2023 |
Ethabet, Haifa; Dadi, Leila; Raissi, Tarek; Aoun, Mohamed L∞ Set-membership Estimation for Continuous-time Switched Linear Systems Conférence 2023. Résumé | Liens | BibTeX | Étiquettes: Bounded error context, Continous time, Continuous time systems, Continuous-time switched system, Interval observers, Linear matrix inequalities, Linear systems, Lyapunov functions, L∞ technique, matrix, Set-membership estimation, State estimation, Switched linear system, Switched system, Unknown but bounded @conference{Ethabet2023b,In this work, we focuses on the problem of designing an interval state estimation for continuous-time Switched Linear Systems (SLS) in the Unknown But Bounded Error (UBBE) context. To do so, we design a new structure of interval observers by introducing weighted matrices not only to give more degrees of design freedom but also to attenuate the conservatism caused by uncertainties. Observer gains are derived from the solution of Linear Matrix Inequalities (LMIs), based on the use of a common Lyapunov function, to ensure cooperativity and stability. An L∞ technique is then introduced to compensate the measurement noise and disturbances’ effects and to enhance the precision of interval estimation. Finally, numerical simulations are given, evaluating the proposed methodology and demonstrating its effectiveness. © 2023 IEEE. |
Aloui, Messaoud; Hamidi, Faical; Jerbi, Houssem; Aoun, Mohamed Estimating and enlarging the domain of attraction for polynomial systems using a deep learning tool Conférence 2023. Résumé | Liens | BibTeX | Étiquettes: Deep learning, Domain of attraction, Learning systems, Learning tool, Linear matrix inequalities, Linear polynomials, Lyapunov functions, Lyapunov’s functions, Neural networks, Non linear, Particle swarm, Particle swarm optimization, Particle swarm optimization (PSO), Polynomial systems, Polynomials, Swarm intelligence, Swarm optimization @conference{Aloui2023b,This Paper deals with the topic of non linear polynomial systems. It explains a way to estimate and enlarge the region of attraction of nonlinear polynomial systems. It provides a deep learning method for estimating the domain of attraction and uses the Particle Swarm Optimization Algorithm to enlarge this domain. Based on an analytic method found in literature, a dataset is generated, used then to train an artificial neural network, which will be an objective function of an optimization algorithm. This method dives an imitation to a previous complicated method, with less complexity and les elapsed time. The benchmark examples show the efficiency of the method and compare results with those obtained with the one using linear matrix inequalities. © 2023 IEEE. |
Ethabet, Haifa; Dadi, Leila; Raissi, Tarek; Aoun, Mohamed L∞ Set-membership Estimation for Continuous-time Switched Linear Systems Conférence 2023. Résumé | Liens | BibTeX | Étiquettes: Bounded error context, Continous time, Continuous time systems, Continuous-time switched system, Interval observers, Linear matrix inequalities, Linear systems, Lyapunov functions, L∞ technique, matrix, Set-membership estimation, State estimation, Switched linear system, Switched system, Unknown but bounded @conference{Ethabet2023,In this work, we focuses on the problem of designing an interval state estimation for continuous-time Switched Linear Systems (SLS) in the Unknown But Bounded Error (UBBE) context. To do so, we design a new structure of interval observers by introducing weighted matrices not only to give more degrees of design freedom but also to attenuate the conservatism caused by uncertainties. Observer gains are derived from the solution of Linear Matrix Inequalities (LMIs), based on the use of a common Lyapunov function, to ensure cooperativity and stability. An L∞ technique is then introduced to compensate the measurement noise and disturbances’ effects and to enhance the precision of interval estimation. Finally, numerical simulations are given, evaluating the proposed methodology and demonstrating its effectiveness. © 2023 IEEE. |
