Model-set identification based on learning-theoretic inequalities

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 15, Issue 1, 2002, Pages 73-78

  Oishi, Yasuaki ^a   Kimura, Hidenori ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Linear programming; Modelling errors; Probabilistic models; Stochastic properties; System identification

Indexed keywords

AUTOMATION; IDENTIFICATION (CONTROL SYSTEMS); LINEAR PROGRAMMING; PLANTS (BOTANY); RISK PERCEPTION; STOCHASTIC SYSTEMS;

MIXING PROPERTY; MODEL SET IDENTIFICATIONS; MODELLING ERROR; NOMINAL MODELS; PLANT DYNAMICS; PROBABILISTIC FRAMEWORK; PROBABILISTIC MODELS; STOCHASTIC PROPERTIES;

STOCHASTIC MODELS;

EID: 84945540354     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20020721-6-es-1901.00998     Document Type: Conference Paper

References (21)

1. Bartlett, P. L., and S. R. Kulkarni (1998). The complexity of model classes, and smoothing noisy data. Systems & Control Letters, 34, 133-140.
2. Campi, M. C., and P. R. Kumar (1998). Learning dynamical systems in a stationary environment. Systems & Control Letters, 34, 125-132.
3. De Vries, D. K., and P. M. J. Van den Hof (1995). Quantification of uncertainty in transfer function estimation: a mixed probabilistic-worst-case approach. Automatica, 31, 543-557.
4. Goodwin, G. C., M. Gevers, and B. Ninness (1992). Quantifying the error in estimated transfer functions with application to model order selection. IEEE Transactions on Automatic Control, 37, 913-928.
5. ∞. IEEE Transactions on Automatic Control, 36, 1163-1176.
6. Karandikar, R. L., and M. Vidyasagar (2001). Rates of uniform convergence of empirical means with mixing processes. Submitted for publication.
7. Khargonekar, P., and A. Tikku (1996). Randomized algorithms for robust control analysis and synthesis have polynomial complexity. Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan (pp. 3470-3475).
8. Milanese, M., and A. Vicino (1991). Optimal estimation theory for dynamic systems with set membership uncertainty: an overview. Automatica, 27, 997-1009.
9. Nobel, A., and A. Dembo (1993). A note on uniform laws of averages for dependent processes. Statistics & Probability Letters, 17, 169-172.
10. Oishi, Y., and H. Kimura (2001). A learning-theoretic approach to model-set identification. Asian Journal of Control, 3, 10-20.
11. Tempo, R., E. W. Bai, and F. Dabbene (1997). Probabilistic robustness analysis: explicit bounds for the minimum number of samples. Systems & Control Letters, 30, 237-242.
12. Tse, D. N. C., M. A. Dahleh, and J. N. Tsitsiklis (1993). Optimal asymptotic identification under bounded disturbances. IEEE Transactions on Automatic Control, 38, 1176-1190.
13. Vapnik, V. N. (1998). Statistical Learning Theory. John Wiley & Sons, New York, NY.
14. Vidyasagar, M. (2001). Randomized algorithms for robust controller synthesis using statistical learning theory. Automatica, 37, 1515-1528.
15. Vidyasagar, M., and R. L. Karandikar (2001). On the behaviour of learning algorithms with β-mixing process inputs. Submitted for publication.
16. Weyer, E. (2000). Finite sample properties of system identification of ARX models under mixing conditions. Automatica, 36, 1291-1299.
17. Weyer, E., and M. C. Campi (1999). Finite sample properties of system identification methods. Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ (pp. 510-515).
18. Weyer, E., and M. C. Campi (2000). Non-asymptotic confidence ellipsoids for the least squares estimate. Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia (pp. 2688-2693).
19. Weyer, E., R. C. Williamson, and I. M. Y. Mareels (1999). Finite sample properties of linear model identification. IEEE Transactions on Automatic Control, 44, 1370-1383.
20. Zhou, T., and H. Kimura (1995). Structure of model uncertainty for a weakly corrupted plant. IEEE Transactions on Automatic Control, 40, 639-655.
21. Zhu, Y. C. (1989). Estimation of transfer functions: asymptotic theory and a bound of model uncertainty. International Journal of Control, 49, 2241-2258.