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Optimal expansions of discrete-time Volterra models using Laguerre functions. (English) Zbl 1050.93031
Summary: 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. Y. Fu and G. A. Dumont [IEEE Trans. Autom. Control 38, 934–938 (1993; Zbl 0800.93033)] 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.

MSC:
93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
93B11 System structure simplification
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