] Han, F.; Wei, G.; Ding, D.; Song, Y., Local condition-based consensus filtering with stochastic nonlinearities and multiple missing measurements, IEEE Transactions on Automatic Control, 62, 9, 4784-4790 (2017) · Zbl 1390.93038
[19] Hinamoto, T., 2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 40, 2, 102-110 (1993) · Zbl 0825.93827
[20] Kaczorek, T., Two-dimensional linear systems (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0593.93031
[21] Karimi, H. R.; Zapateiro, M.; Luo, N., A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations, Journal of Franklin Institute, 347, 6, 957-973 (2010) · Zbl 1201.93033
[22] Khan, U. A.; Moura, J. M.F., Distributing the Kalman filter for large-scale systems, IEEE Transactions on Signal Processing, 56, 10, 4919-4935 (2008) · Zbl 1390.94242
[23] Li, W.; Jia, Y., Distributed consensus filtering for discrete-time nonlinear systems with non-Gaussian noise, Signal Processing, 92, 10, 2464-2470 (2012)
[24] Liu, K.; Fridman, E.; Johansson, K. H., Networked control with stochastic scheduling, IEEE Transactions on Automatic Control, 60, 11, 3071-3076 (2015) · Zbl 1360.93745
[25] Liu, Q.; Wang, Z.; He, X.; Ghinea, G.; Alsaadi, F. E., A resilient approach to distributed filter design for time-varying systems under stochastic nonlinearities and sensor degradation, IEEE Transactions on Signal Processing, 65, 5, 1300-1309 (2017) · Zbl 1414.94370
[26] Liu, Q.; Wang, Z.; He, X.; Zhou, D. H., Event-based distributed filtering with stochastic measurement fading, IEEE Transactions on Industrial Informatics, 11, 6, 1643-1652 (2015)
[27] Liu, Q.; Wang, Z.; He, X.; Zhou, D. H., Event-based recursive distributed filtering over wireless sensor networks, IEEE Transactions on Automatic Control, 60, 9, 2470-2475 (2015) · Zbl 1360.93703
[28] Liu, Y.; Wang, Z.; He, X.; Zhou, D. H., Minimum-variance recursive filtering over sensor networks with stochastic sensor gain degradation: Algorithms and performance analysis, IEEE Transactions on Control of Network Systems, 3, 3, 265-274 (2016) · Zbl 1370.93283
[29] Neuzil, J.; Kreibich, O.; Smid, R., A distributed fault detection system based on IWSN for machine condition monitoring, IEEE Transactions on Industrial Informatics, 10, 2, 1118-1123 (2014)
[30] Niu, Y.; Ho, D. W.C.; Li, C., Filtering for discrete fuzzy stochastic systems with sensor nonlinearities, IEEE Transactions on Fuzzy Systems, 18, 5, 971-978 (2010)
[31] Olfati-Saber, R. (2007). Distributed Kalman filtering for sensor networks. In Proceedings of the 46th IEEE conference on decision and control (pp. 5492-5498). New Orleans, LA, USA.
[32] Petersen, S.; Carlsen, S., WirelessHART versus ISA 100.11a: The format war hits the factory floor, IEEE Industrial Electronics Magazine, 5, 4, 23-34 (2011)
[33] Ribeiro, A.; Giannakis, G. B., Bandwidth-constrained distributed estimation for wireless sensor networks-part I: Gaussian case, IEEE Transactions on Signal Processing, 54, 3, 1131-1143 (2006) · Zbl 1373.94687
[34] Shen, B.; Wang, Z.; Hung, Y. S.; Chesi, G., Distributed \(H_\infty\) filtering for polynomial nonlinear stochastic systems in sensor networks, IEEE Transactions on Industrial Electronics, 58, 5, 1971-1979 (2011)
[35] Sun, S.; Peng, F.; Lin, H., Distributed asynchronous fusion estimator for stochastic uncertain systems with multiple sensors of different fading measurement rates, IEEE Transactions on Signal Processing, 66, 3, 641-653 (2018) · Zbl 1414.94593
[36] Tabbara, M.; Nešić, D., Input-output stability of networked control systems with stochastic protocols and channels, IEEE Transactions on Automatic Control, 53, 5, 1160-1175 (2008) · Zbl 1367.93602
