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 |
2020 |
Frej, Ghazi Bel Haj; Malti, Rachid; Aoun, Mohamed; Raïssi, Tarek Fractional interval observers and initialization of fractional systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 82, 2020, (Cited by: 6; All Open Access, Bronze Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: A-stable, Additive noise, Estimation errors, Fractional systems, Free response, Initialization, Interval observers, Linear systems, Non negatives, Numerical methods, Pseudo state @article{BelHajFrej2020b,In this paper an interval observer is synthesized for fractional linear systems with additive noise and disturbances. The contribution of system whole past to future output is taken into account as an initialization function. Provided the initialization function is upper and lower bounded, it is shown in this paper that the fractional interval observer (FIO) allows to bound pseudo-state free responses by an upper and a lower trajectory. In case interval observers cannot be synthesized straightforwardly, so as to obtain a stable and non-negative estimation error, it is shown that a change of coordinates allows to overcome this problem. The proposed methodology allows to bound fractional systems trajectories when the whole past is unknown but can be bounded. Finally, a numerical example is given to show the effectiveness of the proposed methods on the initialization of fractional linear systems. © 2019 Elsevier B.V. |
Frej, Ghazi Bel Haj; Malti, Rachid; Aoun, Mohamed; Raïssi, Tarek Fractional interval observers and initialization of fractional systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 82, 2020, (Cited by: 6; All Open Access, Bronze Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: A-stable, Additive noise, Estimation errors, Fractional systems, Free response, Initialization, Interval observers, Linear systems, Non negatives, Numerical methods, Pseudo state @article{BelHajFrej2020c,In this paper an interval observer is synthesized for fractional linear systems with additive noise and disturbances. The contribution of system whole past to future output is taken into account as an initialization function. Provided the initialization function is upper and lower bounded, it is shown in this paper that the fractional interval observer (FIO) allows to bound pseudo-state free responses by an upper and a lower trajectory. In case interval observers cannot be synthesized straightforwardly, so as to obtain a stable and non-negative estimation error, it is shown that a change of coordinates allows to overcome this problem. The proposed methodology allows to bound fractional systems trajectories when the whole past is unknown but can be bounded. Finally, a numerical example is given to show the effectiveness of the proposed methods on the initialization of fractional linear systems. © 2019 Elsevier B.V. |
Atitallah, Halima; Aribi, Asma; Aoun, Mohamed Diagnosis of time-delay fractional systems using observer-based methods Article de journal Dans: International Journal of Dynamical Systems and Differential Equations, vol. 10, no. 2, p. 128 – 148, 2020, (Cited by: 2). Résumé | Liens | BibTeX | Étiquettes: Convergence conditions, Diagnosis, Fault detection, Fault detection and isolation, Fault isolation, Fractional systems, Luenberger observers, Residual sensitivities, Structured residuals, Time delay, Timing circuits, Unknown input observer @article{Atitallah2020128b,In this paper, two model-based methods are considered for the diagnosis of time-delay fractional systems. Time-delay fractional Luenberger observer without unknown input and time-delay fractional unknown input observer are developed and used for fault detection and isolation. A single observer scheme is needed for fault detection and a bank of generalized (respectively dedicated) observers is required for fault isolation. A theoretical study investigating the convergence condition for each observer-based method in terms of matrix inequalities is presented. Residual sensitivities to faults and to disturbances are studied. Time-delay fractional unknown input observer parameters are computed to obtain structured residuals. This observer ensures unknown input decoupling from the state which results residual insensitive to unknown inputs. Two numerical examples to validate the efficiency of the proposed approaches are given. Copyright © 2020 Inderscience Enterprises Ltd. |
2019 |
