2007 |
Aoun, M.; Malti, R.; Levron, F.; Oustaloup, A. Synthesis of fractional Laguerre basis for system approximation Article de journal Dans: Automatica, vol. 43, no. 9, p. 1640 – 1648, 2007, (Cited by: 115; All Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Asymptotic stability, Fractional differentiation, Identification (control systems), Integer programming, Laguerre function, Mathematical models, Orthonormal basis @article{Aoun20071640b,Fractional differentiation systems are characterized by the presence of non-exponential aperiodic multimodes. Although rational orthogonal bases can be used to model any L2 [0, ∞ [ 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. © 2007 Elsevier Ltd. All rights reserved. |
2006 |
Sabatier, Jocelyn; Aoun, Mohamed; Oustaloup, Alain; Grégoire, Gilles; Ragot, Franck; Roy, Patrick Fractional system identification for lead acid battery state of charge estimation Article de journal Dans: Signal Processing, vol. 86, no. 10, p. 2645 – 2657, 2006, (Cited by: 269). Résumé | Liens | BibTeX | Étiquettes: Fractional order dynamical systems, Fractional system identification method, Identification (control systems), Lead acid batteries, Mathematical models, Parameter estimation, State of charge estimation, Thermal effects @article{Sabatier20062645b,This paper deals with the application of fractional system identification to lead acid battery state of charge estimation. Fractional behavior of lead acid batteries is justified. A fractional system identification method recently developed is presented and a new fractional model of the battery is proposed. Based on parameter variations of this model, a state of charge estimation method is presented. Validation tests of this method on unknown state of charge are carried out. These validation tests highlights that the proposed estimation method gives a state of charge estimation with an error close to 5% whatever the operating temperature. © 2006 Elsevier B.V. All rights reserved. |
Sabatier, Jocelyn; Aoun, Mohamed; Oustaloup, Alain; Grégoire, Gilles; Ragot, Franck; Roy, Patrick Fractional system identification for lead acid battery state of charge estimation Article de journal Dans: Signal Processing, vol. 86, no. 10, p. 2645 – 2657, 2006, (Cited by: 269). Résumé | Liens | BibTeX | Étiquettes: Fractional order dynamical systems, Fractional system identification method, Identification (control systems), Lead acid batteries, Mathematical models, Parameter estimation, State of charge estimation, Thermal effects @article{Sabatier20062645,This paper deals with the application of fractional system identification to lead acid battery state of charge estimation. Fractional behavior of lead acid batteries is justified. A fractional system identification method recently developed is presented and a new fractional model of the battery is proposed. Based on parameter variations of this model, a state of charge estimation method is presented. Validation tests of this method on unknown state of charge are carried out. These validation tests highlights that the proposed estimation method gives a state of charge estimation with an error close to 5% whatever the operating temperature. © 2006 Elsevier B.V. All rights reserved. |
2004 |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Computer simulation, Continuous time model, Differential equations, Discrete time model, Fractional calculus, Fractional model, Functions, Identification (control systems), Laplace transforms, Mathematical models, Time domain analysis @article{Aoun2004117b,An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters. © 2004 Kluwer Academic Publishers. |
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. |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Computer simulation, Continuous time model, Differential equations, Discrete time model, Fractional calculus, Fractional model, Functions, Identification (control systems), Laplace transforms, Mathematical models, Time domain analysis @article{Aoun2004117,An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters. © 2004 Kluwer Academic Publishers. |
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, François; Oustaloup, Alain Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). Résumé | Liens | BibTeX | Étiquettes: Computer simulation, Differentiation (calculus), Fractional models, Fractional systems, Integration, Laplace transforms, Mathematical models, Transfer functions, Vectors @conference{Aoun2003745b,This paper deals with the design and simulation of continuous-time models with fractional differentiation orders. Two new methods are proposed. The first is an improvement of the approximation of the fractional integration operator using recursive poles and zeros proposed by Oustaloup (1995) and Lin (2001). The second improves the simulation schema by using a modal representation. |
Malti, Rachid; Aoun, Mohamed; Cois, Olivier; Oustaloup, Alain; Levron, François H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). Liens | BibTeX | Étiquettes: Algebra, Computer simulation, Differential equations, Differentiation (calculus), Explicit systems, Fractional differential systems, Impulse response, Laplace transforms, Mathematical models, Theorem proving, Transfer functions @conference{Malti2003729b, |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). Résumé | Liens | BibTeX | Étiquettes: Computer simulation, Differentiation (calculus), Fractional models, Fractional systems, Integration, Laplace transforms, Mathematical models, Transfer functions, Vectors @conference{Aoun2003745,This paper deals with the design and simulation of continuous-time models with fractional differentiation orders. Two new methods are proposed. The first is an improvement of the approximation of the fractional integration operator using recursive poles and zeros proposed by Oustaloup (1995) and Lin (2001). The second improves the simulation schema by using a modal representation. |
Malti, Rachid; Aoun, Mohamed; Cois, Olivier; Oustaloup, Alain; Levron, François H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). Liens | BibTeX | Étiquettes: Algebra, Computer simulation, Differential equations, Differentiation (calculus), Explicit systems, Fractional differential systems, Impulse response, Laplace transforms, Mathematical models, Theorem proving, Transfer functions @conference{Malti2003729, |
Publications
2007 |
Synthesis of fractional Laguerre basis for system approximation Article de journal Dans: Automatica, vol. 43, no. 9, p. 1640 – 1648, 2007, (Cited by: 115; All Open Access, Green Open Access). |
2006 |
Fractional system identification for lead acid battery state of charge estimation Article de journal Dans: Signal Processing, vol. 86, no. 10, p. 2645 – 2657, 2006, (Cited by: 269). |
Fractional system identification for lead acid battery state of charge estimation Article de journal Dans: Signal Processing, vol. 86, no. 10, p. 2645 – 2657, 2006, (Cited by: 269). |
2004 |
Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). |
Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). |
Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). |
Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). |
2003 |
Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). |
H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). |
Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). |
H2 norm of fractional differential systems Conférence vol. 5 A, 2003, (Cited by: 19). |