Publications

@conference{Aribi2012b,

title = {Evaluation of fractional residual},

author = {Asma Aribi and Mohamed Aoun and Slaheddine Najar and Mohamed Naceur Abdelkrim},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84861641365\&doi=10.1109%2fSSD.2012.6197917\&partnerID=40\&md5=d50ae5369b5a376696d8a609ef48f0b1},

doi = {10.1109/SSD.2012.6197917},

year  = {2012},

date = {2012-01-01},

journal = {International Multi-Conference on Systems, Signals and Devices, SSD 2012 - Summary Proceedings},

abstract = {The paper deals with fractional residual evaluation. Three methods to evaluate fractional residuals generated by dynamic parity space method are presented. They are based on the fractional derivative approximations: the Gr\"{u}nwald, the pole-zero and the Diethelm approximations. They are compared in order to select the best method in terms of precision and minimum detection time delay. © 2012 IEEE.},

note = {Cited by: 1},

keywords = {Detection time, Fractional derivatives, Fractional residual, Parity spaces, Pole-zero, residual evaluation},

pubstate = {published},

tppubtype = {conference}

}

@conference{Chetoui2011b,

title = {Third-order cumulants based method for continuous-time Errors-In-Variables system identification by fractional models},

author = {M. Chetoui and R. Malti and M. Thomassin and M. Aoun and S. Najar and M. N. Abdelkrim},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-79957885868\&doi=10.1109%2fSSD.2011.5767441\&partnerID=40\&md5=4b772c437279fdf033e958405ca83efc},

doi = {10.1109/SSD.2011.5767441},

year  = {2011},

date = {2011-01-01},

journal = {International Multi-Conference on Systems, Signals and Devices, SSD'11 - Summary Proceedings},

abstract = {This paper deals with continuous-time system identification using fractional models in a noisy input/output context. The third-order cumulants based least squares method (tocls) is extended here to fractional models. The derivatives of the third-order cumulants are computed using a new fractional state variable filter. A numerical example is used to demonstrate the performance of the proposed method called ftocls (fractional third-order cumulants based least squares). The effect of the signal-to-noise ratio and the hyperparameter is studied. © 2011 IEEE.},

note = {Cited by: 3},

keywords = {Continuous time systems, Cumulants, Errors in variables, Fractional derivatives, Fractional SVF, High order statistics, Identification (control systems), Indium compounds, Least squares approximations, Numerical methods, Religious buildings, Signal to noise ratio},

pubstate = {published},

tppubtype = {conference}

}

@conference{Aoun2011d,

title = {Simulation method of fractional systems based on the discrete-time approximation of the Caputo fractional derivatives},

author = {M. Aoun and M. Amairi and S. Najar and M. N. Abdelkrim},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-79957895222\&doi=10.1109%2fSSD.2011.5767414\&partnerID=40\&md5=21b4749453fc9c125b453521cfad3ec2},

doi = {10.1109/SSD.2011.5767414},

year  = {2011},

date = {2011-01-01},

journal = {International Multi-Conference on Systems, Signals and Devices, SSD'11 - Summary Proceedings},

abstract = {This paper proposes a new method for the simulation of the fractional systems. It deals with the approximation methods of the fractional derivative. It compare the approximation based on Grnwald with Caputo approximation. The efficiency of each approximation methods in termes of execution time and quadratic error is evaluated for different differential orders and stepsize. The best approximation method is used to develop an original simulation method to demonstrate its effectiveness. © 2011 IEEE.},

note = {Cited by: 2},

keywords = {ACFDR, Approximation theory, CFDR, Diethelm's approximation, Differentiation (calculus), Fractional derivatives, Fractional systems, Pole-zero distribution, simulation},

pubstate = {published},

tppubtype = {conference}

}

@conference{Aoun2011f,

title = {On the fractional systems' fault detection: A comparison between fractional and rational residual sensitivity},

