Publications

@conference{Yakoub20221003b,

title = {Bias Recursive Least Squares Method for Fractional Order System Identification},

author = {Zaineb Yakoub and Messaoud Amairi and Manel Chetoui and Mohamed Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85143798506\&doi=10.1109%2fSSD54932.2022.9955869\&partnerID=40\&md5=33815d9cbb662e9c28d357625582a869},

doi = {10.1109/SSD54932.2022.9955869},

year  = {2022},

date = {2022-01-01},

journal = {2022 19th IEEE International Multi-Conference on Systems, Signals and Devices, SSD 2022},

pages = {1003 \textendash 1008},

abstract = {This paper mainly studies the modeling and identification problems for fractional order systems. A novel modeling scheme based on an online identification technique is investigated. Firstly, the recursive least squares algorithm is applied to identify the fractional order system. However, if the measurement of the output signal is affected by an additive noise this algorithm is unable to give consistent estimates. Thus, this contribution implements a technique based on the bias compensation principle. The main idea is to eliminate the introduced bias by adding a correction term in the recursive least squares estimates. The results of the simulated example indicate that the proposed estimator provides good accuracy. © 2022 IEEE.},

note = {Cited by: 0},

keywords = {Additive noise, Algebra, Bias compensation, Fractional order, Fractional order differentiation, Fractional-order systems, Identification, Least Square, Least squares approximations, Model problems, Modelling and identifications, Recursive least-squares method, System-identification},

pubstate = {published},

tppubtype = {conference}

}

@conference{Yakoub201710431b,

title = {Model-based fractional order controller design},

author = {Z. Yakoub and M. Chetoui and M. Amairi and M. Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85031827269\&doi=10.1016%2fj.ifacol.2017.08.1971\&partnerID=40\&md5=c84f02810425251e2e6444d4c36ec8dd},

doi = {10.1016/j.ifacol.2017.08.1971},

year  = {2017},

date = {2017-01-01},

journal = {IFAC-PapersOnLine},

volume = {50},

number = {1},

pages = {10431 \textendash 10436},

abstract = {This paper deals with model-based fractional order controller design. The objective is identification for controller design in order to achieve the desired closed-loop performances. Firstly, the fractional order closed-loop bias-eliminated least squares method is used to identify the process model. Then, based on the numerical optimization of a frequency-domain criterion, the fractional controller is designed. If the proposed algorithm detects any changes in the process parameters, the controller is updated to keep the same performances. A numerical example is presented to show the efficiency of the proposed scheme. © 2017},

note = {Cited by: 3; All Open Access, Bronze Open Access},

keywords = {Bias elimination, Closed loops, Controllers, Fractional differentiation, Frequency domain analysis, Identification for control, Least squares approximations, Optimization, Process control, Recursive least square (RLS)},

pubstate = {published},

tppubtype = {conference}

}

@conference{Yakoub2017271b,

title = {A comparison between the direct and the indirect fractional order closed-loop bias eliminated least squares method},

author = {Z. Yakoub and M. Chetoui and M. Amairi and M. Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85024378403\&doi=10.1109%2fSTA.2016.7951978\&partnerID=40\&md5=f96317e305a1fb9879331639139ecc89},

doi = {10.1109/STA.2016.7951978},

year  = {2017},

date = {2017-01-01},

journal = {2016 17th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering, STA 2016 - Proceedings},

pages = {271 \textendash 282},

abstract = {This paper deals with the fractional closed-loop system identification. A comparison between the direct and the indirect approach is processed. The fractional order bias eliminated least squares method is used to identify the fractional closed-loop transfer function. This method is founded on the ordinary least squares method and the state variable filter. A numerical example is treated to show the efficiency of each approach and discuss results. © 2016 IEEE.},

note = {Cited by: 0},

keywords = {Automation, Closed loops, Direct approach, Fractional differentiation, Identification (control systems), indirect approach, Least Square, Least squares approximations, Process control},

pubstate = {published},

tppubtype = {conference}

}

@conference{Yakoub2015e,

title = {A direct fractional order bias eliminated least squares method for the fractional closed-loop system identification},

author = {Z. Yakoub and M. Chetoui and M. Amairi and M. Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84962688308\&doi=10.1109%2fSSD.2015.7348219\&partnerID=40\&md5=1523b25860bd1afff62b4ced5a164cdd},

doi = {10.1109/SSD.2015.7348219},

year  = {2015},

date = {2015-01-01},

journal = {12th International Multi-Conference on Systems, Signals and Devices, SSD 2015},

