×

Convergence of HLS estimation algorithms for multivariable ARX-like systems. (English) Zbl 1117.93332

Summary: A hierarchical least squares (HLS) algorithm is derived in details for identifying MIMO ARX-like systems based on the hierarchical identification principle. It is shown that the parameter estimation errors by the HLS algorithm consistently converge to zero for bounded noise variances by using the stochastic martingale theory. A numerical example is given.

MSC:

93C35 Multivariable systems, multidimensional control systems
93E11 Filtering in stochastic control theory
93E24 Least squares and related methods for stochastic control systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93E12 Identification in stochastic control theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ding, F.; Chen, T., Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica, 41, 2, 315-325, (2005) · Zbl 1073.93012
[2] 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
[3] F. Ding, D.Q. Zhu, B. Zou, Convergence analysis of hierarchical least squares algorithms for MIMO systems, in: Proceedings of the Second International Conference on Impulsive Dynamical Systems and Applications, Wuxi, China, October 28-30, 2005, pp. 23-31.
[4] 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
[5] Ljung, L., System identification: theory for the user, (1999), Prentice-Hall Englewood Cliffs, NJ
[6] Goodwin, G.C.; Sin, K.S., Adaptive filtering prediction and control, (1984), Prentice-Hall Englewood Cliffs, NJ · Zbl 0653.93001
[7] 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
[8] Ding, F.; Chen, T., Performance bounds of forgetting factor least squares algorithm for time-varying systems with finite measurement data, IEEE transactions on circuits and systems-I: regular papers, 52, 3, 555-566, (2005) · Zbl 1374.93390
[9] 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
[10] Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489, (2005) · Zbl 1086.93063
[11] Ding, F.; Liu, P.; Shi, Y., Convergence analysis of estimation algorithms of dual-rate stochastic systems, Applied mathematics and computation, 176, 1, 245-261, (2006) · Zbl 1095.65056
[12] 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
[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.; Qiu, 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)
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.