[37] Tuan, H. D.; Apkarian, P.; Nguyen, T. Q.; Narikiyo, T., Robust mixed \(H_2 / H_\infty\) filtering of 2-D systems, IEEE Transactions on Signal Processing, 50, 7, 1759-1771 (2002)
[38] Ugrinovskii, V.; Fridman, E., A Round-Robin type protocol for distributed estimation with \(H_\infty\) consensus, Systems & Control Letters, 69, 103-110 (2014) · Zbl 1288.93009
[39] Walsh, G.; Ye, H.; Bushnell, L., Stability analysis of networked control systems, IEEE Transactions on Control Systems Technology, 10, 3, 438-446 (2002)
[40] Wang, S.; Fang, H.; Tian, X., Event-based robust state estimator for linear time-varying system with uncertain observations and randomly occurring uncertainties, Journal of the Franklin Institute, 354, 3, 1403-1420 (2017) · Zbl 1355.93122
[41] Wang, F.; Liang, J.; Wang, Z.; Liu, X., A variance-constrained approach to recursive filtering for nonlinear two-dimensional systems with measurement degradations, IEEE Transactions on Cybernetics, 48, 6, 1877-1887 (2018)
[42] Wang, F.; Wang, Z.; Liang, J.; Liu, X., Resilient filtering for linear time-varying repetitive processes under uniform quantizations and Round-Robin protocols, IEEE Transactions on Circuits and Systems-I: Regular Papers, 65, 9, 2992-3004 (2018) · Zbl 1468.93176
[43] Wang, F.; Wang, Z.; Liang, J.; Liu, X., Recursive state estimation for two-dimensional shift-varying systems with random parameter perturbation and dynamical bias, Automatica, 112 (2020), art. no. 108658 · Zbl 1430.93209
[44] Wang, Y.; Zhao, D.; Li, Y.; Ding, S. X., Unbiased minimum variance fault and state estimation for linear discrete time-varying two-dimensional systems, IEEE Transactions on Automatic Control, 62, 10, 5463-5469 (2017) · Zbl 1390.93773
[45] Wen, C.; Wang, Z.; Geng, T.; Alsaadi, F. E., Event-based distributed recursive filtering for state-saturated systems with redundant channels, Information Fusion, 39, 96-107 (2018)
[46] Yang, F.; Xia, N.; Han, Q.-L., Event-based networked islanding detection for distributed solar PV generation systems, IEEE Transactions on Industrial Informatics, 13, 1, 322-329 (2017)
[47] Yu, W.; Chen, G.; Wang, Z.; Yang, W., Distributed consensus filtering in sensor networks, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 39, 6, 1568-1577 (2009)
[48] Zhang, D.; Cai, W.; Xie, L.; Wang, Q.-G., Nonfragile distributed filtering for T-S fuzzy systems in sensor networks, IEEE Transactions on Fuzzy Systems, 23, 5, 1883-1890 (2015)
[49] Zhang, D.; Xu, Z.; Karimi, H. R.; Wang, Q.-G., Distributed filtering for switched linear systems with sensor networks in presence of packet dropouts and quantization, IEEE Transactions on Circuits and Systems-I: Regular Papers, 64, 10, 2783-2796 (2017)
[50] Zhang, W.-A.; Yu, L.; Feng, G., Optimal linear estimation for networked systems with communication constraints, Automatica, 47, 9, 1992-2000 (2011) · Zbl 1227.93117
[51] Zhao, D.; Ding, S. X.; Karimi, H. R.; Li, Y.; Wang, Y., On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: A least squares method, Automatica, 99, 203-212 (2019) · Zbl 1406.93354
[52] Zou, Y.; Sheng, M.; Zhong, N.; Xu, S., A generalized Kalman filter for 2D discrete systems, Circuits, Systems, and Signal Processing, 23, 5, 351-364 (2004) · Zbl 1062.93042
[53] Zou, L.; Wang, Z.; Gao, H., Observer-based \(H_\infty\) control of networked systems with stochastic communication protocol: The finite-horizon case, Automatica, 63, 366-373 (2016) · Zbl 1329.93041
[54] Zou, L.; Wang, Z.; Hu, J.; Gao, H., On \(H_\infty\) finite-horizon filtering under stochastic protocol: Dealing with high-rate communication networks, IEEE Transactions on Automatic Control, 62, 9, 4884-4890 (2017) · Zbl 1390.93816
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