Abstract
This paper presents an overview of the problem of asymptotic worst-case identification in the presence of bounded noise.
Research Supported by AFOSR under grant AFOSR-91-0368 and by NSF under grant 9157306-ECS.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Blumer, A. Ehrenfeucht. D. Haussler, M. Warmuth, “Occam's Razor”, Information Processing Letters 24, pp.377–380, 1987.
M.A. Dahleh and M.H. Khammash, “Controller Design in the Presence of Structured Uncertainty,” to appear in Automatica special issue on robust control.
M.A. Dahleh, E.D. Sontag, D.N. Tse and J.N. Tsitsiklis, “Worst-Case identification of nonlinear fading memory systems,” to appear in ACC Proc., 1992.
M.A. Dahleh, T. Theodosopoulos, and J.N. Tistsiklis, “The sample complexity of worst-case identification of F.I.R. Linear systems,” To appear in Systems and Control Letters.
J. C. Doyle, “Analysis of feedback systems with structured uncertainty,” IEEE Proceedings 129, 242–250, 1982.
E. Fogel and Y. F. Huang, “On the value of information in system identification-bounded noise case,” Automatica, vol.18, no.2, pp.229–238, 1982.
G.C. Goodwin, M. Gevers and B. Ninness, “Quantifying the error in estimated transfer functions with application to model order selection,” IEEE Trans. A-C, Vol 37, No. 7, July 1992.
G. Gu, P.P. Khargonekar and Y. Li, “Robust convergence of two stage nonlinear algorithms for identification in H ∞,” Systems and Control Letters, Vol 18, No. 4, April 1992.
G. Gu and P.P. Khargonekar, “Linear and nonlinear algorithms for identification in ℓ1 with error bounds,” IEEE Trans. A-C, Vol 37, No. 7, July 1992.
A.J. Helmicki, C.A. Jacobson and C.N. Nett, “Identification in H ∞: A robust convergent nonlinear algorithm,” Proceedings of the 1989 International Symposium on the Mathematical Theory of Networks and System, 1989.
A.J. Helmicki, C.A. Jacobson and C.N. Nett, “Identification in H ∞: Linear Algorithms,” Proceedings of the 1990 American Control Conference, pp 2418–2423.
A.J. Helmicki, C.A. Jacobson and C.N. Nett, “Control-oriented System Identification: A Worst-case/deterministic Approach in H ∞,” IEEE Trans. A-C, Vol 36, No. 10, October 1991.
C.A. Jacobson and C.N. Nett, “Worst-case system identification in l 1: Optimal algorithms and error bounds,” in Proc. of the 1991 American Control Conference, June 1991.
J.M. Krause, G. Stein, P.P. Khargonekar, “Robust Performance of Adaptive Controllers with General Uncertainty Structure,” Proceedings of the 29th Conference on Decision and Control, pp. 3168–3175, 1990.
R. Lozano-Leal and R. Ortega, “Reformulation of the parameter identification problem for systems with bounded disturbances,” Automatica, vol.23, no.2, pp.247–251, 1987.
M.K. Lau, R.L. Kosut, S. Boyd, “Parameter Set Estimation of Systems with Uncertain Nonparametric Dynamics and Disturbances,” Proceedings of the 29th Conference on Decision and Control, pp. 3162–3167, 1990.
M. Milanese and G. Belforte, “Estimation theory and uncertainty intervals evaluation in the presence of unknown but bounded errors: Linear families of models and estimators,” IEEE Trans. Automatic Control, AC-27, pp.408–414, 1982.
M. Milanese and R. Tempo, “Optimal algorithm theory for robust estimation and prediction,” IEEE Trans. Automatic Control, AC-30, pp. 730–738, 1985.
M. Milanese, “Estimation theory and prediction in the presence of unknown and bounded uncertainty: a survey,” in Robustness in Identification and Control, M. Milanese, R. Tempo, A. Vicino Eds, Plenum Press, 1989.
P.M. Makila, “Robust Identification and Galois Sequences,” Technical Report 91-1, Process Control Laboratory, Swedish University of Abo, January, 1991.
P.M. Makila and J.R. Partington, “Robust Approximation and Identification in H ∞,” Proc. 1991 American Control Conference, June, 1991.
J.P. Norton, “Identification and application of bounded-parameter models,” Automatica, vol.23, no.4, pp.497–507, 1987.
K. Poolla and A. Tikku, “On the time complexity of worst-case system identification,” preprint, 1992.
F.C. Schweppe. Uncertain dynamic systems, Prentice-Hall, Englewood cliffs, N.J., 1973.
J.F. Traub and H. Wozniakowski, A General Theory of Optimal Algorithms, Academic Press, New York, 1980.
J.F. Traub, G. Wasilkowski and H. Wazniakowski, Information-Based Complexity, Academic Press, 1988.
D. Tse, M.A. Dahleh and J.N. Tsitsiklis. “Optimal Asymptotic Identification under bounded disturbances,” To appear in IEEE Trans. Automat. Contr..
D.N.C. Tse, M.A. Dahleh, J.N. Tsitsiklis, “Optimal and Robust Identification in the ℓ1 norm,” in Proc. of the 1991 American Control Conference, June 1991.
D.N.C. Tse and J.N. Tsitsiklis, “Sample complexity of system identification under a high probability formulation,” in preparation.
D.N.C. Tse, “Optimal and robust identification under bounded disturbances,” Master's thesis, Dept. of Elec. Eng. and Comp. Sci., M.I.T., February, 1991.
G. Zames, “On the metric complexity of casual linear systems: ε-entropy and ε-dimension for continuous-time,” IEEE Trans. on Automatic Control, Vol. 24, April 1979.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag
About this paper
Cite this paper
Dahleh, M.A. (1994). Asymptotic worst-case identification with bounded noise. In: Smith, R.S., Dahleh, M. (eds) The Modeling of Uncertainty in Control Systems. Lecture Notes in Control and Information Sciences, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036258
Download citation
DOI: https://doi.org/10.1007/BFb0036258
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19870-3
Online ISBN: 978-3-540-39327-6
eBook Packages: Springer Book Archive