×

Hierarchical least-squares based iterative identification for multivariable systems with moving average noises. (English) Zbl 1198.93216

Summary: A hierarchical least-squares based iterative identification algorithm is derived for multivariable systems with moving average noises (i.e., multivariable CARMA-like models). The basic idea is to combine the hierarchical identification principle and iterative identification principle and to decompose a multivariable system into two subsystems, one containing a parameter vector and the other containing a parameter matrix. To solve the difficulty of the information matrix including unmeasurable noise terms, the unknown noise terms are replaced with their iterative residuals, which are computed through the preceding parameter estimates. The algorithm performs a hierarchical computational process at each iteration. The least-squares based iterative algorithm makes full use of all data at each iteration and thus can generate highly accurate parameter estimates. The simulation results indicate that the proposed algorithm works quite well.

MSC:

93E10 Estimation and detection in stochastic control theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Kohandel, M.; Sivaloganathan, S.; Tenti, G., Estimation of the quasi-linear viscoelastic parameters using a genetic algorithm, Mathematical and computer modelling, 47, 3-4, 266-270, (2008) · Zbl 1187.74145
[2] Mocenni, C.; Sparacino, E.; Vicino, A.; Zubelli, J.P., Mathematical modelling and parameter estimation of the serra da mesa basin, Mathematical and computer modelling, 47, 7-8, 765-780, (2008) · Zbl 1134.92040
[3] Figueroa, J.L.; Biagiola, S.I.; Agamennoni, O.E., An approach for identification of uncertain Wiener systems, Mathematical and computer modelling, 48, 1-2, 305-315, (2008) · Zbl 1145.93432
[4] Ding, J.; Ding, F.; Zhang, S., Parameter identification of multi-input, single-output systems based on FIR models and least squares principle, Applied mathematics and computation, 197, 1, 297-305, (2008) · Zbl 1136.93455
[5] 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
[6] Liu, Y.J.; Xiao, Y.S.; Zhao, X.L., Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model, Applied mathematics and computation, 215, 4, 1477-1483, (2009) · Zbl 1177.65095
[7] Han, L.L.; Ding, F., Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital signal processing, 19, 4, 545-554, (2009)
[8] Han, L.L.; Ding, F., Identification for multirate multi-input systems using the multi-innovation identification theory, Computers & mathematics with applications, 57, 9, 1438-1449, (2009) · Zbl 1186.93076
[9] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14, (2007) · Zbl 1140.93488
[10] Ding, F.; Chen, T., Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica, 41, 2, 315-325, (2005) · Zbl 1073.93012
[11] 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
[12] Xiao, Y.S.; Zhang, Y.; Ding, J.; Dai, J.Y., The residual based interactive least squares algorithms and simulation studies, Computers & mathematics with applications, 58, 6, 1190-1197, (2009) · Zbl 1189.62149
[13] 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
[14] 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
[15] 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
[16] Han, L.L.; Sheng, J.; Ding, F.; Shi, Y., Auxiliary model identification method for multirate multi-input systems based on least squares, Mathematical and computer modelling, 50, 7-8, 1100-1106, (2009) · Zbl 1185.93139
[17] Zhang, J.B.; Ding, F.; Shi, Y., Self-tuning control based on multi-innovation stochastic gradient parameter estimation, Systems & control letters, 58, 1, 69-75, (2009) · Zbl 1154.93040
[18] Ding, F.; Chen, T., Iterative least squares solutions of coupled Sylvester matrix equations, Systems & control letters, 54, 2, 95-107, (2005) · Zbl 1129.65306
[19] Ding, F.; Chen, T., Gradient based iterative algorithms for solving a class of matrix equations, IEEE transactions on automatic control, 50, 8, 1216-1221, (2005) · Zbl 1365.65083
[20] Ding, F.; Chen, T., On iterative solutions of general coupled matrix equations, SIAM journal on control and optimization, 44, 6, 2269-2284, (2006) · Zbl 1115.65035
[21] Ding, F.; Liu, P.X.; Ding, J., Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle, Applied mathematics and computation, 197, 1, 41-50, (2008) · Zbl 1143.65035
[22] Xie, L.; Ding, J.; Ding, F., Gradient based iterative solutions for general linear matrix equations, Computers & mathematics with applications, 58, 7, 1441-1448, (2009) · Zbl 1189.65083
[23] Golub, G.H., Matrix computations, (1996), Johns Hopkins Univ. Press Baltimore, MD
[24] Dehghan, M.; Hajarian, M., Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation \(A_1 X_1 B_1 + A_2 X_2 B_2 = C\), Mathematical and computer modelling, 49, 9-10, 1937-1959, (2009) · Zbl 1171.15310
[25] Dehghan, M.; Hajarian, M., An iterative algorithm for solving a pair of matrix equations AYB = E, CYD = F over generalized centro-symmetric matrices, Computers & mathematics with applications, 56, 12, 3246-3260, (2008) · Zbl 1165.15301
[26] Dehghan, M.; Hajarian, M., An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices, Applied mathematical modelling, 34, 3, 639-654, (2010) · Zbl 1185.65054
[27] Liu, X.G.; Qian, J., Modeling, control and optimization of ideal internal thermally coupled distillation columns, Chemical engineering & technology, 23, 3, 235-241, (2000)
[28] Shi, J.; Liu, X.G., Melt index prediction by weighted least squares support vector machines, Journal of applied polymer science, 101, 1, 285-289, (2005)
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.