Atitallah, Halima; Aribi, Asma; Aoun, Mohamed Tracking Control Design for Fractional Systems with Time Delay Conférence 2019, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Automation, Controller parameter, Delay control systems, Fault tolerant control, Fractional systems, Fractional-order systems, Navigation, Numerical methods, Process control, Reference modeling, Time delay, Timing circuits, Tracking controls @conference{Atitallah2019280b,Fault tolerant control has been an important subject for many researchers. Nevertheless, there are few works dealing with fractional systems up to now and especially in presence of time delay. In this context, this paper proposes a tracking control design for fractional order system with time delay. The aim is to control the system in order to obtain the same performances of a time delay fractional reference model. The controller parameters are computed in both nominal and faulty functioning in case the state is available and unavailable for measurement. The efficiency of the proposed method is illustrated through a numerical example. © 2019 IEEE. |
Atitallah, Halima; Aribi, Asma; Aoun, Mohamed Fault estimation using adaptive observer-based technique for time delay fractional-order systems Conférence 2019, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Adaptive observer, Continuous frequency, Convergence criterion, Detection and estimation, Fault detection, Fault estimation, Fractional systems, Fractional-order systems, Linear matrix inequalities, Luenberger observers, Lyapunov functions, Numerical methods, Time delay, Timing circuits @conference{Atitallah2019399b,This paper proposes a technique to detect and estimate faults for fractional-order systems with time delay. Two observers are used in this method. Indeed, a time-delay fractional Luenberger observer is generated to detect fault. An adaptive fractional order with time delay observer is then constructed to estimate the fault by providing an on-line estimation algorithm. The convergence criteria of this observer is expressed via linear matrix inequalities (LMIs) by the use of a specific Lyapunov function considering the continuous frequency disturbed model. The validity of the fault detection and estimation technique is shown by a numerical example. © 2019 IEEE. |
Frej, Ghazi Bel Haj; Malti, Rachid; Aoun, Mohamed; Raïssi, Tarek Fractional Interval Observers And Initialization Of Fractional Systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, p. 105030, 2019, ISSN: 1007-5704. Résumé | Liens | BibTeX | Étiquettes: Fractional systems, Initialization, Interval observers, scopus, Stability of fractional linear systems @article{FREJ2019,In this paper an interval observer is synthesized for fractional linear systems with additive noise and disturbances. The contribution of system whole past to future output is taken into account as an initialization function. Provided the initialization function is upper and lower bounded, it is shown in this paper that the fractional interval observer (FIO) allows to bound pseudo-state free responses by an upper and a lower trajectory. In case interval observers cannot be synthesized straightforwardly, so as to obtain a stable and non-negative estimation error, it is shown that a change of coordinates allows to overcome this problem. The proposed methodology allows to bound fractional systems trajectories when the whole past is unknown but can be bounded. Finally, a numerical example is given to show the effectiveness of the proposed methods on the initialization of fractional linear systems. |
Atitallah, Halima; Aribi, Asma; Aoun, Mohamed Tracking Control Design for Fractional Systems with Time Delay Conférence 2019, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Automation, Controller parameter, Delay control systems, Fault tolerant control, Fractional systems, Fractional-order systems, Navigation, Numerical methods, Process control, Reference modeling, Time delay, Timing circuits, Tracking controls @conference{Atitallah2019280,Fault tolerant control has been an important subject for many researchers. Nevertheless, there are few works dealing with fractional systems up to now and especially in presence of time delay. In this context, this paper proposes a tracking control design for fractional order system with time delay. The aim is to control the system in order to obtain the same performances of a time delay fractional reference model. The controller parameters are computed in both nominal and faulty functioning in case the state is available and unavailable for measurement. The efficiency of the proposed method is illustrated through a numerical example. © 2019 IEEE. |
