This work is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of Laguerre functions associated with a given series truncation error, thus reducing the complexity of the resulting finite-dimensional representation. Fu and Dumont (IEEE Trans. Automatic Control 38(6) (1993) 934) indirectly approached this problem in the context of linear systems by minimizing an upper bound for the error resulting from the truncated Laguerre expansion of impulse response models, which are equivalent to first-order Volterra models. A generalization of the work mentioned above focusing on Volterra models of any order is presented in this paper. The main result is the derivation of analytic strict global solutions for the optimal expansion of the Volterra kernels either using an independent Laguerre basis for each kernel or using a common basis for all the kernels. © 2003 Elsevier Ltd. All rights reserved.405815822Bazaraa, M.S., Sherali, H.D., Shetty, C.M., (1993) Nonlinear Programming: Theory and Algorithms 2nd Ed., , New York: WileyBillings, S.A., Identification of nonlinear systems - A survey (1980) IEE Proceedings Part D, 127 (6), pp. 272-285Boyd, S., Chua, L.O., Fading memory and the problem of approximating nonlinear operators with Volterra series (1985) IEEE Transactions on Circuits and Systems, 32 (11), pp. 1150-1161Broome, P.W., Discrete orthonormal sequences (1965) Journal of the Association for Computing Machinery, 12 (2), pp. 151-168Campello, R.J.G.B., (2002) New Architectures and Methodologies for Modeling and Control of Complex Systems Combining Classical and Modern Tools, , Ph.D. thesis, School of Electrical and Computer Engineering of the State University of Campinas (FEEC/UNICAMP), Campinas/SP, Brazil (in Portuguese)Campello, R.J.G.B., Amaral, W.C., Favier, G., Optimal Laguerre series expansion of discrete Volterra models (2001) Proceedings of the European Control Conference, pp. 372-377. , Porto/PortugalClowes, G.J., Choice of the time-scaling factor for linear system approximation using orthonormal Laguerre functions (1965) IEEE Transactions on Automatic Control, 10, pp. 487-489Desoer, C.A., Vidyasagar, M., (1975) Feedback Systems: Input-output Properties, , New York: Academic PressDoyle III, F.J., Pearson, R.K., Ogunnaike, B.A., (2002) Identification and Control Using Volterra Models, , Berlin: SpringerDumont, G.A., Fu, Y., Non-linear adaptive control via Laguerre expansion of Volterra kernels (1993) International Journal of Adaptive Control and Signal Processing, 7, pp. 367-382Elshafei, A.-L., Dumont, G.A., Elnaggar, A., Adaptive GPC based on Laguerre filters modelling (1994) Automatica, 30 (12), pp. 1913-1920Eykhoff, P., (1974) System Identification: Parameter and State Estimation, , New York: WileyFinn, C., Wahlberg, B., Ydstie, B.E., Constrained predictive control using orthogonal expansions (1993) A.I.Ch.E. Journal, 39 (11), pp. 1810-1826Fu, Y., Dumont, G.A., An optimum time scale for discrete Laguerre network (1993) IEEE Transactions on Automatic Control, 38 (6), pp. 934-938Heuberger, P.S.C., Van Den Hof, P.M.J., Bosgra, O.H., A generalized orthonormal basis for linear dynamical systems (1995) IEEE Transactions on Automatic Control, 40, pp. 451-465Maner, B.R., Doyle III, F.J., Ogunnaike, B.A., Pearson, R.K., Nonlinear model predictive control of a simulated multivariable polymerization reactor using second-order Volterra models (1996) Automatica, 32 (9), pp. 1285-1301Marmarelis, V.Z., Identification of nonlinear biological systems using Laguerre expansions of kernels (1993) Annals of Biomedical Engineering, 21, pp. 573-589Ninness, B., Gustafsson, F., A unifying construction of orthonormal bases for system identification (1997) IEEE Transactions on Automatic Control, 42, pp. 515-521Oliveira, G.H.C., Amaral, W.C., Favier, G., Dumont, G.A., Constrained robust predictive controller for uncertain processes modeled by orthonormal series functions (2000) Automatica, 36 (4), pp. 563-571Schetzen, M., (1980) The Volterra and Wiener Theories of Nonlinear Systems, , New York: WileyTanguy, N., Morvan, R., Vilbé, P., Calvez, L.C., Online optimization of the time scale in adaptive Laguerre-based filters (2000) IEEE Transactions on Signal Processing, 48, pp. 1184-1187Tanguy, N., Vilbé, P., Calvez, L.C., Optimum choice of free parameter in orthonormal approximations (1995) IEEE Transactions on Automatic Control, 40, pp. 1811-1813Wahlberg, B., System identification using Laguerre models (1991) IEEE Transactions on Automatic Control, 36 (5), pp. 551-562Wahlberg, B., System identification using Kautz models (1994) IEEE Transactions on Automatic Control, 39 (6), pp. 1276-1282Wahlberg, B., Ljung, L., Hard frequency-domain model error bounds from least-squares like identification techniques (1992) IEEE Transactions on Automatic Control, 37 (7), pp. 900-912Wahlberg, B., Mäkilä, P.M., Approximation of stable linear dynamical systems using Laguerre and Kautz functions (1996) Automatica, 32 (5), pp. 693-708Wiener, N., (1958) Nonlinear Problems in Random Theory, , New York: WileyZervos, C.C., Dumont, G.A., Deterministic adaptive control based on Laguerre series representation (1988) International Journal of Control, 48 (6), pp. 2333-2359