Abstract
Stochastic and worst case system identification are different and are usually treated separately. We believe that under certain assumptions there exist estimates of unknown systems that are near optimal from both the stochastic and worst case points of view. This paper studies some algorithms that produce such estimates. The algorithms combine a classical least squares or maximum likelihood estimate with a projection. It is shown that the modified estimates are closer to the true system than the least squares and maximum likelihood estimates, and that they are convergent and near optimal in the worst case setting. It is also shown that these results extend to more general cases.
The authors would like to thank Professor G. Gu of LSU and Professor R. Tempo of CNR for their comments on the paper. This research supported in part by NSF Grant ECS-9011359, and DARPA Grant N00174-91-C-0116.
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References
E.W. Bai AND S. Raman, Robust system identification with noisy time/frequency response experimental data: projection and linear algorithms, Automatica (to appear).
A.J. Helmicki, C.A. Jacobson AND C.N. Nett, Control oriented system identification: a worst case/deterministic approach in H∞, IEEE Trans. Automat. Control, vol. AC-36, (1991), pp. 1163–1176.
C.A. Jacobson, C.N. Nett AND J.R. Partington, Worst case system identification in l1: optimal algorithms and error bounds, Syst. and Contr. Letters, vol. 19, (1992), pp. 419–424.
G. Gu AND P.P. Khargonekar, Linear and nonlinear algorithms for identification in H∞ with error bounds, IEEE Trans. Automat. Control, vol. AC-37, (1992), pp. 953–963.
J.M. Krause AND P.P. Khargonekar, A comparison of classical stochastic and deterministic robust identification, IEEE Trans. Automat. Control, vol. AC-37, (1992), pp. 994–1000.
L. Ljung, System Identification: Theory For The User, Prentice-Hall, Englewood Cliffs, NJ, 1987.
R. Tempo AND G.W. Wasilkowski, Maximum likelihood estimators and worst case optimal algorithms for system identification, Syst. and Contr. Letters, vol. 10, (1988), pp. 265–270.
R. Tempo, Robust and optimal algorithms for worst case parametric system identification, (preprint) 1993.
J.F. Traub, G.W. Wasilkowski AND H. Wozniakowski, Information Based Complexity, Academic Press, New York, 1988.
B. Wahlberg AND L. Ljung, Hard frequency-domain model error bounds from least squares like identification techniques, IEEE Trans. Automat. Control, vol. AC-37, (1992), pp. 900–912.
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© 1995 Springer Science+Business Media New York
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Bai, EW., Andersland, M.S. (1995). Compatibility of Stochastic and Worst Case System Identification: Least Squares, Maximum Likelihood and General Cases. In: Åström, K.J., Goodwin, G.C., Kumar, P.R. (eds) Adaptive Control, Filtering, and Signal Processing. The IMA Volumes in Mathematics and its Applications, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8568-2_2
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DOI: https://doi.org/10.1007/978-1-4419-8568-2_2
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