2022
|
Yakoub, Zaineb; Amairi, Messaoud; Chetoui, Manel; Aoun, Mohamed Bias Recursive Least Squares Method for Fractional Order System Identification Conférence 2022, (Cited by: 0). @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}
}
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. |
Yakoub, Zaineb; Naifar, Omar; Amairi, Messaoud; Chetoui, Manel; Aoun, Mohamed; Makhlouf, Abdellatif Ben A Bias-Corrected Method for Fractional Linear Parameter Varying Systems Article de journal Dans: Mathematical Problems in Engineering, vol. 2022, 2022, (Cited by: 1; All Open Access, Gold Open Access). @article{Yakoub2022e,
title = {A Bias-Corrected Method for Fractional Linear Parameter Varying Systems},
author = {Zaineb Yakoub and Omar Naifar and Messaoud Amairi and Manel Chetoui and Mohamed Aoun and Abdellatif Ben Makhlouf},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85128182629\&doi=10.1155%2f2022%2f7278157\&partnerID=40\&md5=6ea775beb03cf2de78d054b3e4819d41},
doi = {10.1155/2022/7278157},
year = {2022},
date = {2022-01-01},
journal = {Mathematical Problems in Engineering},
volume = {2022},
abstract = {This paper proposes an identification algorithm for the fractional Linear Parameter Varying (LPV) system considering noisy scheduling and output measurements. A bias correction technique is provided in order to compensate for the bias caused by the least squares algorithm. This approach was created to estimate either coefficients or fractional-order differentiation, and it has been proven to produce unbiased and reliable results. The suggested method's performance is assessed by the identification of two fractional models and was compared with Nelder-Mead Simplex method. © 2022 Zaineb Yakoub et al.},
note = {Cited by: 1; All Open Access, Gold Open Access},
keywords = {Bias correction, Correction techniques, Fractional model, Fractional order, Identification algorithms, LeastSquare algorithm, Linear parameter varying systems, Linear programming, Linear systems, Nelder-Mead simplex methods, Performance, Reliable results},
pubstate = {published},
tppubtype = {article}
}
This paper proposes an identification algorithm for the fractional Linear Parameter Varying (LPV) system considering noisy scheduling and output measurements. A bias correction technique is provided in order to compensate for the bias caused by the least squares algorithm. This approach was created to estimate either coefficients or fractional-order differentiation, and it has been proven to produce unbiased and reliable results. The suggested method’s performance is assessed by the identification of two fractional models and was compared with Nelder-Mead Simplex method. © 2022 Zaineb Yakoub et al. |
2020
|
Mayoufi, Abir; Chetoui, Manel; Victor, Stephans; Aoun, Mohamed; Malti, Rachid A comparison between two methods for MISO fractional models estimation Conférence 2020, (Cited by: 0). @conference{Mayoufi2020446b,
title = {A comparison between two methods for MISO fractional models estimation},
author = {Abir Mayoufi and Manel Chetoui and Stephans Victor and Mohamed Aoun and Rachid Malti},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85103003953\&doi=10.1109%2fSSD49366.2020.9364187\&partnerID=40\&md5=b9525866e8a24d2426d03414f5810e22},
doi = {10.1109/SSD49366.2020.9364187},
year = {2020},
date = {2020-01-01},
journal = {Proceedings of the 17th International Multi-Conference on Systems, Signals and Devices, SSD 2020},
pages = {446 \textendash 451},
abstract = {This paper proposes two new methods for multiple input-single output system identification with fractional models: The instrumental variable based method and the output-error based method. The fractional orders are supposed known and the linear coefficients are estimated. A comparative study between the developed methods is illustrated via a numerical example. Monte Carlo simulations are used to demonstrate the efficiency of the two methods. © 2020 IEEE.},
note = {Cited by: 0},
keywords = {Comparative studies, Fractional model, Fractional order, Instrumental variables, Linear coefficients, Monte Carlo methods, Multiple input single output systems, Numerical methods, Output errors},
pubstate = {published},
tppubtype = {conference}
}
This paper proposes two new methods for multiple input-single output system identification with fractional models: The instrumental variable based method and the output-error based method. The fractional orders are supposed known and the linear coefficients are estimated. A comparative study between the developed methods is illustrated via a numerical example. Monte Carlo simulations are used to demonstrate the efficiency of the two methods. © 2020 IEEE. |
2016
|
Hamdi, Saif Eddine; Amairi, Messaoud; Aoun, Mohamed Orthotopic set-membership parameter estimation of fractional order model Conférence 2016, (Cited by: 7). @conference{Hamdi2016634b,