Atitallah, Halima; Aribi, Asma; Aoun, Mohamed Fault estimation using adaptive observer-based technique for time delay fractional-order systems Conférence 2019, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Adaptive observer, Continuous frequency, Convergence criterion, Detection and estimation, Fault detection, Fault estimation, Fractional systems, Fractional-order systems, Linear matrix inequalities, Luenberger observers, Lyapunov functions, Numerical methods, Time delay, Timing circuits @conference{Atitallah2019399,This paper proposes a technique to detect and estimate faults for fractional-order systems with time delay. Two observers are used in this method. Indeed, a time-delay fractional Luenberger observer is generated to detect fault. An adaptive fractional order with time delay observer is then constructed to estimate the fault by providing an on-line estimation algorithm. The convergence criteria of this observer is expressed via linear matrix inequalities (LMIs) by the use of a specific Lyapunov function considering the continuous frequency disturbed model. The validity of the fault detection and estimation technique is shown by a numerical example. © 2019 IEEE. |
2018 |
Hamdi, Saif Eddine; Amairi, Messaoud; Aoun, Mohamed Recursive set-membership parameter estimation of fractional systems using orthotopic approach Article de journal Dans: Transactions of the Institute of Measurement and Control, vol. 40, no. 15, p. 4185 – 4197, 2018, (Cited by: 5). Résumé | Liens | BibTeX | Étiquettes: Bounded error context, Bounded errors, Errors, Fractional systems, Fractional-order systems, Iterative algorithm, Iterative methods, Monte Carlo methods, Order estimation, Parameter estimation, Set membership approach, Unknown but bounded @article{Hamdi20184185b,In this paper, set-membership parameter estimation of linear fractional-order systems is addressed for the case of unknown-but-bounded equation error. In such bounded-error context with a-priori known noise bounds, the main goal is to characterize the set of all feasible parameters. This characterization is performed using an orthotopic strategy adapted for fractional system parameter estimation. In the case of a fractional commensurate system, an iterative algorithm is proposed to deal with commensurate-order estimation. The performances of the proposed algorithm are illustrated by a numerical example via a Monte Carlo simulation. © The Author(s) 2018. |
2017 |
Raïssi, Tarek; Aoun, Mohamed On robust pseudo state estimation of fractional order systems Article de journal Dans: Lecture Notes in Control and Information Sciences, vol. 471, p. 97 – 111, 2017, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Continuous-time linear systems, Estimation errors, Fractional dynamics, Fractional systems, Fractional-order systems, Interval observers, Linear systems, Measurement Noise, Robust estimation, State estimation, State space methods, Uncertainty analysis @article{Ra\"{i}ssi201797b,The goal of this chapter is to design robust observers for fractional dynamic continuous-time linear systems described by pseudo state space representation. The fractional observer is guaranteed to compute a domain enclosing all the system pseudo states that are consistent with the model, the disturbances and the measurement noise realizations. Uncertainties on the initial pseudo state and noises are propagated in a reliable way to estimate the bounds of the fractional pseudo state. Only the bounds of the uncertainties are used and no additional assumptions about their stationarity or ergodicity are taken into account. A fractional observer is firstly built for a particular case where the estimation error can be designed to be positive. Then, the general case is investigated through changes of coordinates. Some numerical simulations illustrate the proposed methodology. © Springer International Publishing AG 2017. |
Atitallah, Halima; Aribi, Asma; Aoun, Mohamed Diagnosis of time-delay fractional systems Conférence 2017, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: Automation, Bilinear matrix inequality, Convergence conditions, Convergence of numerical methods, Delay control systems, Diagnosis, Fault detection, Fault indicators, Fractional systems, Fractional-order systems, Luenberger observers, Model based diagnosis, Numerical methods, Process control, residual, Time delay @conference{Atitallah2017284b,In this paper, a model-based diagnosis method, called Luenberger diagnosis observer, recently developed for fractional order systems, is extended for time-delay fractional systems. A sufficient convergence condition of the fault indicator using Bilinear Matrix Inequalities is detailed. A numerical example illustrating the method’s validity in detecting faults is finally presented. © 2016 IEEE. |
