Choice of free parameters in expansions of discrete-time Volterra models using Kautz functions

Automatica

Volumn 43, Issue 6, 2007, Pages 1084-1091

  da Rosa, Alex ^a   Campello, Ricardo J G B ^a,b   Amaral, Wagner C ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Nonlinear systems; Optimization; System identification; Two parameter Kautz functions; Volterra series

Indexed keywords

ERROR ANALYSIS; IDENTIFICATION (CONTROL SYSTEMS); MATHEMATICAL MODELS; OPTIMIZATION; PARAMETERIZATION; PROBLEM SOLVING;

KAUTZ FUNCTIONS; VOLTERRA KERNELS; VOLTERRA SERIES;

NONLINEAR SYSTEMS;

EID: 34247498558     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.12.007     Document Type: Article

References (34)

1. Bazaraa M.S., Sherali H.D., and Shetty C.M. Nonlinear programming: theory and algorithms (1993), Wiley, New York
2. Bokor J., and Schipp F. Approximate identification in Laguerre and Kautz bases. Automatica 34 4 (1998) 463-468
3. Boyd S., and Chua L.O. Fading memory and the problem of approximation nonlinear operators with Volterra series. IEEE Transactions on Circuits and Systems 32 11 (1985) 1150-1161
4. Broome P.W. Discrete orthonormal sequences. Journal of the Association for Computing Machinery 12 2 (1965) 151-168
5. Campello R.J.G.B., Amaral W.C., and Favier G. A note on the optimal expansion of Volterra models using Laguerre functions. Automatica 42 4 (2006) 689-693
6. Campello R.J.G.B., Favier G., and Amaral W.C. Optimal expansions of discrete-time Volterra models using Laguerre functions. Automatica 40 5 (2004) 815-822
7. Clowes G.J. Choice of time-scaling factor for linear system approximation using orthonormal Laguerre functions. IEEE Transactions on Automatic Control 10 4 (1965) 487-489
8. da Rosa, A. (2005). Expansion of discrete-time Volterra models using Kautz functions. M.Sc. thesis, School of Electrical and Computer Engineering of the State University of Campinas (FEEC/UNICAMP), Campinas-SP, Brazil (in Portuguese).
9. da Rosa, A., Amaral, W. C., & Campello, R. J. G. B. (2005). Choice of free parameters in expansions of discrete-time Volterra models using Kautz functions. In Proceedings of the 16th IFAC world congress. Prague, Czech Republic.
10. den Brinker A.C., Benders F.P.A., and Silva T.O. Optimality conditions for truncated Kautz series. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 43 2 (1996) 117-122
11. Van den Hof P.M.J., Heuberger P.S.C., and Bokor J. System identification with generalized orthonormal basis functions. Automatica 31 12 (1995) 1821-1834
12. Doyle III F.J., Pearson R.K., and Ogunnaike B.A. Identification and control using Volterra models (2002), Springer, Berlin
13. Dumont G.A., and Fu Y. Non-linear adaptive control via Laguerre expansion of Volterra kernels. International Journal of Adaptive Control and Signal Processing 7 5 (1993) 367-382
14. Eykhoff P. System identification: parameter and state estimation (1974), Wiley, New York
15. Fu Y., and Dumont G.A. An optimum time scale for discrete Laguerre network. IEEE Transactions on Automatic Control 38 6 (1993) 934-938
16. Heuberger P.S.C., Van den Hof P.M.J., and Bosgra O.H. A generalized orthonormal basis for linear dynamical systems. IEEE Transactions on Automatic Control 40 3 (1995) 451-465
17. Heuberger P.S.C., Van den Hof P.M.J., and Wahlberg B. Modelling and identification with rational orthogonal basis functions (2005), Springer, Berlin
18. Kautz W.H. Transient synthesis in the time domain. IRE Transactions on Circuit Theory 1 3 (1954) 29-39
19. Masnadi-Shirazi M.A., and Ahmed N. Optimum Laguerre networks for a class of discrete-time systems. IEEE Transactions on Signal Processing 39 9 (1991) 2104-2108
20. Ninness B., and Gustafsson F. A unifying construction of orthonormal bases for system identification. IEEE Transactions on Automatic Control 42 4 (1997) 515-521
21. Oliveira G.H.C., Amaral W.C., Favier G., and Dumont G.A. Constrained robust predictive controller for uncertain processes modeled by orthonormal series functions. Automatica 36 4 (2000) 563-571
22. Rugh W.J. Nonlinear system theory-the Volterra/Wiener approach (1981), The Johns Hopkins University Press, Baltimore, MD
23. Schetzen M. The Volterra and Wiener theories of nonlinear systems (1989), Robert Krieger Publishing Company, USA
24. Silva T.O. Optimality conditions for truncated Laguerre networks. IEEE Transactions on Signal Processing 42 9 (1994) 2528-2530
25. Silva T.O. Optimality conditions for truncated Kautz networks with two periodically repeating complex conjugate poles. IEEE Transactions on Automatic Control 40 2 (1995) 342-346
26. 2 error surface of the generalized orthonormal basis functions lattice filter. Signal Processing 56 3 (1997) 233-253
27. Takenaka S. On the orthogonal functions and a new formula of interpolation. Japanese Journal of Mathematics II (1925) 129-145
28. Tanguy N., Morvan R., Vilbé P., and Calvez L.C. Optimum choice of free parameter in orthonormal approximations. IEEE Transactions on Automatic Control 40 10 (1995) 1811-1813
29. Tanguy N., Morvan R., Vilbé P., and Calvez L.C. Pertinent parameters for Kautz approximation. Electronic Letters 36 8 (2000) 769-771
30. Tanguy N., Morvan R., Vilbé P., and Calvez L.C. Pertinent choice of parameters for discrete Kautz approximation. IEEE Transactions on Automatic Control 47 5 (2002) 783-787
31. Wahlberg B. System identification using Laguerre models. IEEE Transactions on Automatic Control 36 5 (1991) 551-562
32. Wahlberg B. System identification using Kautz models. IEEE Transactions on Automatic Control 39 6 (1994) 1276-1282
33. Wahlberg B., and Mäkilä P.M. Approximation of stable linear dynamical systems using Laguerre and Kautz functions. Automatica 32 5 (1996) 693-708
34. Wiener N. Nonlinear problems in random theory (1958), Wiley, New York