2022 |
Victor, Stéphane; Mayoufi, Abir; Malti, Rachid; Chetoui, Manel; Aoun, Mohamed System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). Résumé | Liens | BibTeX | Étiquettes: Continous time, Continuous time systems, Fractional model, Fractional systems, Instrumental variables, Intelligent systems, Monte Carlo methods, Multiple input single output systems, Multiple inputs single outputs, Optimization, Optimization algorithms, Order estimation, Order optimizations, Parameter estimation, Religious buildings, System-identification @article{Victor2022b,This paper deals with continuous-time system identification of multiple-input single-output (MISO) fractional differentiation models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. A new definition of structured-commensurability (or S-commensurability) is introduced to better cope with differentiation order estimation. Three variants of the algorithm are then proposed: (i) first, all differentiation orders are set as integer multiples of a global S-commensurate order, (ii) then, the differentiation orders are set as integer multiples of a local S-commensurate orders (one S-commensurate order for each subsystem), (iii) finally, all differentiation orders are estimated by releasing the S-commensurability constraint. The first variant has the smallest number of parameters and is used as a good initial hit for the second variant which in turn is used as a good initial hit for the third variant. Such a progressive increase of the number of parameters allows better performance of the optimization algorithm evaluated by Monte Carlo simulation analysis. © 2022 Elsevier Ltd |
Victor, Stéphane; Mayoufi, Abir; Malti, Rachid; Chetoui, Manel; Aoun, Mohamed System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). Résumé | Liens | BibTeX | Étiquettes: Continous time, Continuous time systems, Fractional model, Fractional systems, Instrumental variables, Intelligent systems, Monte Carlo methods, Multiple input single output systems, Multiple inputs single outputs, Optimization, Optimization algorithms, Order estimation, Order optimizations, Parameter estimation, Religious buildings, System-identification @article{Victor2022,This paper deals with continuous-time system identification of multiple-input single-output (MISO) fractional differentiation models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. A new definition of structured-commensurability (or S-commensurability) is introduced to better cope with differentiation order estimation. Three variants of the algorithm are then proposed: (i) first, all differentiation orders are set as integer multiples of a global S-commensurate order, (ii) then, the differentiation orders are set as integer multiples of a local S-commensurate orders (one S-commensurate order for each subsystem), (iii) finally, all differentiation orders are estimated by releasing the S-commensurability constraint. The first variant has the smallest number of parameters and is used as a good initial hit for the second variant which in turn is used as a good initial hit for the third variant. Such a progressive increase of the number of parameters allows better performance of the optimization algorithm evaluated by Monte Carlo simulation analysis. © 2022 Elsevier Ltd |
2016 |
Salem, Thouraya; Chetoui, Manel; Aoun, Mohamed 2016, (Cited by: 9). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Continuous-time, Differential equations, Estimation, Fractional differential equations, Fractional differentiation, Identification (control systems), Instrumental variables, Intelligent systems, Linear parameter varying models, Linear parameter varying systems, Linear systems, LPV systems, Monte Carlo methods, Parameter estimation, Refined instrumental variables, Religious buildings @conference{Salem2016640b,This paper deals with continuous-time linear parameter varying (LPV) system identification with fractional models. Two variants of instrumental variables based techniques are proposed to estimate continuous-time parameters of a fractional differential equation linear parameter varying model when all fractional orders are assumed known a priori: the first one is the instrumental variables estimator based in an auxiliary model. The second one is the simplified refined instrumental variables estimator. A comparison study between the developed estimators is done via a numerical example. A Monte Carlo simulation analysis results are presented to illustrate the performances of the proposed methods in the presence of an additive output noise. © 2016 IEEE. |
