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. 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. |
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). |
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). |