### “Convergence Properties of an Extended Least Squares (ELS) Variant”

**Authors:**Rolf Henriksen,

**Affiliation:**NTNU, Department of Engineering Cybernetics

**Reference:**2000, Vol 21, No 2, pp. 105-119.

**Keywords:**ELS methods, convergence analysis, adaptive control

**Abstract:**By factorizing the A- and B-polynomials in an ARMAX model and filtering the input/output data with the appropriate factors thereof, the parameters of the model can be estimated in a decentralized fashion. This may improve the robustness of sonic estimators significantly, e.g., when applied to very stiff systems. Earlier work on these techniques has established both local and global properties for some LS, IV, and PE variants. An ELS variant has, however, never been considered, and a variant of this type is introduced. Local and global convergence properties of this variant are analyzed.

PDF (3245 Kb) DOI: 10.4173/mic.2000.2.3

**References:**

[1] CLARY, J.P. FRANKLIN, G.F. (1984). Self-tuning control with a priori plant knowledge, Proc. 23rd IEEE Conference on Decision and Control, Las Vegas, Nevada, December 1984, pp. 369-374.

[2] HENRIKSEN, R. (1988). Convergence analysis of some decentralized estimators, Prot: 8th IFAC/IFORS Symposium on Identification and System Parameter Estimation (selected papers), Beijing, P.R. China, August 27-31, pp. 361-366 (IFAC Proceedings Series, 1989, Number 8, Volume 1, Pergamon Press).

[3] HENRIKSEN, R. (1989). Convergence analysis of some decentralized estimators, Modeling. Identification and Control, 10, No. 1, pp. 13-34 doi:10.4173/mic.1989.1.2

[4] HENRIKSEN, R. (1991). Accuracy of some robust estimators based upon prefiltering of the input/output data, Proc. 9th IFAC/IFORS Symposium on Identification and System Parameter Estimation, Budapest, Hungary, August 8-12.

[5] HENRIKSEN, R. (1992). Asymptotic properties of some estimators based upon prefiltering of the input/output data, Proc. 11th IASTED International Conference Modeling, Identification and Control, Innsbruck, Austria, February 10-12, pp. 231-235.

[6] HENRIKSEN, R. WEYER, E. (1990). Convergence aspects of some robust estimators based upon prefiltering of the input/output data, Proc. 11th IFAC World Congress, Tallinn, Estonia, August 13-17, Vol. 3, pp. 215-220.

[7] LJUNG, L. (1977). Analysis of recursive stochastic algorithms, IEEE Trans. Automatic Control, AC-22,551-575 doi:10.1109/TAC.1977.1101561

[8] LJUNG, L. (1987). System Identification: Theory for the User, Prentice Hall.

[9] LJUNG, L. SÖDERSTRÖM, T. (1983). Theory and Practice of Recursive Identification, The MIT Press, Cambridge, Massachusetts.

[10] SÖDERSTRÖM, T. STOICA, P. (1989). System Identification, Prentice Hall.

[11] WELLSTEAD, P.E. ZARROP, M.B. (1991). Self-tuning Systems - Control and Signal Processing, John Wiley and Sons.

[12] WEYER, E. (1991). A recursive decentralized parameter estimator for a general linear SISO system, Proc. 9th IFAC/IFORS Symposium on Identification and System Parameter Estimation, Budapest, Hungary, August 8-12.

[13] YOUNG, R.E., HENRIKSEN, R. MELLICHAMP, D.A. (1987). A multi-rate decentralized parameter estimation method for stiff systems, Proc. 26th IEEE Conference on Decision and Control, Los Angeles, California, December 1987, pp. 1902-1907.

**BibTeX:**

@article{MIC-2000-2-3,

title={{Convergence Properties of an Extended Least Squares (ELS) Variant}},

author={Henriksen, Rolf},

journal={Modeling, Identification and Control},

volume={21},

number={2},

pages={105--119},

year={2000},

doi={10.4173/mic.2000.2.3},

publisher={Norwegian Society of Automatic Control}

};