Pertinent choice of parameters for discrete Kautz approximation

Abstract

International audienceKautz functions have received much attention in the recent mathematical modeling and identification literature. These functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior. We consider here the choice of the free parameters in discrete (two-parameter) Kautz approximation. Using a key relationship between Kautz and Laguerre expansions we derive an upper bound for the quadratic truncation error. Minimization of this upper bound yields pertinent parameters, whose computation then requires reduced knowledge of the function to be modeled

An optimal expansion of Volterra models using independent Kautz bases for each kernel dimension

“…Theorem 3 extends previous results (Tanguy et al 2002, da Rosa et al 2007 in the sense that different Kautz poles can now be set for each dimension l ¼ 1, 2, . .…”

“…The list of works dealing with the Laguerre pole location also include Silva (1994), which derived optimality conditions for linear truncated Laguerre networks. These conditions of great theoretical interest can however result in complicated computations in practical cases, as already observed in Tanguy et al (2002).…”

“…Optimality conditions for truncated Kautz series in linear discrete-time models have been derived in den Brinker et al (1996) by minimizing the error between the impulse response of a given system and its corresponding Kautz model. In the context of pole location of the Kautz bases, a sub-optimal choice of Kautz poles in the representation of discrete-time linear systems was proposed in Tanguy et al (2002), whereas the corresponding non-linear counterpart was later addressed in da Rosa et al (2005Rosa et al ( , 2007. Such approaches are said sub-optimal because they consider the optimal selections of only one of the Kautz parameters, and involve the minimization of an upper bound for the kernel truncation error.…”

Multiform optimization of predictive functional control based on Kautz model

“…This will enable us to derive predictive expressions of plant outputs in straightforward manner. For more information see paper [4] [5] .…”

Identificação e controle de processos via desenvolvimentos em séries ortonormais. Parte A: identificação

“…Resultado análogo foi apresentado em (Tanguy et al, 1995;Tanguy et al, 2000) e posteriormente estendido para o caso de modelos de Volterra de segunda ordem em (Campello et al, 2001; e modelos de Volterra de qualquer ordem em (Campello, Favier and Amaral, 2003;Campello, Favier and Amaral, 2004;Kibangou et al, 2005b;Campello et al, 2006). Soluções para problemas similares envolvendo outras bases de funções ortonormais têm sido também investigadas (Oliveira e Silva, 1995b;Tanguy et al, 2002;Favier et al, 2003;Kibangou et al, 2003;Kibangou et al, 2005a;Kibangou et al, 2005c;da Rosa, 2005;da Rosa et al, 2006;da Rosa et al, 2007).…”