Salem, Thouraya; Chetoui, Manel; Aoun, Mohamed 2016, (Cited by: 9). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Continuous-time, Differential equations, Estimation, Fractional differential equations, Fractional differentiation, Identification (control systems), Instrumental variables, Intelligent systems, Linear parameter varying models, Linear parameter varying systems, Linear systems, LPV systems, Monte Carlo methods, Parameter estimation, Refined instrumental variables, Religious buildings @conference{Salem2016640,This paper deals with continuous-time linear parameter varying (LPV) system identification with fractional models. Two variants of instrumental variables based techniques are proposed to estimate continuous-time parameters of a fractional differential equation linear parameter varying model when all fractional orders are assumed known a priori: the first one is the instrumental variables estimator based in an auxiliary model. The second one is the simplified refined instrumental variables estimator. A comparison study between the developed estimators is done via a numerical example. A Monte Carlo simulation analysis results are presented to illustrate the performances of the proposed methods in the presence of an additive output noise. © 2016 IEEE. |
2015 |
Yakoub, Z.; Amairi, M.; Chetoui, M.; Aoun, M. On the Closed-Loop System Identification with Fractional Models Article de journal Dans: Circuits, Systems, and Signal Processing, vol. 34, no. 12, p. 3833 – 3860, 2015, (Cited by: 20). Résumé | Liens | BibTeX | Étiquettes: Algorithms, Closed loop systems, Closed loop transfer function, Closed loops, Fractional model, Identification (control systems), Information criterion, Instrumental variable methods, Instrumental variables, Intelligent systems, Least Square, Monte Carlo methods, Non-linear optimization algorithms, Nonlinear programming, Optimization, Religious buildings @article{Yakoub20153833b,In this paper, the fractional closed-loop system identification problem is addressed. Using the indirect approach, which supposes the knowledge of the controller, both coefficients and fractional orders of the process are estimated. The optimal instrumental variable method combined with a nonlinear optimization algorithm is handled to identify the fractional closed-loop transfer function. Also, two techniques are used for model selection the Akaike’s information criterion and the $$R_T^2$$RT2 criterion. The performances of the proposed scheme are illustrated by a numerical example via Monte Carlo simulation and by real electronic system identification. © 2015, Springer Science+Business Media New York. |
Yakoub, Z.; Chetoui, M.; Amairi, M.; Aoun, M. 2015, (Cited by: 2). Résumé | Liens | BibTeX | Étiquettes: 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 @conference{Yakoub2015e,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. |
Yakoub, Z.; Chetoui, M.; Amairi, M.; Aoun, M. A bias correction method for fractional closed-loop system identification Article de journal Dans: Journal of Process Control, vol. 33, p. 25 – 36, 2015, (Cited by: 21). Résumé | Liens | BibTeX | Étiquettes: Active filters, Algorithms, Bias-correction methods, Bias-eliminated least squares methods, Closed loop systems, Commensurate-order, Continuous time systems, Electromagnetic wave attenuation, Fractional differentiation, Identification (control systems), Intelligent systems, Least Square, Least squares approximations, Least-squares estimator, Monte Carlo methods, Non-linear optimization algorithms, Nonlinear programming, Numerical methods, Optimization, Religious buildings, State-variable filters @article{Yakoub201525b,Abstract In this paper, the fractional closed-loop system identification using the indirect approach is presented. A bias correction method is developed to deal with the bias problem in the continuous-time fractional closed-loop system identification. This method is based on the least squares estimator combined with the state variable filter approach. The basic idea is to eliminate the estimation bias by adding a correction term in the least squares estimates. The proposed algorithm is extended, using a nonlinear optimization algorithm, to estimate both coefficients and commensurate-order of the process. Numerical example shows the performances of the fractional order bias eliminated least squares method via Monte Carlo simulations. © 2015 Elsevier Ltd. |
2014 |
