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An auxiliary model based least squares algorithm for a dual-rate state space system with time-delay using the data filtering. (English) Zbl 1395.93530
Summary: For dual-rate state space systems with time-delay, this paper combines the auxiliary model identification idea with the filtering technique, transforms the state space model into the identification model with different input and output sampling rates, and presents a filtering and auxiliary model based recursive least squares identification algorithm with finite measurement input-output data. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm can generate more accurate parameter estimates and has a higher computational efficiency because the dimensions of its covariance matrices become small.

##### MSC:
 93E11 Filtering in stochastic control theory 93E10 Estimation and detection in stochastic control theory 93E12 Identification in stochastic control theory 93E24 Least squares and related methods for stochastic control systems 93B15 Realizations from input-output data 93C35 Multivariable systems, multidimensional control systems
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##### References:
 [1] Galanin, M.; Lototsky, A.; Rodin, A., The mathematical modelling of liner movement in a magnetic compressorelastic, liquid and plastic liner models comparison, Math. Modell. Anal., 17, 1, 31-46, (2012) · Zbl 1242.78005 [2] Kim, H. C.; Dharmayanda, H. R.; Kang, T.; Budiyono, A.; Lee, G. G.; Adiprawita, W., Parameter identification and design of a robust attitude controller using H-infinity methodology for the raptor E620 small-scale helicopter, Int. J. Control Autom. Syst., 10, 1, 88-101, (2012) [3] Lim, Z. S.; Kwon, S. T.; Joo, M. G., Multi-object identification for mobile robot using ultrasonic sensors, Int. J. Control Autom. Syst., 10, 3, 589-593, (2012) [4] Pintelon, R.; Schoukens, J.; Guillaume, P., Box-Jenkins identification revisited—part iiimultivariable systems, Automatica, 43, 5, 868-875, (2007) · Zbl 1117.93331 [5] Barenthin, M.; Bombois, X.; Hjalmarsson, H.; Scorletti, G., Identification for control of multivariable systemscontroller validation and experiment design via lmis, Automatica, 44, 12, 3070-3078, (2008) · Zbl 1153.93344 [6] Ding, F., Coupled-least-squares identification for multivariable systems, IET Control Theory Appl., 7, 1, 68-79, (2013) [7] Mercère, G.; Bako, L., Parameterization and identification of multivariable state-space systemsa canonical approach, Automatica, 47, 8, 1547-1555, (2011) · Zbl 1226.93038 [8] Jafari, M.; Salimifard, M.; Dehghani, M., Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm, ISA Trans., 53, 4, 1243-1252, (2014) [9] Campbell, S. L.; Horton, K. G.; Nikoukhah, R., Auxiliary signal design for rapid multi-model identification using optimization, Automatica, 38, 8, 1313-1325, (2002) · Zbl 1010.93033 [10] Liu, Y. J.; Xiao, Y. S.; Zhao, X. L., Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model, Appl. Math. Comput., 215, 4, 1477-1483, (2009) · Zbl 1177.65095 [11] Ding, F.; Liu, X. P., Auxiliary model-based stochastic gradient algorithm for multivariable output error systems, Acta Autom. Sin., 36, 7, 993-998, (2010) · Zbl 1240.93341 [12] Li, H.; Shi, Y., Robust H-infinity filtering for nonlinear stochastic systems with uncertainties and random delays modeled by Markov chains, Automatica, 48, 1, 159-166, (2012) [13] Cong, S.; Hong, L.; Layne, J. R., Iterative robust filtering for ground target tracking, IET Control Theory Appl., 1, 1, 372-380, (2007) [14] Torokhti, A.; Miklavcic, S. J., Filtering of infinite sets of stochastic signalsan approach based on interpolation techniques, Signal Process., 91, 11, 2556-2566, (2011) · Zbl 1221.94024 [15] Hsieh, C. S., State estimation for descriptor systems via the unknown input filtering method, Automatica, 49, 5, 1281-1286, (2013) · Zbl 1319.93074 [16] Gu, Y.; Ding, F.; Li, J. H., State filtering and parameter estimation for linear systems with d-step state-delay, IET Signal Process., 8, 6, 639-646, (2014) [17] Ding, F.; Wang, Y. J.; Ding, J., Recursive