title = {Orthotopic set-membership parameter estimation of fractional order model},
author = {Saif Eddine Hamdi and Messaoud Amairi and Mohamed Aoun},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84986192298\&doi=10.1109%2fMED.2016.7535873\&partnerID=40\&md5=067a264b24cef790e92783d5e4cfc584},
doi = {10.1109/MED.2016.7535873},
year = {2016},
date = {2016-01-01},
journal = {24th Mediterranean Conference on Control and Automation, MED 2016},
pages = {634 \textendash 639},
abstract = {This paper presents a new orthotopic set-membership method for the identification of linear fractional orders systems. This method consists in recursively constructing an outer orthotope that contains all feasible parameters when the probability distribution of the disturbances is unknown but bounded and when the differentiation orders are known. A numerical example shows the effectiveness of the proposed method. © 2016 IEEE.},
note = {Cited by: 7},
keywords = {Fractional order, Fractional order models, Numerical methods, Orthotopic, Probability distributions, Set membership, Set membership method, Unknown but bounded},
pubstate = {published},
tppubtype = {conference}
}
This paper presents a new orthotopic set-membership method for the identification of linear fractional orders systems. This method consists in recursively constructing an outer orthotope that contains all feasible parameters when the probability distribution of the disturbances is unknown but bounded and when the differentiation orders are known. A numerical example shows the effectiveness of the proposed method. © 2016 IEEE. |
2015
|
Hmed, A. Ben; Amairi, M.; Aoun, M. Stability and resonance conditions of the non-commensurate elementary fractional transfer functions of the second kind Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 22, no. 1-3, p. 842 – 865, 2015, (Cited by: 12). @article{BenHmed2015842b,
title = {Stability and resonance conditions of the non-commensurate elementary fractional transfer functions of the second kind},
author = {A. Ben Hmed and M. Amairi and M. Aoun},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84916894266\&doi=10.1016%2fj.cnsns.2014.07.014\&partnerID=40\&md5=ba0f57ffe315daafa9f4cbffa794490f},
doi = {10.1016/j.cnsns.2014.07.014},
year = {2015},
date = {2015-01-01},
journal = {Communications in Nonlinear Science and Numerical Simulation},
volume = {22},
number = {1-3},
pages = {842 \textendash 865},
abstract = {This paper deals with stability and resonance conditions of the non-commensurate elementary fractional transfer function of the second kind. This transfer function is a generalization of the elementary fractional transfer function of the second kind to an arbitrary order. It is written in the canonical form and characterized by a non-commensurate order, a pseudo-damping factor and a natural frequency. Stability and resonance analysis is done in terms of the pseudo-damping factor and the non-commensurate order. Also, an overall study of frequency-domain and time-domain performances of the considered system is done. Therefore many time-domain and frequency-domain curves are presented to help obtaining system parameters for a specified fractional order. Many illustrative examples show the efficiency of this study. Also, an application to the control of a spherical tank is also presented to show the usefulness of this study. © 2014 Elsevier B.V.},
note = {Cited by: 12},
keywords = {Convergence of numerical methods, Damping, Fractional order, Fractional systems, Frequency domain analysis, Frequency domain curves, Frequency domains, Functions of the second kind, Resonance, Resonance analysis, Resonance condition, Stability, Time domain, Transfer functions},
pubstate = {published},
tppubtype = {article}
}
This paper deals with stability and resonance conditions of the non-commensurate elementary fractional transfer function of the second kind. This transfer function is a generalization of the elementary fractional transfer function of the second kind to an arbitrary order. It is written in the canonical form and characterized by a non-commensurate order, a pseudo-damping factor and a natural frequency. Stability and resonance analysis is done in terms of the pseudo-damping factor and the non-commensurate order. Also, an overall study of frequency-domain and time-domain performances of the considered system is done. Therefore many time-domain and frequency-domain curves are presented to help obtaining system parameters for a specified fractional order. Many illustrative examples show the efficiency of this study. Also, an application to the control of a spherical tank is also presented to show the usefulness of this study. © 2014 Elsevier B.V. |