Chetoui, Manel; Thomassin, Magalie; Malti, Rachid; Aoun, Mohamed; Abdelkrim, Mohamed Naceur 2014, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Additive noise, Additives, commensurate order, Continuous time systems, Continuous-time, Differential equations, Electronic systems, Errors in variables, Fourth-order cumulants, Fractional differentiation, Higher order statistics, Identification (control systems), Nonlinear programming, Religious buildings, Signal processing @conference{Chetoui2014b,This paper considers the problem of identifying continuous-time fractional systems from noisy input/output measurements. Firstly, the differentiation orders are fixed and the differential equation coefficients are estimated using an estimator based on Higher-Order Statistics: fractional fourth-order cumulants based least squares (ffocls). Then, the commensurate order is estimated along with the differential equation coefficients using a non linear optimization technique combined to the ffocls algorithm (co-ffocls). Under some assumptions on the distributional properties of additive noises and the noise-free input signals, the developed estimators give consistent results. Hence, the noise-free input signal is assumed to be non gaussian, whereas the additive noises are assumed to be gaussian. The performances of the developed algorithms are assessed through a practical application for modeling a real electronic system. © 2014 IEEE. |
Yakoub, Z.; Chetoui, M.; Amairi, M.; Aoun, M. Indirect approach for closed-loop system identification with fractional models Conférence 2014, (Cited by: 4). Résumé | Liens | BibTeX | Étiquettes: 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 @conference{Yakoub2014c,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. |
Yakoub, Z.; Amairi, M.; Chetoui, M.; Aoun, M. 2014, (Cited by: 5). Résumé | Liens | BibTeX | Étiquettes: 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 @conference{Yakoub2014128b,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. |
Chetoui, Manel; Thomassin, Magalie; Malti, Rachid; Aoun, Mohamed; Abdelkrim, Mohamed Naceur 2014, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Additive noise, Additives, commensurate order, Continuous time systems, Continuous-time, Differential equations, Electronic systems, Errors in variables, Fourth-order cumulants, Fractional differentiation, Higher order statistics, Identification (control systems), Nonlinear programming, Religious buildings, Signal processing @conference{Chetoui2014,This paper considers the problem of identifying continuous-time fractional systems from noisy input/output measurements. Firstly, the differentiation orders are fixed and the differential equation coefficients are estimated using an estimator based on Higher-Order Statistics: fractional fourth-order cumulants based least squares (ffocls). Then, the commensurate order is estimated along with the differential equation coefficients using a non linear optimization technique combined to the ffocls algorithm (co-ffocls). Under some assumptions on the distributional properties of additive noises and the noise-free input signals, the developed estimators give consistent results. Hence, the noise-free input signal is assumed to be non gaussian, whereas the additive noises are assumed to be gaussian. The performances of the developed algorithms are assessed through a practical application for modeling a real electronic system. © 2014 IEEE. |
2012 |
Chetoui, Manel; Malti, Rachid; Thomassin, Magalie; Aoun, Mohamed; Najar, Slaheddine; Oustaloup, Alain; Abdelkrim, Mohamed Naceur EIV methods for system identification with fractional models Conférence vol. 16, no. PART 1, 2012, (Cited by: 14). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Continuous-time, Cumulants, Differential equations, Errors in variables, Fractional SVF, Higher order statistics, Identification (control systems), Iterative, Iterative methods, Least Square, Monte Carlo methods, Religious buildings @conference{Chetoui20121641b,This paper deals with continuous-time system identification with fractional models in Errors-In-Variables context. Two estimators based on Higher-Order Statistics (third-order cumulants) are proposed. A State Variable Filter approach is extended to fractional orders to compute fractional derivatives of third-order cumulants estimates. The performance of the proposed algorithms is illustrated in a numerical example. Firstly, differentiation orders are fixed and differential equation coefficients are estimated. The consistency of the proposed estimators is evaluated through a study of the tuning parameter and Monte Carlo simulations. Then, the commensurate differentiation order is optimized along with the differential equation coefficients. © 2012 IFAC. |
