×

Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. (English) Zbl 1177.65095

Summary: In order to reduce computational burden and improve the convergence rate of identification algorithms, an auxiliary model based multi-innovation stochastic gradient (AM-MISG) algorithm is derived for the multiple-input single-output systems by means of the auxiliary model identification idea and multi-innovation identification theory. The basic idea is to replace the unknown outputs of the fictitious subsystems in the information vector with the outputs of the auxiliary models and to present an auxiliary model based stochastic gradient algorithm, and then to derive the AM-MISG algorithm by expanding the scalar innovation to innovation vector and introducing the innovation length. The simulation example shows that the proposed algorithms work quite well.

MSC:

65K10 Numerical optimization and variational techniques
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ding, J.; Ding, F.; Zhang, S., Parameter multi-input identification of single-output systems based on FIR models and least squares principle, Applied mathematics and computation, 197, 1, 297-305, (2008) · Zbl 1136.93455
[2] Zheng, W.X., On a least squares based algorithm for identification of stochastic linear systems, IEEE transactions on signal processing, 46, 6, 1631-1638, (1998) · Zbl 1039.93065
[3] Zheng, W.X., Least-squares identification of a class of multivariable systems with correlated disturbances, Journal of franklin institute, 336, 8, 1309-1324, (1999) · Zbl 0967.93093
[4] Ding, F.; Chen, T.; Qiu L, L., Bias compensation based recursive least squares identification algorithm for MISO systems, IEEE transactions on circuits and systems - II: express briefs, 53, 5, 349-353, (2006)
[5] Ding, F.; Chen, H.B.; Li, M., Multi-innovation least squares identification methods based on the auxiliary model for MISO systems, Applied mathematics and computation, 187, 2, 658-668, (2007) · Zbl 1114.93101
[6] Ding, F.; Shi, Y.; Chen, T., Performance analysis of estimation algorithms of non-stationary ARMA processes, IEEE transactions on signal processing, 54, 3, 1041-1053, (2006) · Zbl 1373.94569
[7] Ding, F.; Chen, T., Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica, 41, 2, 315-325, (2005) · Zbl 1073.93012
[8] Ding, F.; Chen, T., Hierarchical least squares identification methods for multivariable systems, IEEE transactions on automatic control, 50, 3, 397-402, (2005) · Zbl 1365.93551
[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] Ding, F.; Qiu, L.; Chen, T., Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems, Automatica, 45, 2, 324-332, (2009) · Zbl 1158.93365
[11] Ding, F.; Liu, P.X.; Yang, H.Z., Parameter identification and intersample output estimation for dual-rate systems, IEEE transactions on systems man and cybernetics part A: systems and humans, 38, 4, 966-975, (2008)
[12] Ding, F.; Yang, H.Z.; Liu, F., Performance analysis of stochastic gradient algorithms under weak conditions, Science in China series F-information sciences, 51, 9, 1269-1280, (2008) · Zbl 1145.93050
[13] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14, (2007) · Zbl 1140.93488
[14] 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
[15] 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
[16] Ding, F.; Shi, Y.; Chen, T., Auxiliary model based least-squares identification methods for Hammerstein output-error systems, Systems and control letters, 56, 5, 373-380, (2007) · Zbl 1130.93055
[17] Zhang, J.B.; Ding, F.; Shi, Y., Self-tuning control based on multi-innovation stochastic gradient parameter estimation, Systems and control letters, 58, 1, 69-75, (2009) · Zbl 1154.93040
[18] Ding, F.; Liu, P.X.; Liu, G., Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, Signal processing, 89, 10, 1883-1890, (2009) · Zbl 1178.94137
[19] Han, L.L.; Ding, F., Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital signal processing, 19, 4, 545-554, (2009)
[20] Han, L.L.; Ding, F., Identification for multirate multi-input systems using the multi-innovation identification theory, Computers and mathematics with applications, 57, 9, 1438-1449, (2009) · Zbl 1186.93076
[21] Ljung, L., System identification: theory for the user, (1999), Prentice-Hall Englewood Cliffs, NJ
[22] Goodwin, G.C.; Sin, K.S., Adaptive filtering prediction and control, (1984), Prentice-Hall Englewood Cliffs, NJ · Zbl 0653.93001
[23] Ding, F.; Chen, T., Identification of dual-rate systems based on finite impulse response models, International journal of adaptive control and signal processing, 18, 7, 589-598, (2004) · Zbl 1055.93018
[24] Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489, (2005) · Zbl 1086.93063
[25] Wang, D.Q.; Ding, F., Extended stochastic gradient identification algorithms for hammerstein – wiener ARMAX systems, Computers and mathematics with applications, 56, 12, 3157-3164, (2008) · Zbl 1165.65308
[26] Wang, L.Y.; Xie, L.; Wang, X.F., The residual based interactive stochastic gradient algorithms for controlled moving average models, Applied mathematics and computation, 211, 2, 442-449, (2009) · Zbl 1162.93037
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.