Hmed, A. Ben; Amairi, M.; Aoun, M. Stability and resonance conditions of the non-commensurate elementary fractional transfer functions of the second kind Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 22, no. 1-3, p. 842 – 865, 2015, (Cited by: 12). @article{BenHmed2015842c,
title = {Stability and resonance conditions of the non-commensurate elementary fractional transfer functions of the second kind},
author = {A. Ben Hmed and M. Amairi and M. Aoun},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84916894266\&doi=10.1016%2fj.cnsns.2014.07.014\&partnerID=40\&md5=ba0f57ffe315daafa9f4cbffa794490f},
doi = {10.1016/j.cnsns.2014.07.014},
year = {2015},
date = {2015-01-01},
journal = {Communications in Nonlinear Science and Numerical Simulation},
volume = {22},
number = {1-3},
pages = {842 \textendash 865},
abstract = {This paper deals with stability and resonance conditions of the non-commensurate elementary fractional transfer function of the second kind. This transfer function is a generalization of the elementary fractional transfer function of the second kind to an arbitrary order. It is written in the canonical form and characterized by a non-commensurate order, a pseudo-damping factor and a natural frequency. Stability and resonance analysis is done in terms of the pseudo-damping factor and the non-commensurate order. Also, an overall study of frequency-domain and time-domain performances of the considered system is done. Therefore many time-domain and frequency-domain curves are presented to help obtaining system parameters for a specified fractional order. Many illustrative examples show the efficiency of this study. Also, an application to the control of a spherical tank is also presented to show the usefulness of this study. © 2014 Elsevier B.V.},
note = {Cited by: 12},
keywords = {Convergence of numerical methods, Damping, Fractional order, Fractional systems, Frequency domain analysis, Frequency domain curves, Frequency domains, Functions of the second kind, Resonance, Resonance analysis, Resonance condition, Stability, Time domain, Transfer functions},
pubstate = {published},
tppubtype = {article}
}
This paper deals with stability and resonance conditions of the non-commensurate elementary fractional transfer function of the second kind. This transfer function is a generalization of the elementary fractional transfer function of the second kind to an arbitrary order. It is written in the canonical form and characterized by a non-commensurate order, a pseudo-damping factor and a natural frequency. Stability and resonance analysis is done in terms of the pseudo-damping factor and the non-commensurate order. Also, an overall study of frequency-domain and time-domain performances of the considered system is done. Therefore many time-domain and frequency-domain curves are presented to help obtaining system parameters for a specified fractional order. Many illustrative examples show the efficiency of this study. Also, an application to the control of a spherical tank is also presented to show the usefulness of this study. © 2014 Elsevier B.V. |
2010
|
Amairi, Messaoud; Najar, Slaheddine; Aoun, Mohamed; Abdelkrim, M. N. Guaranteed output-error identification of fractional order model Conférence vol. 2, 2010, (Cited by: 13). @conference{Amairi2010246b,
title = {Guaranteed output-error identification of fractional order model},
author = {Messaoud Amairi and Slaheddine Najar and Mohamed Aoun and M. N. Abdelkrim},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-77957959879\&doi=10.1109%2fICACC.2010.5486678\&partnerID=40\&md5=529c5385abe1d52046a96f58bae0e649},
doi = {10.1109/ICACC.2010.5486678},
year = {2010},
date = {2010-01-01},
journal = {Proceedings - 2nd IEEE International Conference on Advanced Computer Control, ICACC 2010},
volume = {2},
pages = {246 \textendash 250},
abstract = {A global optimization technique for identifying an output-error fractional order model is proposed. The proposed technique use a modified version of Hansen algorithm. It is capable of estimating the fractional orders and the parameters, with guaranteed convergence. The technique is applied to identify a fractional order system in deterministic and stochastic context. © 2010 IEEE.},
note = {Cited by: 13},
keywords = {Fractional differentiation, Fractional model, Fractional order, Fractional order models, Fractional-order systems, Global optimization, Global optimization techniques, Guaranteed convergence, Identification (control systems), Interval analysis, Optimization, System identifications},
pubstate = {published},
tppubtype = {conference}
}
A global optimization technique for identifying an output-error fractional order model is proposed. The proposed technique use a modified version of Hansen algorithm. It is capable of estimating the fractional orders and the parameters, with guaranteed convergence. The technique is applied to identify a fractional order system in deterministic and stochastic context. © 2010 IEEE. |