Raïssi, Tarek; Aoun, Mohamed On robust pseudo state estimation of fractional order systems Article de journal Dans: Lecture Notes in Control and Information Sciences, vol. 471, p. 97 – 111, 2017, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Continuous-time linear systems, Estimation errors, Fractional dynamics, Fractional systems, Fractional-order systems, Interval observers, Linear systems, Measurement Noise, Robust estimation, State estimation, State space methods, Uncertainty analysis @article{Ra\"{i}ssi201797,The goal of this chapter is to design robust observers for fractional dynamic continuous-time linear systems described by pseudo state space representation. The fractional observer is guaranteed to compute a domain enclosing all the system pseudo states that are consistent with the model, the disturbances and the measurement noise realizations. Uncertainties on the initial pseudo state and noises are propagated in a reliable way to estimate the bounds of the fractional pseudo state. Only the bounds of the uncertainties are used and no additional assumptions about their stationarity or ergodicity are taken into account. A fractional observer is firstly built for a particular case where the estimation error can be designed to be positive. Then, the general case is investigated through changes of coordinates. Some numerical simulations illustrate the proposed methodology. © Springer International Publishing AG 2017. |
Atitallah, Halima; Aribi, Asma; Aoun, Mohamed Diagnosis of time-delay fractional systems Conférence 2017, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: Automation, Bilinear matrix inequality, Convergence conditions, Convergence of numerical methods, Delay control systems, Diagnosis, Fault detection, Fault indicators, Fractional systems, Fractional-order systems, Luenberger observers, Model based diagnosis, Numerical methods, Process control, residual, Time delay @conference{Atitallah2017284,In this paper, a model-based diagnosis method, called Luenberger diagnosis observer, recently developed for fractional order systems, is extended for time-delay fractional systems. A sufficient convergence condition of the fault indicator using Bilinear Matrix Inequalities is detailed. A numerical example illustrating the method’s validity in detecting faults is finally presented. © 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). Résumé | Liens | BibTeX | Étiquettes: 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 @article{BenHmed2015842b,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). Résumé | Liens | BibTeX | Étiquettes: 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 @article{BenHmed2015842c,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. |
Azaiez, Wiem; Chetoui, Manel; Aoun, Mohamed Analytic approach to design PID controller for stabilizing fractional systems with time delay Conférence 2015, (Cited by: 1). Résumé | Liens | BibTeX | Étiquettes: Controllers, dual-locus diagram, Electric control equipment, Fractional differentiation, Fractional systems, Graphical criteria, Optimal controller, PID controller design, PID controllers, Proportional control systems, Stability regions, Three term control systems, Time delay @conference{Azaiez2015b,The paper considers the problem of PID controller design for stabilizing fractional systems with time delay. An analytic approach developed for rational systems with time delay is extended for fractional systems with time delay. It consists in determining the stability regions in the PID controller parameters planes and choosing the optimal controller by analyzing the stability of the closed-loop corrected system using a graphical criterion, like the dual-locus diagram. The performances of the proposed approach are illustrated using two numerical examples. © 2015 IEEE. |
2014 |
Hmed, A. Ben; Amairi, M.; Aoun, M. Fractional order controller design using time-domain specifications Conférence 2014, (Cited by: 1). Résumé | Liens | BibTeX | Étiquettes: Automation, Closed loop systems, Closed-loop behavior, Control design, Controller designs, Controllers, Convergence of numerical methods, Design, Fractional controllers, Fractional systems, Fractional-order controllers, Numerical methods, Resonance, Time domain, Time domain analysis, Time-domain specifications @conference{BenHmed2014462b,This paper deals with the design of a fractional controller to achieve a desired closed loop system. Based on the resonance and time-domain studies of the desired closed-loop behavior, the controller design is carried out by a pole-compensator method. Numerical examples are proposed to show the efficiency of the proposed technique. © 2014 IEEE. |
Hmed, A. Ben; Amairi, M.; Aoun, M. Fractional order controller design using time-domain specifications Conférence 2014, (Cited by: 1). Résumé | Liens | BibTeX | Étiquettes: Automation, Closed loop systems, Closed-loop behavior, Control design, Controller designs, Controllers, Convergence of numerical methods, Design, Fractional controllers, Fractional systems, Fractional-order controllers, Numerical methods, Resonance, Time domain, Time domain analysis, Time-domain specifications @conference{BenHmed2014462c,This paper deals with the design of a fractional controller to achieve a desired closed loop system. Based on the resonance and time-domain studies of the desired closed-loop behavior, the controller design is carried out by a pole-compensator method. Numerical examples are proposed to show the efficiency of the proposed technique. © 2014 IEEE. |
