Squared and absolute errors in optimal approximation of nonlinear systems

Automatica

Volumn 39, Issue 11, 2003, Pages 1865-1876

  Mäkilä, Pertti M ^a  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

Approximation; Nonlinear systems; Optimal approximation; Static nonlinearities

Indexed keywords

ERROR ANALYSIS; POLYNOMIAL APPROXIMATION;

STATIC NONLINEARITIES;

NONLINEAR SYSTEMS;

EID: 0141865693     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(03)00200-0     Document Type: Article

References (34)

1. p with orthonormal basis functions Systems and Control Letters. 39:2000;365-376.
2. An H.-Z., Chen Z.-G. On convergence of LAD estimates in autoregression with infinite variance. Journal of Multivariate Analysis. 12:1982;335-345.
3. Barron A.R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory. 39:1993;930-945.
4. Bhikkaji B., Söderström T. Reduced order models for diffusion systems. International Journal of Control. 74:2001;1543-1557.
5. Denoël E., Solvay J.-P. Linear prediction of speech with a least absolute error criterion. IEEE Transactions on Acoustics, Speech, and Signal Processing. ASSP-33:1985;1397-1403.
6. Enqvist, M., & Ljung, L. (2002). Estimating nonlinear systems in a neighborhood of LTI-approximants. In Proceedings of the 41st IEEE conference on decision and control, Las Vegas (pp. 1005-1010).
7. Glover K., Lam J., Partington J.R. Rational approximation of a class of infinite-dimensional systems I. Singular values of Hankel operators Mathematics of Control, Signals, and Systems. 3:1990;325-344.
8. Gustafsson T.K., Mäkilä P.M. Modelling of uncertain systems via linear programming. Automatica. 32:1996;319-335.
9. Gustafsson T.K., Mäkilä P.M. Modelling of uncertain systems with application to robust process control. Journal of Process Control. 11:2001;251-264.
10. Haber, R., & Keviczky, L. (1999). Nonlinear system identification - input-output modeling approach, Vol. 1. Dordrecht: Kluwer.
11. Ilow J., Hatzinakos D. Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers. IEEE Transactions on Signal Processing. 46:1998;1601-1611.
12. Lin L., Wang L.Y., Zames G. Time complexity and model complexity of fast identification of continuous-time LTI systems. IEEE Transactions on Automatic Control. 44:1999;1814-1828.
13. Ljung L. System identification. 1999;NJ: Prentice-Hall, Upper Saddle River.
14. Ljung L. Estimating linear time-invariant models of nonlinear time-varying systems. European Journal of Control. 7:2001;203-219.
15. Lorentz G.G. Approximation of functions. 1986;Chelsea, New York.
16. Mäkilä, P. M. (2002). On optimal LTI approximation of nonlinear systems. Submitted for publication.
17. Mäkilä, P. M. (2003). Optimal approximation and model quality estimation for nonlinear systems. IFAC SYSID'2003, Rotterdam, to be presented.
18. Mäkilä P.M., Partington J.R. On linear models for nonlinear systems. Automatica. 39:2003;1-13.
19. Mäkilä P.M., Partington J.R., Gustafsson T.K. Worst-case control-relevant identification. Automatica. 31:1995;1799-1819.
20. Mäkilä P.M., Partington J.R., Norlander T. Bounded power signal spaces for robust control and modeling. SIAM Journal of Control and Optimization. 37:1998;92-117.
21. Masry E. Alpha-stable signals and adaptive filtering. IEEE Transactions on Signal Processing. 48:2000;3011-3016.
22. Meerschaert M.M., Scheffler H.-P. Limit distributions for sums of independent random vectors. 2001;Wiley, New York.
23. Milanese M., Vicino A. Information based complexity and nonparametric worst-case system identification. Journal of Complexity. 9:1993;427-446.
24. Partington J.R. Interpolation, identification and sampling. 1997;Oxford University Press, Oxford.
25. Partington J.R., Mäkilä P.M. On system gains for linear and nonlinear systems. Systems and Control Letters. 46:2002;129-136.
26. Pintelon R., Schoukens J. System identification: A frequency domain approach. 2001;IEEE Press, Piscataway, NJ.
27. Rice J.R., White J.S. Norms for smoothing and estimation. SIAM Review. 6:1964;243-256.
28. Sastry S. Nonlinear systems: Analysis, stability, and control. 1999;Springer, New York.
29. Slotine J.-J.E., Li W. Applied nonlinear control. 1991;Prentice-Hall, Englewood Cliffs, NJ.
30. Söderström T., Stoica P. System identification. 1989;Prentice-Hall, London.
31. Wahlberg B., Mäkilä P.M. On approximation of stable linear dynamical systems using Laguerre and Kautz functions. Automatica. 32:1996;693-708.
32. Wiener N. The spectrum of an array and its application to the study of the translation properties of a simple class of arithmetical functions, Part I. Journal of Mathematics and Physics. 6:1927;145-157.
33. Wiener N. The Fourier integral. 1930;Cambridge University Press, London.
34. Zhou K., Doyle J.C., Glover K. Robust and optimal control. 1996;Prentice-Hall, Englewood Cliffs, NJ