Choice Of Free Parameters In Expansions Of Discrete-time Volterra Models Using Kautz Functions

The present paper involves the approximation of nonlinear systems using Wiener/Volterra models with Kautz orthonormal functions. It focuses on the problem of selecting the free complex pole which characterizes these functions. The problem is solved by minimizing an upper bound of the error arising from the truncated approximation of Volterra kernels using Kautz functions. An analytical solution for the optimal choice of one of the parameters related to the Kautz pole is thus obtained, with the results valid for any-order Wiener/Volterra models. An example illustrates the application of the mathematical results derived. Copyright © 2005 IFAC.16761766Broome, P.W., Discrete orthonormal sequences Journal of Association Computing Machinary, 12 (2), pp. 151-168Campello, R.J.G.B., Favier, G., Amaral, W.C., Optimal expansions of discrete-time volterra models using laguerre functions (2003) Proc. 13th IFAC Symposium on System Identifcation, pp. 1844-1849. , Rotterdam, The NetherlandsCampello, R.J.G.B., Favier, G., Amaral, W.C., Optimal expansions of discrete-time volterra models using laguerre functions (2004) Automatica, 40 (5), pp. 815-822Da Rosa, A., (2004) Expansion of Discrete-Time Volterra Models Using Kautz Functions, , MSc thesis, School of Electrical and Computer Engineering of the State University of Campinas (DCA/FEEC/UNICAMP), Campinas/SP, Brazil, To appear (in Portuguese)Eykhoff, P., (1974) System Identifcation: Parameter and State Estimation, , John Wiley & Sons, LondonFu, Y., Dumont, G.A., An optimum time scale for discrete laguerre network (1993) IEEE Transactions on Automatic Control, 38 (6), pp. 934-938Van Den Hof, P.M.J., Heuberger, P.S.C., Bokor, J., System identification with generalized orthonormal basis functions (1995) Automatica, 31 (12), pp. 1821-1834Masnadi-Shirazi, M.A., Ahmed, N., Optimum laguerre networks for a class of discrete-time systems (1991) IEEE Transactions on Signal Processing, 39 (9), pp. 2104-2108Rugh, W.J., (1991) Nonlinear System Theory - The Volterra/Wiener Approach, , The Johns Hopkins University Press, LondonSchetzen, M., (1989) The Volterra and Wiener Theories of Nonlinear Systems, , Robert Krieger Publishing Company, FloridaTanguy, N., Morvan, R., Vilbé, P., Calvez, L.C., Pertinent parameters for kautz approximation (2000) Eletronic Letters, 36 (8), pp. 769-771Tanguy, N., Morvan, R., Vilbé, P., Calvez, L.C., Pertinent choice of parameters for discrete kautz approximation (2002) IEEE Transactions on Automatic Control, 47 (5), pp. 783-787Wahlberg, B., System identification using Kautz models (1994) IEEE Transactions on Automatic Control, 39 (6), pp. 1276-1282Wahlberg, B., Mäkilä, P.M., On approximation of stable linear dinamical systems using laguerre and kautz functions (1996) Automatica, 32 (5), pp. 693-70