2005 |
Aoun, Mohamed; Malti, Rachid; Oustaloup, Alain Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Calculations, Dynamical systems, Fractional calculus, Fractional derivatives, Fractional systems, Identification (control systems), Multimodes, Orthogonal basis, Orthogonal functions, Orthonormal basis, Rational orthogonal basis, simulation @conference{Aoun2005321b,Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to capture the aperiodic multi-mode behaviour of fractional systems in a limited number of terms. The classical definition of orthogonal Laguerre, Kautz, and GOB functions has been extended for the use of fractional derivatives. An appropriate diagram is thus proposed for simulation. Copyright © 2005 IFAC. |
Aoun, Mohamed; Malti, Rachid; Oustaloup, Alain Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Calculations, Dynamical systems, Fractional calculus, Fractional derivatives, Fractional systems, Identification (control systems), Multimodes, Orthogonal basis, Orthogonal functions, Orthonormal basis, Rational orthogonal basis, simulation @conference{Aoun2005321,Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to capture the aperiodic multi-mode behaviour of fractional systems in a limited number of terms. The classical definition of orthogonal Laguerre, Kautz, and GOB functions has been extended for the use of fractional derivatives. An appropriate diagram is thus proposed for simulation. Copyright © 2005 IFAC. |
2004 |
Malti, Rachid; Aoun, Mohamed; Oustaloup, Alain Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Differential equations, Dynamical systems, Extrapolation, Fractional calculus, Fractional derivatives, Generalized orthogonal basis (GOB), Identification (control systems), Laplace transforms, Linear control systems, Mathematical models, Model reduction, Orthogonal functions, Polynomials, Set theory, System stability, Transfer functions @conference{Malti2004835b,Fractional Kautz-like functions are synthesized extrapolating the definition of classical Kautz functions to fractional derivatives. The synthesized bases has two periodically repeating complex conjugate modes. The new basis extends the definition of the fractional Laguerre basis, by allowing the modes to be complex. An example is then provided in system identification context. |
Malti, Rachid; Aoun, Mohamed; Oustaloup, Alain Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Differential equations, Dynamical systems, Extrapolation, Fractional calculus, Fractional derivatives, Generalized orthogonal basis (GOB), Identification (control systems), Laplace transforms, Linear control systems, Mathematical models, Model reduction, Orthogonal functions, Polynomials, Set theory, System stability, Transfer functions @conference{Malti2004835,Fractional Kautz-like functions are synthesized extrapolating the definition of classical Kautz functions to fractional derivatives. The synthesized bases has two periodically repeating complex conjugate modes. The new basis extends the definition of the fractional Laguerre basis, by allowing the modes to be complex. An example is then provided in system identification context. |
2003 |
Aoun, Mohamed; Malti, Rachid; Levron, Francois; Oustaloup, Alain Orthonormal basis functions for modeling continuous-time fractional systems Conférence vol. 36, no. 16, 2003, (Cited by: 11; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Fourier analysis, Fourier coefficients, Fractional differentiation, Fractional systems, Identification (control systems), Laguerre filter, Laguerre functions, Least squares approximations, Least squares errors, Least squares methods, Orthogonal functions, Orthonormal basis functions, Poles, Religious buildings @conference{Aoun20031333b,The classical Laguerre functions are known to be divergent as soon as their differentiation order is non-integer. They are hence inappropriate for representing fractional differentiation systems. A complete orthogonal basis, having fractional differentiation orders and a single pole, is synthesized. It extends the well-known definition of Laguerre functions to fractional systems. Hence a new class of fixed denominator models is provided for system identification. Fourier coefficients are computed using a least squares method. The least squares error is plotted versus the differentiation order and the pole, in an example, and shows that an optimal differentiation order may be located away from an integer number. Hence, the use of the synthesized basis is fully justitied. © 2003 International Federation of Automatic Control. |
Aoun, Mohamed; Malti, Rachid; Levron, Francois; Oustaloup, Alain Orthonormal basis functions for modeling continuous-time fractional systems Conférence vol. 36, no. 16, 2003, (Cited by: 11; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Fourier analysis, Fourier coefficients, Fractional differentiation, Fractional systems, Identification (control systems), Laguerre filter, Laguerre functions, Least squares approximations, Least squares errors, Least squares methods, Orthogonal functions, Orthonormal basis functions, Poles, Religious buildings @conference{Aoun20031333,The classical Laguerre functions are known to be divergent as soon as their differentiation order is non-integer. They are hence inappropriate for representing fractional differentiation systems. A complete orthogonal basis, having fractional differentiation orders and a single pole, is synthesized. It extends the well-known definition of Laguerre functions to fractional systems. Hence a new class of fixed denominator models is provided for system identification. Fourier coefficients are computed using a least squares method. The least squares error is plotted versus the differentiation order and the pole, in an example, and shows that an optimal differentiation order may be located away from an integer number. Hence, the use of the synthesized basis is fully justitied. © 2003 International Federation of Automatic Control. |
Publications
2005 |
Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). |
Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). |
2004 |
Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). |
Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). |
2003 |
Orthonormal basis functions for modeling continuous-time fractional systems Conférence vol. 36, no. 16, 2003, (Cited by: 11; All Open Access, Bronze Open Access). |
Orthonormal basis functions for modeling continuous-time fractional systems Conférence vol. 36, no. 16, 2003, (Cited by: 11; All Open Access, Bronze Open Access). |