2013 |
Hamdi, S. E.; Amairi, M.; Aoun, M.; Abdelkrim, M. N. Interval state observer design for fractional systems Conférence 2013, (Cited by: 2). Résumé | Liens | BibTeX | Étiquettes: Bounded errors, Design, Differential equations, Fractional differential equations, Fractional systems, Initial value problems, Interval analysis, observer, Observer-based, Prediction-correction, State estimation, State observer @conference{Hamdi2013b,This paper presents a design method for interval state observer for fractional systems in a bounded-error context. A causal observer based on prediction-correction approach is proposed. The prediction part consists on a validated solving of an Initial Value Problem (IVP) for a Fractional Differential Equation (FDE) and the correction part uses set inversion algorithm. A numerical example is presented to show the effectiveness of the proposed design method. © 2013 IEEE. |
2012 |
Amairi, Messaoud; Aoun, Mohamed; Najar, Slaheddine; Abdelkrim, Mohamed Naceur Guaranteed frequency-domain identification of fractional order systems: Application to a real system Article de journal Dans: International Journal of Modelling, Identification and Control, vol. 17, no. 1, p. 32 – 42, 2012, (Cited by: 20). Résumé | Liens | BibTeX | Étiquettes: Algebra, Constrained optimization, Fractional differentiation, Fractional systems, Frequency domain analysis, Frequency domains, Global optimisation, Global optimization, Identification (control systems), Parameter estimation, Real intervals, Satisfaction problem @article{Amairi201232b,This paper presents a new guaranteed approach for frequency-domain identification of fractional order systems. Estimated parameters (coefficients and differential orders) are expressed as intervals. Then, an interval-based global optimisation algorithm is used to estimate the set of all feasible parameters. It combines the Hansen’s algorithm with forward-backward contractor. The approach is applied to a numerical example as well as to a real electronic system. Copyright © 2012 Inderscience Enterprises Ltd. |
Amairi, Messaoud; Aoun, Mohamed; Najar, Slaheddine; Abdelkrim, Mohamed Naceur Set membership parameter estimation of linear fractional systems using parallelotopes Conférence 2012, (Cited by: 11). Résumé | Liens | BibTeX | Étiquettes: Algorithms, Fractional model, Fractional systems, Parameter estimation, Set-membership, Time domain @conference{Amairi2012c,The paper deals with set-membership parameter estimation of fractional models in the time-domain. In such a context, the noise is supposed to be unknown-but-bounded with a priori known bounds. The proposed algorithm computes the set of all feasible parameters represented by a parallelotop. Simulation results and performance comparaison with the ellipsoidal approach are also given. © 2012 IEEE. |
2011 |
Aoun, Mohamed; Aribi, Asma; Najar, Slaheddine; Abdelkrim, Mohamed Naceur 2011, (Cited by: 8). Résumé | Liens | BibTeX | Étiquettes: Detection methods, Fault detection, fault diagnosis, Fractional derivatives, Fractional systems, Numerical example, Parity spaces, Residual generator, residual sensitivity, Signal detection @conference{Aoun2011f,This paper shows the interest of extending the dynamic parity space fault detection method for fractional systems. Accordingly, a comparison between fractional and rational residual generators using the later method is presented. An analysis of fractional and rational residuals’ sensitivity shows the merits of the fractional residual generators. A numerical example illustrating the advantage of using fractional residual generators for fractional systems diagnosis is given. © 2011 IEEE. |
Aoun, M.; Amairi, M.; Lassoued, Z.; Najar, S.; Abdelkrim, M. N. An ellipsoidal set-membership parameter estimation of fractional orders systems Conférence 2011, (Cited by: 4). Résumé | Liens | BibTeX | Étiquettes: Algorithms, Fogel-Huang algorithm, Fractional differentiation, Fractional systems, Identification (control systems), Numerical methods, OBE, Parameter estimation, Probability distributions, Set-membership, system identification @conference{Aoun2011e,This paper presents a new ellipsoidal set-membership method for the identification of linear fractional orders systems. It use the Optimal Bounding Ellipsoid (OBE) algorithm. When the probability distribution of the disturbances is unknown but bounded and when the differentiation orders are known, the proposed method can estimate all the feasible parameters. A numerical example shows the effectiveness of the proposed method. © 2011 IEEE. |