least squares parameter identification for systems with colored noise using the filtering technique and the auxiliary model, Digit. Signal Process., 37, 100-108, (2015) [18] Bae, K.; Meseguer, J.; Ölveczky, P. C., Formal patterns for multirate distributed real-time systems, Sci. Comput. Prog., 91, 3-44, (2014) [19] Tanc, A. K.; Kayran, A. H., Maximum entropy power spectrum estimation for 2-D multirate systems, Circuits Syst. Signal Process., 31, 1, 271-281, (2012) · Zbl 1252.94031 [20] Üstüntürk, A., Output feedback stabilization of nonlinear dual-rate sampled-data systems via an approximate discrete-time model, Automatica, 48, 8, 1796-1802, (2012) · Zbl 1267.93148 [21] Cimino, M.; Pagilla, P. R., Input-state model matching and ripple-free response for dual-rate systems, Syst. Control Lett., 60, 10, 815-824, (2011) · Zbl 1226.93039 [22] Harris, F. J., Multirate signal processing for communication systems, (2004), Prentice Hall Englewood Cliffs, NJ [23] Chen, J., Several gradient parameter estimation algorithms for dual-rate sampled systems, J. Frankl. Inst. - Eng. Appl. Math., 351, 1, 543-554, (2014) · Zbl 1293.93505 [24] Ding, F.; Chen, T., Parameter estimation of dual-rate stochastic systems by using an output error method, IEEE Trans. Autom. Control, 50, 9, 1436-1441, (2005) · Zbl 1365.93480 [25] Ding, J.; Fan, C. X.; Lin, J. X., Auxiliary model based parameter estimation for dual-rate output error systems with colored noise, Appl. Math. Modell., 37, 4051-4058, (2013) [26] Ding, J.; Lin, J. X., Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique, Circuits Syst. Signal Process., 33, 5, 1439-1449, (2014) [27] Liu, Y. J.; Ding, F.; Shi, Y., Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle, Circuits Syst. Signal Process., 31, 6, 1985-2000, (2012) · Zbl 1269.93127 [28] Goodwin, G. C.; Sin, K. S., Adaptive filtering prediction and control, (1984), Prentice Hall Englewood Cliffs, NJ · Zbl 0653.93001 [29] Ljung, L., System identification: theory for the user, (1999), Prentice Hall Englewood Cliffs, NJ [30] (Golub, G. H.; Van Loan, C. F., Matrix Computations, (1996), Johns Hopkins University Press Baltimore, MD) · Zbl 0865.65009 [31] Xu, L., A proportional differential control method for a time-delay system using the Taylor expansion approximation, Appl. Math. Comput., 236, 391-399, (2014) · Zbl 1334.93125 [32] Xu, L.; Chen, L.; Xiong, W. L., Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration, Nonlinear Dyn., 79, 3, 2155-2163, (2015) [33] Xu, L., Application of the Newton iteration algorithm to the parameter estimation for dynamical systems, J. Comput. Appl. Math., 288, 33-43, (2015) · Zbl 1314.93062 [34] Chen, H. B.; Xiao, Y. S.; Ding, F., Hierarchical gradient parameter estimation algorithm for Hammerstein nonlinear systems using the key term separation principle, Appl. Math. Comput., 247, 1202-1210, (2014) · Zbl 1343.62055 [35] Hu, Y. B.; Liu, B. L.; Zhou, Q., A multi-innovation generalized extended stochastic gradient algorithm for output nonlinear autoregressive moving average systems, Appl. Math. Comput., 247, 218-224, (2014) · Zbl 1343.62059 [36] Filipovic, V. Z., Consistency of the robust recursive Hammerstein model identification algorithm, J. Frankl. Inst., 352, 5, 1932-1945, (2015) · Zbl 1395.93169 [37] F. Ding, X.H. Wang, Q.J. Chen, Y.S. Xiao, Recursive least squares parameter estimation for a class of output nonlinear systems based on the model decomposition, Circuits Syst. Signal Process. 35 (2016). doi: 10.1007/s00034-015-0190-6 [38] Y.J. Wang, F. Ding, Iterative estimation for a nonlinear IIR filter with moving average noise by means of the data filtering technique, IMA J. Math. Control Inf. (2016). doi: 10.1093/imamci/dnv067 [39] methods for dual-rate Hammerstein systems, IEEE Trans. Control Syst. Technol. 23 (5) (2015) 1952-1960 [40] Yang, X. Q.; Gao, H. J., Multiple model approach to linear parameter varying time-delay system identification with EM algorithm, J. Frankl. Inst., 351, 12, 5565-5581, (2014) · Zbl 1393.93032
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