Amairi, M.; Aoun, M.; Najar, S.; Abdelkrim, M. N. A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation Article de journal Dans: Applied Mathematics and Computation, vol. 217, no. 5, p. 2162 – 2168, 2010, (Cited by: 18). @article{Amairi20102162b,
title = {A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation},
author = {M. Amairi and M. Aoun and S. Najar and M. N. Abdelkrim},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-77957308442\&doi=10.1016%2fj.amc.2010.07.015\&partnerID=40\&md5=a58a0a9b4b825b67caa7c949631264c1},
doi = {10.1016/j.amc.2010.07.015},
year = {2010},
date = {2010-01-01},
journal = {Applied Mathematics and Computation},
volume = {217},
number = {5},
pages = {2162 \textendash 2168},
abstract = {This paper presents a new method for validating existence and uniqueness of the solution of an initial value problems for fractional differential equations. An algorithm selecting a stepsize and computing a priori constant enclosure of the solution is proposed. Several illustrative examples, with linear and nonlinear fractional differential equations, are given to demonstrate the effectiveness of the method. © 2010 Elsevier Inc. All rights reserved.},
note = {Cited by: 18},
keywords = {Caputo fractional derivatives, Differential equations, Enclosures, Existence and uniqueness, Fractional order, Initial value problems, Initial values, Interval analysis, Nonlinear equations, Validated computing},
pubstate = {published},
tppubtype = {article}
}
This paper presents a new method for validating existence and uniqueness of the solution of an initial value problems for fractional differential equations. An algorithm selecting a stepsize and computing a priori constant enclosure of the solution is proposed. Several illustrative examples, with linear and nonlinear fractional differential equations, are given to demonstrate the effectiveness of the method. © 2010 Elsevier Inc. All rights reserved. |
2003
|
Malti, R.; Aoun, M.; Battaglia, J. -L.; Oustaloup, A.; Madani, K. Fractional Multimodels – Application to Heat Transfer Modeling Conférence vol. 36, no. 16, 2003, (Cited by: 4). @conference{Malti20031663b,
title = {Fractional Multimodels - Application to Heat Transfer Modeling},
author = {R. Malti and M. Aoun and J. -L. Battaglia and A. Oustaloup and K. Madani},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84875296967\&doi=10.1016%2fS1474-6670%2817%2934999-6\&partnerID=40\&md5=4d376fa9be56a199ca80c932be521309},
doi = {10.1016/S1474-6670(17)34999-6},
year = {2003},
date = {2003-01-01},
journal = {IFAC Proceedings Volumes (IFAC-PapersOnline)},
volume = {36},
number = {16},
pages = {1663 \textendash 1668},
abstract = {This paper deals with identification of non linear systems using non linear fractional differentiation multimodels. All sub-models are described by fractional differentiation transfer functions. Performance of the newly proposed class of models is illustrated on a heat transfer process near a phase change temperature. © 2003 International Federation of Automatic Control.},
note = {Cited by: 4},
keywords = {Fractional differentiation, Fractional dynamics, Fractional order, Heat transfer model, Heat transfer performance, Heat transfer process, Identification (control systems), Linear systems, Multi-model, Multi-models, Nonlinear systems, Phase change temperature},
pubstate = {published},
tppubtype = {conference}
}
This paper deals with identification of non linear systems using non linear fractional differentiation multimodels. All sub-models are described by fractional differentiation transfer functions. Performance of the newly proposed class of models is illustrated on a heat transfer process near a phase change temperature. © 2003 International Federation of Automatic Control. |
Malti, R.; Aoun, M.; Battaglia, J. -L.; Oustaloup, A.; Madani, K. Fractional Multimodels – Application to Heat Transfer Modeling Conférence vol. 36, no. 16, 2003, (Cited by: 4). @conference{Malti20031663,
title = {Fractional Multimodels - Application to Heat Transfer Modeling},
author = {R. Malti and M. Aoun and J. -L. Battaglia and A. Oustaloup and K. Madani},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84875296967\&doi=10.1016%2fS1474-6670%2817%2934999-6\&partnerID=40\&md5=4d376fa9be56a199ca80c932be521309},
doi = {10.1016/S1474-6670(17)34999-6},
year = {2003},
date = {2003-01-01},
journal = {IFAC Proceedings Volumes (IFAC-PapersOnline)},
volume = {36},
number = {16},
pages = {1663 \textendash 1668},
abstract = {This paper deals with identification of non linear systems using non linear fractional differentiation multimodels. All sub-models are described by fractional differentiation transfer functions. Performance of the newly proposed class of models is illustrated on a heat transfer process near a phase change temperature. © 2003 International Federation of Automatic Control.},