Aoun, M.; Amairi, M.; Najar, S.; Abdelkrim, M. N. 2011, (Cited by: 2). Résumé | Liens | BibTeX | Étiquettes: ACFDR, Approximation theory, CFDR, Diethelm’s approximation, Differentiation (calculus), Fractional derivatives, Fractional systems, Pole-zero distribution, simulation @conference{Aoun2011d,This paper proposes a new method for the simulation of the fractional systems. It deals with the approximation methods of the fractional derivative. It compare the approximation based on Grnwald with Caputo approximation. The efficiency of each approximation methods in termes of execution time and quadratic error is evaluated for different differential orders and stepsize. The best approximation method is used to develop an original simulation method to demonstrate its effectiveness. © 2011 IEEE. |
2009 |
Abdelhamid, Moufida; Aoun, Mohamed; Najar, Slaheddine; Abdelhamid, Mohamed Naceur Discrete fractional Kalman filter Conférence vol. 2, no. PART 1, 2009, (Cited by: 20; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Algorithms, Discrete time control systems, Discrete-time Kalman filters, Fractional differentiation, Fractional Kalman filter, Fractional kalman filters, Fractional systems, Intelligent control, Kalman filters, Linear state estimation, Numerical example, Signal processing, State estimation @conference{Abdelhamid2009b,This paper presents a generalization of the classical discrete time Kalman filter algorithm to the case of the fractional systems. Motivations for the use of this filter are given and the algorithm is detailed. The document also shows a simple numerical example of linear state estimation. Copyright © 2007 International Federation of Automatic Control. |
Abdelhamid, Moufida; Aoun, Mohamed; Najar, Slaheddine; Abdelhamid, Mohamed Naceur Discrete fractional Kalman filter Conférence vol. 2, no. PART 1, 2009, (Cited by: 20; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Algorithms, Discrete time control systems, Discrete-time Kalman filters, Fractional differentiation, Fractional Kalman filter, Fractional kalman filters, Fractional systems, Intelligent control, Kalman filters, Linear state estimation, Numerical example, Signal processing, State estimation @conference{Abdelhamid2009,This paper presents a generalization of the classical discrete time Kalman filter algorithm to the case of the fractional systems. Motivations for the use of this filter are given and the algorithm is detailed. The document also shows a simple numerical example of linear state estimation. Copyright © 2007 International Federation of Automatic Control. |
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. |
2005 |
Aoun, Mohamed; Malti, Rachid; Oustaloup, Alain Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Calculations, Dynamical systems, Fractional calculus, Fractional derivatives, Fractional systems, Identification (control systems), Multimodes, Orthogonal basis, Orthogonal functions, Orthonormal basis, Rational orthogonal basis, simulation @conference{Aoun2005321b,Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to capture the aperiodic multi-mode behaviour of fractional systems in a limited number of terms. The classical definition of orthogonal Laguerre, Kautz, and GOB functions has been extended for the use of fractional derivatives. An appropriate diagram is thus proposed for simulation. Copyright © 2005 IFAC. |
Aoun, Mohamed; Malti, Rachid; Oustaloup, Alain Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Calculations, Dynamical systems, Fractional calculus, Fractional derivatives, Fractional systems, Identification (control systems), Multimodes, Orthogonal basis, Orthogonal functions, Orthonormal basis, Rational orthogonal basis, simulation @conference{Aoun2005321,Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to capture the aperiodic multi-mode behaviour of fractional systems in a limited number of terms. The classical definition of orthogonal Laguerre, Kautz, and GOB functions has been extended for the use of fractional derivatives. An appropriate diagram is thus proposed for simulation. Copyright © 2005 IFAC. |
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, François; Oustaloup, Alain Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). Résumé | Liens | BibTeX | Étiquettes: Computer simulation, Differentiation (calculus), Fractional models, Fractional systems, Integration, Laplace transforms, Mathematical models, Transfer functions, Vectors @conference{Aoun2003745,This paper deals with the design and simulation of continuous-time models with fractional differentiation orders. Two new methods are proposed. The first is an improvement of the approximation of the fractional integration operator using recursive poles and zeros proposed by Oustaloup (1995) and Lin (2001). The second improves the simulation schema by using a modal representation. |