Chetoui, Manel; Malti, Rachid; Thomassin, Magalie; Aoun, Mohamed; Najar, Slaheddine; Oustaloup, Alain; Abdelkrim, Mohamed Naceur EIV methods for system identification with fractional models Conférence vol. 16, no. PART 1, 2012, (Cited by: 14). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Continuous-time, Cumulants, Differential equations, Errors in variables, Fractional SVF, Higher order statistics, Identification (control systems), Iterative, Iterative methods, Least Square, Monte Carlo methods, Religious buildings @conference{Chetoui20121641,This paper deals with continuous-time system identification with fractional models in Errors-In-Variables context. Two estimators based on Higher-Order Statistics (third-order cumulants) are proposed. A State Variable Filter approach is extended to fractional orders to compute fractional derivatives of third-order cumulants estimates. The performance of the proposed algorithms is illustrated in a numerical example. Firstly, differentiation orders are fixed and differential equation coefficients are estimated. The consistency of the proposed estimators is evaluated through a study of the tuning parameter and Monte Carlo simulations. Then, the commensurate differentiation order is optimized along with the differential equation coefficients. © 2012 IFAC. |
2011 |
Chetoui, M.; Malti, R.; Thomassin, M.; Aoun, M.; Najar, S.; Abdelkrim, M. N. 2011, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: 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 @conference{Chetoui2011b,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. |
Chetoui, M.; Malti, R.; Thomassin, M.; Aoun, M.; Najar, S.; Abdelkrim, M. N. 2011, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: 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 @conference{Chetoui2011,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. |
2006 |
Sabatier, Jocelyn; Aoun, Mohamed; Oustaloup, Alain; Grégoire, Gilles; Ragot, Franck; Roy, Patrick Estimation of lead acid battery state of charge with a novel fractional model Conférence vol. 2, no. PART 1, 2006, (Cited by: 6; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Application programs, Battery management systems, Charging (batteries), Estimation methods, Fractional behavior, Fractional model, Fractional systems, Identification (control systems), Lead acid batteries, Operating temperature, Religious buildings, State-of-charge estimation, Unknown state, Validation test @conference{Sabatier2006296b,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 less than 5% whatever the operating temperature. |
Sabatier, Jocelyn; Aoun, Mohamed; Oustaloup, Alain; Grégoire, Gilles; Ragot, Franck; Roy, Patrick Estimation of lead acid battery state of charge with a novel fractional model Conférence vol. 2, no. PART 1, 2006, (Cited by: 6; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Application programs, Battery management systems, Charging (batteries), Estimation methods, Fractional behavior, Fractional model, Fractional systems, Identification (control systems), Lead acid batteries, Operating temperature, Religious buildings, State-of-charge estimation, Unknown state, Validation test @conference{Sabatier2006296,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 less than 5% whatever the operating temperature. |
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
2022 |
System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). |
System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). |
2016 |
2016, (Cited by: 9). |
2016, (Cited by: 9). |
2015 |
On the Closed-Loop System Identification with Fractional Models Article de journal Dans: Circuits, Systems, and Signal Processing, vol. 34, no. 12, p. 3833 – 3860, 2015, (Cited by: 20). |
2015, (Cited by: 2). |
A bias correction method for fractional closed-loop system identification Article de journal Dans: Journal of Process Control, vol. 33, p. 25 – 36, 2015, (Cited by: 21). |
2014 |
2014, (Cited by: 0). |
Indirect approach for closed-loop system identification with fractional models Conférence 2014, (Cited by: 4). |
2014, (Cited by: 5). |
2014, (Cited by: 0). |
2012 |
EIV methods for system identification with fractional models Conférence vol. 16, no. PART 1, 2012, (Cited by: 14). |
EIV methods for system identification with fractional models Conférence vol. 16, no. PART 1, 2012, (Cited by: 14). |
2011 |
2011, (Cited by: 3). |
2011, (Cited by: 3). |
2006 |
Estimation of lead acid battery state of charge with a novel fractional model Conférence vol. 2, no. PART 1, 2006, (Cited by: 6; All Open Access, Bronze Open Access). |
Estimation of lead acid battery state of charge with a novel fractional model Conférence vol. 2, no. PART 1, 2006, (Cited by: 6; All Open Access, Bronze Open Access). |
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). |