×

zbMATH — the first resource for mathematics

Distributed Kalman filtering for time-varying discrete sequential systems. (English) Zbl 1406.93341
Summary: Discrete sequential system (DSS) consisting of different dynamical subsystems is a sequentially-connected dynamical system, and has found applications in many fields such as automation processes and series systems. However, few results are focused on the state estimation of DSSs. In this paper, the distributed Kalman filtering problem is studied for time-varying DSSs with Gaussian white noises. A locally optimal distributed estimator is designed in the linear minimum variance sense, and a stability condition is derived such that the mean square error of the distributed estimator is bounded. An illustrative example is given to demonstrate the effectiveness of the proposed methods.

MSC:
93E11 Filtering in stochastic control theory
93E10 Estimation and detection in stochastic control theory
93A14 Decentralized systems
60H40 White noise theory
93-04 Software, source code, etc. for problems pertaining to systems and control theory
93A15 Large-scale systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson, B. D.O.; Moore, J. B., Optimal filtering, (1979), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0688.93058
[2] Bezzi, M.; Celada, F.; Ruffo, S.; Seiden, P. E., The transition between immue and discrete states in a celluar automaton model of clonal immune response, Physical A, 245, 1-2, 145-163, (1997)
[3] Chen, B.; Ho, D. W.C.; Zhang, W.; Yu, L., Networked fusion estimation with bounded noises, IEEE Transactions on Automatic Control, 62, 10, 5415-5421, (2017) · Zbl 1390.93779
[4] Chui, C. K.; Chen, G., Kalman filtering with real-time applications, (2009), Springer · Zbl 1206.93110
[5] Cline, T., Near-optimal state estimation for interconnected systems, IEEE Transactions on Automatic Control, 20, 3, 348-351, (1975) · Zbl 0301.93055
[6] Dao, C. D.; Zuo, M. J., Selective maintenance for multistate series systems with s-dependent components, IEEE Transactions on Reliability, 65, 2, 525-539, (2016)
[7] Farian, M.; Ferrari-Trecate, G.; Scattolini, R., Moving-horizon partition-based state estimation of large-scale systems, Automatica, 46, 910-918, (2010) · Zbl 1191.93130
[8] Gao, H.; Lam, J.; Xie, L.; Wang, C., New approach to mixed \(H_2 / H_\infty\) filtering for ploytopic discrete-time systems, IEEE Transactions on Signal Processing, 53, 8, 3183-3191, (2005)
[9] Haber, A.; Verhaegen, M., Moving horizon estimation for large-scale interconnected systems, IEEE Transactions on Automatic Control, 58, 11, 2834-2847, (2013) · Zbl 1369.93594
[10] Khan, U. A.; Moura, J. M.F., Distributed the Kalman filter for large-scale systems, IEEE Transactions on Signal Processing, 56, 10, 4919-4935, (2008) · Zbl 1390.94242
[11] Li, X.; Jilkov, V., Survey of maneuvering target tracking. Part I: Dynamic Models, IEEE Transactions on Aerospace and Electronic Systems, 39, 3, 1333-1364, (2003)
[12] Marelli, D. E.; Fu, M., Distributed weighted least-squares estimation with fast convergence for large-scale systems, Automatica, 51, 27-39, (2015) · Zbl 1309.93159
[13] Park, S.; Martins, N. C., Design of distributed LTI observers for state omniscience, IEEE Transactions on Automatic Control, 62, 2, 561-576, (2016) · Zbl 1364.93435
[14] Ramamoorthy, C. V., Connetivity consideration of graphs representing discrete squential systems, IEEE Transactions on Electronic Computing, EC-14, 5, 724-727, (1965) · Zbl 0148.39805
[15] Riverso, S.; Farina, M.; Ferrari-Trecate, G., Plug-and-play state estimation and application to distributed output feedback model predictive control, European Journa of Control, 25, 17-26, (2015) · Zbl 1360.93073
[16] Riverso, S., Farina, M., Scattolini, R., & Ferrari-Trecate, G. (2013). Plug-and-play distributed state estimation for linear systems. In Proceedings of the 52nd IEEE conference on decision and control, Florence, Italy (pp. 4889-4894).
[17] Sanders, C. W.; Tacker, E. C.; Linton, T. D., A new class of decentralized filters for interconnected systems, IEEE Transactions on Automatic Control, 19, 3, 259-262, (1974) · Zbl 0275.93048
[18] Sanders, C. W.; Tacker, E. C.; Linton, T. D.; Ling, R. Y.-S., Specific structures for large-scale state estimation algorithms having information exchange, IEEE Transactions on Automatic Control, 23, 2, 255-261, (1978) · Zbl 0379.93007
[19] Stanković, S. S.; Stanković, M. S.; Stipanović, D. M., Consensus based overlapping decentralized estimator, IEEE Transactions on Automatic Control, 54, 2, 410-415, (2009) · Zbl 1367.93634
[20] Świder, J.; Hetmańczyk, M., The visualization of discrete sequential systems, Journal of Achievements in Matherials and Manufacturing Engineering, 34, 2, 196-203, (2009)
[21] Ugrinovski, V., Distributed robust estimation over randomly switching networks using \(H_\infty\) consensus, Automatica, 49, 160-168, (2013) · Zbl 1257.93094
[22] Vadigepalli, R.; Doyle, F. J., A distributed state estimation and control algorithm for plantwide processes, IEEE Transactions on Control Systems Technology, 11, 1, 119-127, (2003)
[23] Wang, Z. D.; Liu, Y. R.; Liu, X. H., \(H_\infty\) filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica, 44, 5, 1268-1277, (2008) · Zbl 1283.93284
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.