Aloui, Messaoud; Hamidi, Faical; Jerbi, Houssem; Aoun, Mohamed Estimating and enlarging the domain of attraction for polynomial systems using a deep learning tool Conférence 2023. Résumé | Liens | BibTeX | Étiquettes: Deep learning, Domain of attraction, Learning systems, Learning tool, Linear matrix inequalities, Linear polynomials, Lyapunov functions, Lyapunov’s functions, Neural networks, Non linear, Particle swarm, Particle swarm optimization, Particle swarm optimization (PSO), Polynomial systems, Polynomials, Swarm intelligence, Swarm optimization @conference{Aloui2023,This Paper deals with the topic of non linear polynomial systems. It explains a way to estimate and enlarge the region of attraction of nonlinear polynomial systems. It provides a deep learning method for estimating the domain of attraction and uses the Particle Swarm Optimization Algorithm to enlarge this domain. Based on an analytic method found in literature, a dataset is generated, used then to train an artificial neural network, which will be an objective function of an optimization algorithm. This method dives an imitation to a previous complicated method, with less complexity and les elapsed time. The benchmark examples show the efficiency of the method and compare results with those obtained with the one using linear matrix inequalities. © 2023 IEEE. |
2022 |
Jerbi, Houssem; Dabbagui, Boudour; Hamidi, Faical; Aoun, Mohamad; Bouazzi, Yassine; Aoun, Sondess Ben Computing the Domain of Attraction using Numerical Techniques Conférence 2022, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Asymptotically stable equilibrium, Basins of attraction, Carleman linearization, Domain of attraction, Iterative methods, Linearization, Lyapunov functions, Lyapunov’s functions, Lypaunov functions, MATLAB, Non-linear modelling, Nonlinear systems, Numerical methods, Numerical techniques, Quadratic lyapunov function, Stability analyze, System stability @conference{Jerbi2022b,Stability analysis of controlled nonlinear systems is a problem of fundamental importance in system engineering. This paper elaborates an explicit numerical technique to maximize a quadratic Lyapunov function for the class of polynomial nonlinear models. Using the computed Lyapunov function an enlarged subsets of the basin of attraction of an asymptotically stable equilibrium can be computed in an iterative analytical way. We mainly use the Carleman linearization technique that converts a nonlinear autonomous system of finite dimension into an equivalent linear infinite dimension one. We implement the sampling technique as a numerical tool allowing the maximization of estimated regions of attraction. An example is given to demonstrate the efficiency of the proposed approach. The numerical study analysis of the designed scheme is led using the Matlab software environment. © 2022 IEEE. |
Jerbi, Houssem; Dabbagui, Boudour; Hamidi, Faical; Aoun, Mohamad; Bouazzi, Yassine; Aoun, Sondess Ben Computing the Domain of Attraction using Numerical Techniques Conférence 2022, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Asymptotically stable equilibrium, Basins of attraction, Carleman linearization, Domain of attraction, Iterative methods, Linearization, Lyapunov functions, Lyapunov’s functions, Lypaunov functions, MATLAB, Non-linear modelling, Nonlinear systems, Numerical methods, Numerical techniques, Quadratic lyapunov function, Stability analyze, System stability @conference{Jerbi2022,Stability analysis of controlled nonlinear systems is a problem of fundamental importance in system engineering. This paper elaborates an explicit numerical technique to maximize a quadratic Lyapunov function for the class of polynomial nonlinear models. Using the computed Lyapunov function an enlarged subsets of the basin of attraction of an asymptotically stable equilibrium can be computed in an iterative analytical way. We mainly use the Carleman linearization technique that converts a nonlinear autonomous system of finite dimension into an equivalent linear infinite dimension one. We implement the sampling technique as a numerical tool allowing the maximization of estimated regions of attraction. An example is given to demonstrate the efficiency of the proposed approach. The numerical study analysis of the designed scheme is led using the Matlab software environment. © 2022 IEEE. |
2019 |
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. |
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. |
Publications
2023 |
L∞ Set-membership Estimation for Continuous-time Switched Linear Systems Conférence 2023. |
Estimating and enlarging the domain of attraction for polynomial systems using a deep learning tool Conférence 2023. |
L∞ Set-membership Estimation for Continuous-time Switched Linear Systems Conférence 2023. |
Estimating and enlarging the domain of attraction for polynomial systems using a deep learning tool Conférence 2023. |
2022 |
Computing the Domain of Attraction using Numerical Techniques Conférence 2022, (Cited by: 0). |
Computing the Domain of Attraction using Numerical Techniques Conférence 2022, (Cited by: 0). |
2019 |
Fault estimation using adaptive observer-based technique for time delay fractional-order systems Conférence 2019, (Cited by: 0). |
Fault estimation using adaptive observer-based technique for time delay fractional-order systems Conférence 2019, (Cited by: 0). |