Publications

@article{Hamdi20184185b,

title = {Recursive set-membership parameter estimation of fractional systems using orthotopic approach},

author = {Saif Eddine Hamdi and Messaoud Amairi and Mohamed Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85045302403\&doi=10.1177%2f0142331217744853\&partnerID=40\&md5=40ffcf990575c0015868048fce18b27a},

doi = {10.1177/0142331217744853},

year  = {2018},

date = {2018-01-01},

journal = {Transactions of the Institute of Measurement and Control},

volume = {40},

number = {15},

pages = {4185 \textendash 4197},

abstract = {In this paper, set-membership parameter estimation of linear fractional-order systems is addressed for the case of unknown-but-bounded equation error. In such bounded-error context with a-priori known noise bounds, the main goal is to characterize the set of all feasible parameters. This characterization is performed using an orthotopic strategy adapted for fractional system parameter estimation. In the case of a fractional commensurate system, an iterative algorithm is proposed to deal with commensurate-order estimation. The performances of the proposed algorithm are illustrated by a numerical example via a Monte Carlo simulation. © The Author(s) 2018.},

note = {Cited by: 5},

keywords = {Bounded error context, Bounded errors, Errors, Fractional systems, Fractional-order systems, Iterative algorithm, Iterative methods, Monte Carlo methods, Order estimation, Parameter estimation, Set membership approach, Unknown but bounded},

pubstate = {published},

tppubtype = {article}

}

@article{Amairi2016543,

title = {Recursive set membership estimation for output-error fractional models with unknown-but-bounded errors},

author = {M. Amairi},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84990238923\&doi=10.1515%2famcs-2016-0038\&partnerID=40\&md5=3071b9bc8873072497af16513fb3d8b8},

doi = {10.1515/amcs-2016-0038},

issn = {1641876X},

year  = {2016},

date = {2016-01-01},

journal = {International Journal of Applied Mathematics and Computer Science},

volume = {26},

number = {3},

pages = {543-553},

publisher = {Walter de Gruyter GmbH},

abstract = {This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results. © 2016 Messaoud Amairi, published by De Gruyter Open.},

note = {cited By 4},

keywords = {Calculations; Estimation, Errors, Fractional calculus; Fractional model; Fractional systems; Measurement Noise; Optimal bounding ellipsoid algorithms; Set membership; Set-membership estimation; Unknown but bounded},

pubstate = {published},

tppubtype = {article}

}

@article{Chetoui2013860b,

title = {New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models},

author = {Manel Chetoui and Magalie Thomassin and Rachid Malti and Mohamed Aoun and Slaheddine Najar and Mohamed Naceur Abdelkrim and Alain Oustaloup},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84881481608\&doi=10.1016%2fj.camwa.2013.04.028\&partnerID=40\&md5=d4b467860744e79a3cee47ab860f3daf},

doi = {10.1016/j.camwa.2013.04.028},

year  = {2013},

date = {2013-01-01},

journal = {Computers and Mathematics with Applications},

volume = {66},

number = {5},

pages = {860 \textendash 872},

abstract = {The errors-in-variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables rational models. This paper presents new consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models. First, differentiation orders are assumed to be known and only differential equation coefficients are estimated. Two estimators based on Higher-Order Statistics (third-order cumulants) are developed: the fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils). Then, they are extended, using a nonlinear optimization algorithm, to estimate both the differential equation coefficients and the commensurate order. The performances of the proposed algorithms are illustrated with a numerical example.},

note = {Cited by: 30; All Open Access, Bronze Open Access},

keywords = {Algorithms, commensurate order, Differential equations, Errors, Errors in variables, Estimation, Fractional differentiation, Higher order statistics, Identification (control systems), Identification problem, Iterative least squares, Least squares algorithm, Non-linear optimization algorithms, Third-order cumulant},

pubstate = {published},

tppubtype = {article}

}

@article{Chetoui2013860,

title = {New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models},

author = {Manel Chetoui and Magalie Thomassin and Rachid Malti and Mohamed Aoun and Slaheddine Najar and Mohamed Naceur Abdelkrim and Alain Oustaloup},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84881481608\&doi=10.1016%2fj.camwa.2013.04.028\&partnerID=40\&md5=d4b467860744e79a3cee47ab860f3daf},

doi = {10.1016/j.camwa.2013.04.028},

year  = {2013},

date = {2013-01-01},

journal = {Computers and Mathematics with Applications},

volume = {66},

number = {5},

pages = {860 \textendash 872},

abstract = {The errors-in-variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables rational models. This paper presents new consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models. First, differentiation orders are assumed to be known and only differential equation coefficients are estimated. Two estimators based on Higher-Order Statistics (third-order cumulants) are developed: the fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils). Then, they are extended, using a nonlinear optimization algorithm, to estimate both the differential equation coefficients and the commensurate order. The performances of the proposed algorithms are illustrated with a numerical example.},

note = {Cited by: 30; All Open Access, Bronze Open Access},

keywords = {Algorithms, commensurate order, Differential equations, Errors, Errors in variables, Estimation, Fractional differentiation, Higher order statistics, Identification (control systems), Identification problem, Iterative least squares, Least squares algorithm, Non-linear optimization algorithms, Third-order cumulant},

pubstate = {published},

tppubtype = {article}

}