A solution to the blow-up problem in adaptive controllers

“A solution to the blow-up problem in adaptive controllers”

Authors: Steinar Sælid, Olav Egeland and Bjarne A. Foss,
Affiliation: Kongsberg Maritime, NTNU, Department of Engineering Cybernetics and SINTEF
Reference: 1985, Vol 6, No 1, pp. 39-56.

Keywords: Adaptive control, blow-up problems, variable forgetting factor

Abstract: This paper addresses the blow-up problem associated with the parameter estimation part of an adaptive controller. A partial solution to the problem has been devised by the introduction of a variable forgetting factor. However, this does not eliminate the blow-up possibility. This is shown by simulation experiments on two different models.

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PDF (2591 Kb) DOI: 10.4173/mic.1985.1.3

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[6] A. Vahidi, M. Druzhinina, A. Stefanopoulou and Huei Peng (2003), doi:10.1109/ACC.2003.1242508

[7] G. Kreisselmeier (1990), doi:10.1109/9.50342

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[11] Daniel Sbarbaro, Pablo Espinoza, Felipe Mujica and Guillermo Cortes (2004), doi:10.1016/S1474-6670(17)31058-3

[12] D.F. Garcia, H. Lopez and A.B. Diez (1991), doi:10.1016/S1474-6670(17)52464-7

[13] Andries van Grootheest, Daan M. Pool, Marinus van Paassen and Max Mulder (2018), doi:10.2514/6.2018-0118

[14] Ruohan Guo and Weixiang Shen (2024), doi:10.1109/TIE.2023.3314844

References:
[1] ÅSTRÖM, K.J., BORRISSON, V., LJUNG, L., WITTENMARK, B. (1977). Theory and application of self-tuning regulators, Automatica, 13, p. 457 doi:10.1016/0005-1098(77)90067-X
[2] CLARKE, D., GAWTHROP, P. (1979). Self-tuning control, Proc. I.E.E..Part D, 126, 663- 640.
[3] CORDERO, A.O., MAYNE, D.Q. (1981). Deterministic convergence of a self-tuning regulator with variable forgetting factor, Proc. I.E.E..Pan D, 128,19-23.
[4] FORTESCUE, T.R., KERSCHENBAUM, L.S., YDSTIE, B.E. (1981). Implementation of self-tuning regulators with variable forgetting factors, Automatica, 17, 831-835 doi:10.1016/0005-1098(81)90070-4
[5] GOODWIN, G.C., ELLIOT, H., TEOH, E.K. (1983). Deterministic convergence of a self tuning regulator with covariance resetting, Proc. I.E.E.E..Part D, 130, 6-8.
[6] HÄGGLUND, T. (1983). Recursive least squares identification with forgetting old data, Dept. of Automatic Control, Lund Institute of Technology, March 1983.
[7] LANDAU, I.D., LOZANO, R. (1981). Unification of discrete time explicit model reference adaptive control design, Automatica, 17, 593-611 doi:10.1016/0005-1098(81)90031-5
[8] LJUNG, L. (1977). Analysis of recursive stochastic algorithms, I.E.E.E. Trans., AC-22, 551-575 doi:10.1109/TAC.1977.1101561
[9] LJUNG, L. (1981). Analysis of a general recursive prediction error identification algorithm, Automatica, 17, 89-99 doi:10.1016/0005-1098(81)90086-8
[10] SAELID, S., SVANES, T., ONSHUS, T., JENSSEN, N.A. (1984). Design considerations, analysis and practical experience with an adaptive ships autopilot, Preprints, IFAC 9th World Congress, Budapest, Hungary, July 1984, vol. 2, pp. 35-40.
[11] SAELID, S., JENSSEN, N.A. (1982). Adaptive autopilot with wave filter, Proc. IFAC Symp. on Identification and System Parameter Estimation, Washington, pp. 1220-1225.
[12] SAELID, S., JENSSEN, N.A., BALCHEN, J.G. (1983). Design and analysis of a dynamic positioning system based on Kalman filtering and optimal control, IEEE Trans., AC-28, 331-339 doi:10.1109/TAC.1983.1103225
[13] SAELID, S., FOSS, B. (1983). Adaptive controllers with a vector variable forgetting factor, Proc. of the 22nd IEEE CDC Conf, San Antonio, Texas, pp. 1488-1494.
[14] SÖDERSTRÖM, T., LJUNG, L., GUSTAVSSON, I. (1978). A theoretical analysis of recursive identification methods, Automatica, 14, 231-244 doi:10.1016/0005-1098(78)90088-2

BibTeX:
@article{MIC-1985-1-3,
  title={{A solution to the blow-up problem in adaptive controllers}},
  author={Sælid, Steinar and Egeland, Olav and Foss, Bjarne A.},
  journal={Modeling, Identification and Control},
  volume={6},
  number={1},
  pages={39--56},
  year={1985},
  doi={10.4173/mic.1985.1.3},
  publisher={Norwegian Society of Automatic Control}
};

Article

“A solution to the blow-up problem in adaptive controllers”