note = {Cited by: 4},
keywords = {Fractional differentiation, Fractional dynamics, Fractional order, Heat transfer model, Heat transfer performance, Heat transfer process, Identification (control systems), Linear systems, Multi-model, Multi-models, Nonlinear systems, Phase change temperature},
pubstate = {published},
tppubtype = {conference}
}
This paper deals with identification of non linear systems using non linear fractional differentiation multimodels. All sub-models are described by fractional differentiation transfer functions. Performance of the newly proposed class of models is illustrated on a heat transfer process near a phase change temperature. © 2003 International Federation of Automatic Control. |
2002
|
Aoun, Mohamed; Malti, Rachid; Cois, Olivier; Oustaloup, Alain System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). @conference{Aoun2002265b,
title = {System identification using fractional hammerstein models},
author = {Mohamed Aoun and Rachid Malti and Olivier Cois and Alain Oustaloup},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84945550683\&doi=10.3182%2f20020721-6-es-1901.01030\&partnerID=40\&md5=106ff8852a5dbedf91e03c25f0e7bb03},
doi = {10.3182/20020721-6-es-1901.01030},
year = {2002},
date = {2002-01-01},
journal = {IFAC Proceedings Volumes (IFAC-PapersOnline)},
volume = {15},
number = {1},
pages = {265 \textendash 269},
abstract = {Identification of continuous-time non-linear systems characterised by fractional order dynamics is studied. The Riemann-Liouville definition of fractional differentiation is used. A new identification method is proposed through the extension of Hammerstein-type models by allowing their linear part to belong to the class of fractional models. Fractional models are compact and so are used here to model complex dynamics with few parameters. Copyright © 2002 IFAC.},
note = {Cited by: 23},
keywords = {Automation, Continuous time systems, Fractional differentiation, Fractional model, Fractional order, Hammerstein model, Hammerstein-type models, Identification (control systems), Identification method, Linear systems, Non-linear modelling, Nonlinear systems, Riemann-liouville definitions},
pubstate = {published},
tppubtype = {conference}
}
Identification of continuous-time non-linear systems characterised by fractional order dynamics is studied. The Riemann-Liouville definition of fractional differentiation is used. A new identification method is proposed through the extension of Hammerstein-type models by allowing their linear part to belong to the class of fractional models. Fractional models are compact and so are used here to model complex dynamics with few parameters. Copyright © 2002 IFAC. |
Aoun, Mohamed; Malti, Rachid; Cois, Olivier; Oustaloup, Alain System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). @conference{Aoun2002265,
title = {System identification using fractional hammerstein models},
author = {Mohamed Aoun and Rachid Malti and Olivier Cois and Alain Oustaloup},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84945550683\&doi=10.3182%2f20020721-6-es-1901.01030\&partnerID=40\&md5=106ff8852a5dbedf91e03c25f0e7bb03},
doi = {10.3182/20020721-6-es-1901.01030},
year = {2002},
date = {2002-01-01},
journal = {IFAC Proceedings Volumes (IFAC-PapersOnline)},
volume = {15},
number = {1},
pages = {265 \textendash 269},
abstract = {Identification of continuous-time non-linear systems characterised by fractional order dynamics is studied. The Riemann-Liouville definition of fractional differentiation is used. A new identification method is proposed through the extension of Hammerstein-type models by allowing their linear part to belong to the class of fractional models. Fractional models are compact and so are used here to model complex dynamics with few parameters. Copyright © 2002 IFAC.},
note = {Cited by: 23},
keywords = {Automation, Continuous time systems, Fractional differentiation, Fractional model, Fractional order, Hammerstein model, Hammerstein-type models, Identification (control systems), Identification method, Linear systems, Non-linear modelling, Nonlinear systems, Riemann-liouville definitions},
pubstate = {published},
tppubtype = {conference}
}
Identification of continuous-time non-linear systems characterised by fractional order dynamics is studied. The Riemann-Liouville definition of fractional differentiation is used. A new identification method is proposed through the extension of Hammerstein-type models by allowing their linear part to belong to the class of fractional models. Fractional models are compact and so are used here to model complex dynamics with few parameters. Copyright © 2002 IFAC. |
