Identification for multirate multi-input systems using the multi-innovation identification theory. (English) Zbl 1186.93076

Summary: This paper considers identification problems of multirate multi-input sampled-data systems. Using the continuous-time system discretization technique with zero-order holds, the mapping relationship (state-space model) between available multirate input and output data is set up. The multi-innovation identification theory is applied to estimate the parameters of the obtained multirate models and to present a multi-innovation stochastic gradient algorithm for the multirate systems from the multirate input-output data. Furthermore, the convergence properties of the proposed algorithm are analyzed. An illustrative example is given.


93E12 Identification in stochastic control theory
Full Text: DOI


[1] Wang, D.Q.; Ding, F., Extended stochastic gradient identification algorithms for hammerstein – wiener ARMAX systems, Computers & mathematics with applications, 56, 12, 3157-3164, (2008) · Zbl 1165.65308
[2] Ding, J.; Ding, F., The residual based extended least squares identification method for dual-rate systems, Computers & mathematics with applications, 56, 6, 1479-1487, (2008) · Zbl 1155.93435
[3] Sheng, J.; Chen, T.; Shah, S.L., Optimal filtering for multirate systems, IEEE transactions on circuits and systems, 52, 4, 228-232, (2005)
[4] Li, W.H.; Shah, S.H.; Xiao, D.Y., Kalman filters in non-uniformly sampled multirate systems: for FDI and beyonds, Automatica, 44, 1, 199-208, (2008) · Zbl 1138.93056
[5] Shi, Y.; Chen, T., 2-norm based iterative design of filterbank transceivers: A control perspective, Journal of control science and engineering, 7, (2008), Article ID 143085 · Zbl 1229.94020
[6] Shi, Y.; Ding, F.; Chen, T., 2-norm based recursive design of transmultiplexers with designable filter length, Circuits, systems, and signal processing, 25, 4, 447-462, (2006) · Zbl 1130.94312
[7] Lu, N.Y.; Yang, Y.; Gao, F.R.; Wang, F.L., Multirate dynamic inferential modeling for multivariable process, Chemical engineering science, 59, 4, 855-864, (2004)
[8] Li, D.; Shah, S.L.; Chen, T., Identification of fast-rate models from multirate data, International journal of control, 74, 7, 680-689, (2001) · Zbl 1038.93017
[9] Ding, F.; Chen, T., Hierarchical identification of lifted state – space models for general dual-rate systems, IEEE transactions on circuits and systems-I: regular papers, 52, 6, 1179-1187, (2005) · Zbl 1374.93342
[10] Yu, B.; Shi, Y.; Huang, H., \(l_2 - l_\infty\) filtering for multirate systems using lifted models, Circuits, systems, and signal processing, 27, 5, 699-711, (2008) · Zbl 1173.93360
[11] Ding, F.; Chen, T., Combined parameter and output estimation of dual-rate systems using an auxiliary model, Automatica, 40, 10, 1739-1748, (2004) · Zbl 1162.93376
[12] Ding, F.; Chen, T., Parameter estimation of dual-rate stochastic systems by using an output error method, IEEE transactions on automatic control, 50, 9, 1436-1441, (2005) · Zbl 1365.93480
[13] Shi, Y.; Ding, F.; Chen, T., Multirate crosstalk identification in xdsl systems, IEEE transactions on communication, 54, 10, 1878-1886, (2006)
[14] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14, (2007) · Zbl 1140.93488
[15] Chen, T.; Qiu, L., \(\mathcal{H}_\infty\) design of general multirate sampled-data control systems, Automatica, 30, 7, 1139-1152, (1994) · Zbl 0806.93038
[16] Qiu, L.; Chen, T., \(\mathcal{H}_2\)-optimal design of multirate sampled-data systems, IEEE transactions on automatic control, 39, 12, 2506-2511, (1994) · Zbl 0825.93436
[17] Chen, T.; Francis, B., Optimal sampled-data control systems, (1995), Springer-Verlag London · Zbl 0847.93040
[18] Goodwin, G.C.; Sin, K.S., Adaptive filtering prediction and control, (1984), Prentice-hall Englewood Cliffs, New Jersey · Zbl 0653.93001
[19] L.L. Han, F. Ding, Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital Signal Processing, 19 (2009), in press (doi:10.1016/j.dsp.2008.12.002)
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.