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. |
2002 |
Aoun, Mohamed; Malti, Rachid; Cois, Olivier; Oustaloup, Alain System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). Résumé | Liens | BibTeX | Étiquettes: 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 @conference{Aoun2002265b,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). Résumé | Liens | BibTeX | Étiquettes: 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 @conference{Aoun2002265,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. |
Publications
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). |
2002 |
System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). |
System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). |