2022 |
Yakoub, Zaineb; Amairi, Messaoud; Chetoui, Manel; Aoun, Mohamed Bias Recursive Least Squares Method for Fractional Order System Identification Conférence 2022, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: 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 @conference{Yakoub20221003b,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. |
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 |
Publications
2022 |
Bias Recursive Least Squares Method for Fractional Order System Identification Conférence 2022, (Cited by: 0). |
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). |