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. |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). Résumé | Liens | BibTeX | Étiquettes: Computer simulation, Differentiation (calculus), Fractional models, Fractional systems, Integration, Laplace transforms, Mathematical models, Transfer functions, Vectors @conference{Aoun2003745b,This paper deals with the design and simulation of continuous-time models with fractional differentiation orders. Two new methods are proposed. The first is an improvement of the approximation of the fractional integration operator using recursive poles and zeros proposed by Oustaloup (1995) and Lin (2001). The second improves the simulation schema by using a modal representation. |
Publications
2022 |
System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). |
2020 |
Fractional interval observers and initialization of fractional systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 82, 2020, (Cited by: 6; All Open Access, Bronze Open Access, Green Open Access). |
Fractional interval observers and initialization of fractional systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 82, 2020, (Cited by: 6; All Open Access, Bronze Open Access, Green Open Access). |
Diagnosis of time-delay fractional systems using observer-based methods Article de journal Dans: International Journal of Dynamical Systems and Differential Equations, vol. 10, no. 2, p. 128 – 148, 2020, (Cited by: 2). |
2019 |
Tracking Control Design for Fractional Systems with Time Delay Conférence 2019, (Cited by: 0). |
Fault estimation using adaptive observer-based technique for time delay fractional-order systems Conférence 2019, (Cited by: 0). |
Fractional Interval Observers And Initialization Of Fractional Systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, p. 105030, 2019, ISSN: 1007-5704. |
Tracking Control Design for Fractional Systems with Time Delay Conférence 2019, (Cited by: 0). |
Fault estimation using adaptive observer-based technique for time delay fractional-order systems Conférence 2019, (Cited by: 0). |
2018 |
Recursive set-membership parameter estimation of fractional systems using orthotopic approach Article de journal Dans: Transactions of the Institute of Measurement and Control, vol. 40, no. 15, p. 4185 – 4197, 2018, (Cited by: 5). |
2017 |
On robust pseudo state estimation of fractional order systems Article de journal Dans: Lecture Notes in Control and Information Sciences, vol. 471, p. 97 – 111, 2017, (Cited by: 3). |
Diagnosis of time-delay fractional systems Conférence 2017, (Cited by: 3). |
On robust pseudo state estimation of fractional order systems Article de journal Dans: Lecture Notes in Control and Information Sciences, vol. 471, p. 97 – 111, 2017, (Cited by: 3). |
Diagnosis of time-delay fractional systems Conférence 2017, (Cited by: 3). |
2015 |
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). |
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). |
Analytic approach to design PID controller for stabilizing fractional systems with time delay Conférence 2015, (Cited by: 1). |
2014 |
Fractional order controller design using time-domain specifications Conférence 2014, (Cited by: 1). |
Fractional order controller design using time-domain specifications Conférence 2014, (Cited by: 1). |
2013 |
Interval state observer design for fractional systems Conférence 2013, (Cited by: 2). |
2012 |
Guaranteed frequency-domain identification of fractional order systems: Application to a real system Article de journal Dans: International Journal of Modelling, Identification and Control, vol. 17, no. 1, p. 32 – 42, 2012, (Cited by: 20). |
Set membership parameter estimation of linear fractional systems using parallelotopes Conférence 2012, (Cited by: 11). |
2011 |
2011, (Cited by: 8). |
An ellipsoidal set-membership parameter estimation of fractional orders systems Conférence 2011, (Cited by: 4). |
2011, (Cited by: 2). |
2009 |
Discrete fractional Kalman filter Conférence vol. 2, no. PART 1, 2009, (Cited by: 20; All Open Access, Bronze Open Access). |
Discrete fractional Kalman filter Conférence vol. 2, no. PART 1, 2009, (Cited by: 20; All Open Access, Bronze Open Access). |
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). |
2005 |
Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). |
Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green 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). |
Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). |
Orthonormal basis functions for modeling continuous-time fractional systems Conférence vol. 36, no. 16, 2003, (Cited by: 11; All Open Access, Bronze Open Access). |
Numerical simulations of fractional systems Conférence vol. 5 A, 2003, (Cited by: 16). |