Distributed \(\mathcal H_{\infty}\) state estimation with stochastic parameters and nonlinearities through sensor networks: the finite-horizon case. (English) Zbl 1267.93167

Ding, Derui; Wang, Zidong; Dong, Hongli; Shu, Huisheng

Automatica 48, No. 8, 1575-1585 (2012).

Summary: This paper deals with the distributed \(\mathcal H_{\infty}\) state estimation problem for a class of discrete time-varying nonlinear systems with both stochastic parameters and stochastic nonlinearities. The system measurements are collected through sensor networks with sensors distributed according to a given topology. The purpose of the addressed problem is to design a set of time-varying estimators such that the average estimation performance of the networked sensors is guaranteed over a given finite-horizon. Through available output measurements from not only the individual sensor but also its neighboring sensors, a necessary and sufficient condition is established to achieve the \(\mathcal H_{\infty}\) performance constraint, and then the estimator design scheme is proposed via a certain \(\mathcal H_{2}\)-type criterion. The desired estimator parameters can be obtained by solving coupled backward recursive Riccati Difference Equations (RDEs). A numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed estimator design approach.

MSC:

93E10	Estimation and detection in stochastic control theory
93B36	\(H^\infty\)-control
93C10	Nonlinear systems in control theory

Keywords:

discrete time-varying systems; distributed \(\mathcal H_{\infty}\) state estimation; recursive Riccati difference equations; sensor networks; stochastic nonlinearities; stochastic parameters

References:

[1]	Ahmad, A.; Gani, M.; Yang, F., Decentralized robust Kalman filtering for uncertain stochastic systems over heterogeneous sensor networks, Signal processing, 88, 8, 1919-1928, (2008) · Zbl 1151.94335
[2]	Aitrami, M.; Chen, X.; Zhou, X., Discrete-time indefinite LQ control with state and control dependent noises, Journal of global optimization, 23, 3-4, 245-265, (2002) · Zbl 1035.49024
[3]	Aliyu, M.D.S.; Boukas, E., Mixed \(\mathcal{H}_2 / \mathcal{H}_\infty\) nonlinear filtering, International journal of robust and nonlinear control, 19, 4, 394-417, (2009) · Zbl 1157.93520
[4]	Basin, M.; Elvira-Ceja, S.; Sanchez, E., Mean-square \(\mathcal{H}_\infty\) filtering for stochastic systems: application to a 2DOF helicopter, Signal processing, 92, 3, 801-806, (2012)
[5]	Basin, M.; Shi, P.; Calderon-Alvarez, D., Approximate finite-dimensional filtering for polynomial states over polynomial observations, International journal of control, 83, 4, 724-730, (2010) · Zbl 1209.93149
[6]	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
[7]	Basin, M.; Shi, P.; Calderon-Alvarez, D.; Wang, J., Central suboptimal \(\mathcal{H}_\infty\) filter design for linear time-varying systems with state or measurement delay, Circuits, systems, and signal processing, 28, 2, 305-330, (2009) · Zbl 1173.93011
[8]	Bouhtouri, A.E.; Hinrichsen, D.; Pritchard, A., \(\mathcal{H}_\infty\)-type control for discrete-time stochastic systems, International journal of robust and nonlinear control, 9, 13, 923-948, (1999) · Zbl 0934.93022
[9]	Caballero-Aguila, R.; Hermoso-Carazo, A.; Jimenez-Lopez, J.D.; Linares-Perez, J.; Nakamori, S., Signal estimation with multiple delayed sensors using covariance information, Digital signal processing, 20, 2, 528-540, (2010)
[10]	Calafiore, G.C.; Abrate, F., Distributed linear estimation over sensor networks, International journal of control, 82, 5, 868-882, (2009) · Zbl 1165.93032
[11]	Carli, R.; Chiuso, A.; Schenato, L.; Zampieri, S., Distributed Kalman filtering based on consensus strategies, IEEE journal on selected areas in communications, 26, 4, 622-633, (2008)
[12]	Farahmand, S.; Roumeliotis, S.I.; Giannakis, G.B., Set-membership constrained particle filter: distributed adaptation for sensor networks, IEEE transactions on signal processing, 59, 9, 4122-4138, (2011) · Zbl 1392.94202
[13]	Farina, M., Ferrari-Trecate, G., & Scattolini, R. (2009). Distributed moving horizon estimation for sensor networks. In Proc. 1st IFAC workshop estim. control netw. syst. (pp. 126-131). · Zbl 1244.93008
[14]	Gao, H.; Lam, J.; Wang, C., Induced \(l_2\) and generalized \(\mathcal{H}_2\) filtering for systems with repeated scalar nonlinearities, IEEE transactions on signal processing, 53, 11, 4215-4226, (2005) · Zbl 1370.94125
[15]	Gershon, E.; Shaked, U.; Berman, N., \(\mathcal{H}_\infty\) control and estimation of retarded state-multiplicative stochastic systems, IEEE transactions on automatic control, 52, 9, 1773-1779, (2007) · Zbl 1366.93701
[16]	Gershon, E.; Shaked, U.; Yaesh, I., Control and estimation of state-multiplicative linear systems, (2005), Springer-Verlag London Limited London, UK · Zbl 1077.93016
[17]	He, X.; Wang, Z.; Zhou, D., Robust \(\mathcal{H}_\infty\) filtering for networked systems with multiple state delays, International journal of control, 80, 8, 1217-1232, (2007) · Zbl 1133.93314
[18]	Hou, T.; Zhang, W.; Ma, H., Finite horizon \(\mathcal{H}_2 / \mathcal{H}_\infty\) control for discrete-time stochastic systems with Markovian jumps and multiplicative noise, IEEE transactions on automatic control, 55, 5, 1185-1191, (2010) · Zbl 1368.93661
[19]	Hung, Y.S.; Yang, F., Robust \(\mathcal{H}_\infty\) filtering with error variance constraints for discrete time-varying systems with uncertainty, Automatica, 39, 7, 1185-1194, (2003) · Zbl 1022.93046
[20]	Jacobson, D., A general result in stochastic optimal control of nonlinear discrete-time systems with quadratic performance criteria, Journal of mathematical analysis and applications, 47, 1, 153-161, (1974) · Zbl 0281.93017
[21]	Jafarizadeh, S.; Jamalipour, A., Fastest distributed consensus problem on fusion of two star sensor networks, IEEE sensors journal, 11, 10, 2494-2506, (2011)
[22]	Karimi, H.R., Robust \(\mathcal{H}_\infty\) filter design for uncertain linear systems over network with network-induced delays and output quantization, Modeling, identification and control, 30, 1, 27-37, (2009)
[23]	Li, J.; AlRegib, G., Rate-constrained distributed estimation in wireless sensor networks, IEEE transactions on signal processing, 55, 5, 1634-1643, (2007) · Zbl 1391.94021
[24]	Liang, J.; Wang, Z.; Liu, X., Distributed state estimation for discrete-time sensor networks with randomly varying nonlinearities and missing measurements, IEEE transactions on neural networks, 22, 3, 66-86, (2011)
[25]	Luo, Y.; Zhu, Y.; Luo, D.; Zhou, J.; Song, E.; Wang, D., Globally optimal multisensor distributed random parameter matrices Kalman filtering fusion with applications, Sensors, 8, 12, 8086-8103, (2008)
[26]	Olfati-Saber, R. (2007). Distributed Kalman filtering for sensor networks. In Proc. 46th IEEE conf. decis. control. (pp. 1-7).
[27]	Ribeiro, A.; Giannakis, G.B., Bandwidth-constrained distributed estimation for wireless sensor networks-part part I: Gaussian case, IEEE transactions on signal processing, 54, 3, 1131-1143, (2006) · Zbl 1373.94687
[28]	Ribeiro, A.; Giannakis, G.B., Bandwidth-constrained distributed estimation for wireless sensor networks-part II: unknown probability density function, IEEE transactions on signal processing, 54, 7, 2784-2796, (2006) · Zbl 1373.94688
[29]	Ribeiro, A.; Schizas, I.D.; Roumeliotis, S.I.; Giannakis, G.B., Kalman filtering in wireless sensor networks, IEEE control systems magazine, 30, 2, 66-86, (2010)
[30]	Shaked, U.; Berman, N., \(\mathcal{H}_\infty\) nonlinear filtering of discrete-time processes, IEEE transactions on signal processing, 43, 9, 2205-2209, (1995)
[31]	Shaked, U.; Suplin, V., A new bounded real lemma representation for the continuous-time case, IEEE transactions on automatic control, 46, 9, 1420-1426, (2001) · Zbl 1006.93016
[32]	Shen, B.; Wang, Z.; Hung, Y.S., Distributed \(\mathcal{H}_\infty\)-consensus filtering in sensor networks with multiple missing measurements: the finite-horizon case, Automatica, 46, 10, 1682-1688, (2010) · Zbl 1204.93122
[33]	Shen, B.; Wang, Z.; Shu, H.; Wei, G., Robust \(\mathcal{H}_\infty\) finite-horizon filtering with randomly occurred nonlinearities and quantization effects, Automatica, 46, 11, 1743-1751, (2010) · Zbl 1218.93103
[34]	Speranzon, A.; Fischione, C.; Johansson, K.H.; Sangiovanni-Vincentelli, A., A distributed minimum variance estimator for sensor networks, IEEE journal on selected areas in communications, 26, 4, 609-621, (2008)
[35]	Teng, J.; Snoussi, H.; Richard, C., Collaborative multi-target tracking in wireless sensor networks, International journal of systems science, 42, 9, 1427-1443, (2011) · Zbl 1241.93052
[36]	Wang, T.; Chang, L.; Chen, P., A collaborative sensor-fault detection scheme for robust distributed estimation in sensor networks, IEEE transactions on communications, 57, 10, 3045-3058, (2009)
[37]	Wu, L.; Ho, D.W.C., Reduced-order \(\mathcal{L}_2 - \mathcal{L}_\infty\) filtering of switched nonlinear stochastic systems, IET control theory & applications, 3, 5, 493-508, (2009)
[38]	Yang, W.; Wang, X.; Shi, H., Optimal consensus-based distributed estimation with intermittent communication, International journal of systems science, 42, 9, 1521-1529, (2011) · Zbl 1230.93088
[39]	Yaz, E.; Skelton, R.E., Parametrization of all linear compensators for discrete-time stochastic parameter systems, Automatica, 30, 6, 945-955, (1994) · Zbl 0799.93039
[40]	Yaz, E.; Yaz, Y., State estimation of uncertain nonlinear stochastic systems with general criteria, Applied mathematics letters, 14, 5, 605-610, (2001) · Zbl 0976.93078
[41]	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)