abstract = {The paper deals with the continuous-time fractional closed-loop system identification in a noisy output context. Both coefficients and fractional orders of the process are estimated using the direct approach. The proposed method is based on the least squares technique and the state variable filter. It is an extension of the bias eliminated least squares method to the fractional systems. It is combined to a nonlinear optimization algorithm in order to estimate both coefficients and fractional orders of the fractional process. A numerical example is presented to illustrate the performances of the proposed methods. © 2015 IEEE.},

note = {Cited by: 2},

keywords = {Algorithms, Closed loop systems, Closed loops, Continuous time systems, Continuous-time, Direct approach, Fractional differentiation, Identification (control systems), Least Square, Least squares approximations, Nonlinear programming, Numerical methods, Optimization, Religious buildings, State-variable filters},

pubstate = {published},

tppubtype = {conference}

}

@conference{Yakoub2014c,

title = {Indirect approach for closed-loop system identification with fractional models},

author = {Z. Yakoub and M. Chetoui and M. Amairi and M. Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84918521162\&doi=10.1109%2fICFDA.2014.6967441\&partnerID=40\&md5=d666e64f7fc6c6a967f8001f8f810bf2},

doi = {10.1109/ICFDA.2014.6967441},

year  = {2014},

date = {2014-01-01},

journal = {2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014},

abstract = {This paper deals with fractional closed-loop system identification using the indirect approach. Firstly, all differentiation orders are supposed known and only the coefficients of the closed-loop fractional transfer function are estimated using two methods based on least squares techniques. Then, the fractional open-loop process is determined by the knowledge of the regulator. A numerical example is presented to show the effectiveness of the proposed scheme. © 2014 IEEE.},

note = {Cited by: 4},

keywords = {Calculations, Closed loop systems, Closed loops, Differentiation (calculus), Fractional calculus, Fractional model, Identification (control systems), Least Square, Least squares approximations, Least squares techniques, Open-loop process, Religious buildings, State-variable filters},

pubstate = {published},

tppubtype = {conference}

}

@conference{Yakoub2014128b,

title = {A bias-eliminated least squares method for continuous-time fractional closed-loop system identification},

author = {Z. Yakoub and M. Amairi and M. Chetoui and M. Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84920520477\&doi=10.1109%2fCCA.2014.6981340\&partnerID=40\&md5=1e18e1e8dcd7b25d35f5589188cfe8a6},

doi = {10.1109/CCA.2014.6981340},

year  = {2014},

date = {2014-01-01},

journal = {2014 IEEE Conference on Control Applications, CCA. Part of 2014 IEEE Multi-conference on Systems and Control, MSC 2014},

pages = {128 \textendash 133},

abstract = {This paper deals with continuous-time fractional closed-loop system identification in a noisy output context. A bias correction method called the bias-eliminated least squares is extended for indirect approach identification of closed-loop system with fractional models. This method is based on the least squares method combined with the state variable filter and assumes that the regulator order can not be lower than the process order. The performances of the proposed method are assessed through a numerical example. © 2014 IEEE.},

note = {Cited by: 5},

keywords = {Closed loop systems, Closed loops, Continuous time systems, Continuous-time, Fractional differentiation, Identification (control systems), Least Square, Least squares approximations, Numerical methods, Religious buildings, State-variable filters},

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{Chetoui2011,

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{Aoun20031333b,

title = {Orthonormal basis functions for modeling continuous-time fractional systems},

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

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017520336\&doi=10.1016%2fS1474-6670%2817%2934945-5\&partnerID=40\&md5=51049a0530b07591d53a06e9bfa5d400},

doi = {10.1016/S1474-6670(17)34945-5},

year  = {2003},

date = {2003-01-01},

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

volume = {36},

number = {16},

pages = {1333 \textendash 1338},

abstract = {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.},

note = {Cited by: 11; All Open Access, Bronze Open Access},

keywords = {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},

pubstate = {published},

tppubtype = {conference}

}

@conference{Aoun20031333,

title = {Orthonormal basis functions for modeling continuous-time fractional systems},

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

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017520336\&doi=10.1016%2fS1474-6670%2817%2934945-5\&partnerID=40\&md5=51049a0530b07591d53a06e9bfa5d400},

doi = {10.1016/S1474-6670(17)34945-5},

year  = {2003},

date = {2003-01-01},

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

volume = {36},

number = {16},

pages = {1333 \textendash 1338},

abstract = {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.},

note = {Cited by: 11; All Open Access, Bronze Open Access},

keywords = {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},

pubstate = {published},

tppubtype = {conference}

}