Synthesis of fractional Laguerre basis for system approximation
Language
en
Article de revue
This item was published in
Automatica. 2007-09, vol. 43, n° 9, p. 1640-1648
Elsevier
English Abstract
Fractional differentiation systems are characterized by the presence of non-exponential aperiodic multimodes. Although rational orthogonal bases can be used to model any $L_2[0, \infty[$ system, they fail to quickly capture ...Read more >
Fractional differentiation systems are characterized by the presence of non-exponential aperiodic multimodes. Although rational orthogonal bases can be used to model any $L_2[0, \infty[$ system, they fail to quickly capture the aperiodic multimode behavior with a limited number of terms. Hence, fractional orthogonal bases are expected to better approximate fractional models with fewer parameters. Intuitive reasoning could lead to simply extending the differentiation order of existing bases from integer to any positive real number. However, classical Laguerre, and by extension Kautz and generalized orthogonal basis functions, are divergent as soon as their differentiation order is non-integer. In this paper, the first fractional orthogonal basis is synthesized, extrapolating the definition of Laguerre functions to any fractional order derivative. Completeness of the new basis is demonstrated. Hence, a new class of fixed denominator models is provided for fractional system approximation and identification.Read less <
English Keywords
Orthonormal basis
fractional differentiation
Laguerre function
system approximation
identification
Origin
Hal imported