author = {Mohamed Aoun and Asma Aribi and Slaheddine Najar and Mohamed Naceur Abdelkrim},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-79957903547\&doi=10.1109%2fSSD.2011.5767424\&partnerID=40\&md5=2e22d74f672e2ae986db94c4dbcd72e6},

doi = {10.1109/SSD.2011.5767424},

year  = {2011},

date = {2011-01-01},

journal = {International Multi-Conference on Systems, Signals and Devices, SSD'11 - Summary Proceedings},

abstract = {This paper shows the interest of extending the dynamic parity space fault detection method for fractional systems. Accordingly, a comparison between fractional and rational residual generators using the later method is presented. An analysis of fractional and rational residuals' sensitivity shows the merits of the fractional residual generators. A numerical example illustrating the advantage of using fractional residual generators for fractional systems diagnosis is given. © 2011 IEEE.},

note = {Cited by: 8},

keywords = {Detection methods, Fault detection, fault diagnosis, Fractional derivatives, Fractional systems, Numerical example, Parity spaces, Residual generator, residual sensitivity, Signal detection},

pubstate = {published},

tppubtype = {conference}

}

@conference{Aoun2005321b,

title = {Synthesis and simulation of fractional orthonormal bases},

author = {Mohamed Aoun and Rachid Malti and Alain Oustaloup},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-79960728807\&doi=10.3182%2f20050703-6-cz-1902.00054\&partnerID=40\&md5=5c498af2463f1ea3d44d2514622362c8},

doi = {10.3182/20050703-6-cz-1902.00054},

year  = {2005},

date = {2005-01-01},

journal = {IFAC Proceedings Volumes (IFAC-PapersOnline)},

volume = {16},

pages = {321 \textendash 326},

abstract = {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.},

note = {Cited by: 1; All Open Access, Green Open Access},

keywords = {Calculations, Dynamical systems, Fractional calculus, Fractional derivatives, Fractional systems, Identification (control systems), Multimodes, Orthogonal basis, Orthogonal functions, Orthonormal basis, Rational orthogonal basis, simulation},

pubstate = {published},

tppubtype = {conference}

}

@conference{Aoun2005321,

title = {Synthesis and simulation of fractional orthonormal bases},

author = {Mohamed Aoun and Rachid Malti and Alain Oustaloup},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-79960728807\&doi=10.3182%2f20050703-6-cz-1902.00054\&partnerID=40\&md5=5c498af2463f1ea3d44d2514622362c8},

doi = {10.3182/20050703-6-cz-1902.00054},

year  = {2005},

date = {2005-01-01},

journal = {IFAC Proceedings Volumes (IFAC-PapersOnline)},

volume = {16},

pages = {321 \textendash 326},

abstract = {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.},

note = {Cited by: 1; All Open Access, Green Open Access},

keywords = {Calculations, Dynamical systems, Fractional calculus, Fractional derivatives, Fractional systems, Identification (control systems), Multimodes, Orthogonal basis, Orthogonal functions, Orthonormal basis, Rational orthogonal basis, simulation},

pubstate = {published},

tppubtype = {conference}

}

@conference{Malti2004835b,

title = {Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes},

author = {Rachid Malti and Mohamed Aoun and Alain Oustaloup},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-3042685548\&partnerID=40\&md5=957efcea75f0a5a34f4a77d45bd6e85c},

year  = {2004},

date = {2004-01-01},

journal = {International Symposium on Control, Communications and Signal Processing, ISCCSP},

pages = {835 \textendash 839},

abstract = {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.},

note = {Cited by: 19},

keywords = {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},

pubstate = {published},

tppubtype = {conference}

}

@conference{Malti2004835,

title = {Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes},

author = {Rachid Malti and Mohamed Aoun and Alain Oustaloup},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-3042685548\&partnerID=40\&md5=957efcea75f0a5a34f4a77d45bd6e85c},

year  = {2004},

date = {2004-01-01},

journal = {International Symposium on Control, Communications and Signal Processing, ISCCSP},

pages = {835 \textendash 839},

abstract = {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.},

note = {Cited by: 19},

keywords = {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},

pubstate = {published},

tppubtype = {conference}

}