2023 |
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. |
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. |
2004 |
Malti, Rachid; Aoun, Mohamed; Oustaloup, Alain Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Differential equations, Dynamical systems, Extrapolation, Fractional calculus, Fractional derivatives, Generalized orthogonal basis (GOB), Identification (control systems), Laplace transforms, Linear control systems, Mathematical models, Model reduction, Orthogonal functions, Polynomials, Set theory, System stability, Transfer functions @conference{Malti2004835b,Fractional Kautz-like functions are synthesized extrapolating the definition of classical Kautz functions to fractional derivatives. The synthesized bases has two periodically repeating complex conjugate modes. The new basis extends the definition of the fractional Laguerre basis, by allowing the modes to be complex. An example is then provided in system identification context. |
Malti, Rachid; Aoun, Mohamed; Oustaloup, Alain Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Differential equations, Dynamical systems, Extrapolation, Fractional calculus, Fractional derivatives, Generalized orthogonal basis (GOB), Identification (control systems), Laplace transforms, Linear control systems, Mathematical models, Model reduction, Orthogonal functions, Polynomials, Set theory, System stability, Transfer functions @conference{Malti2004835,Fractional Kautz-like functions are synthesized extrapolating the definition of classical Kautz functions to fractional derivatives. The synthesized bases has two periodically repeating complex conjugate modes. The new basis extends the definition of the fractional Laguerre basis, by allowing the modes to be complex. An example is then provided in system identification context. |
Publications
2023 |
Estimating and enlarging the domain of attraction for polynomial systems using a deep learning tool Conférence 2023. |
Estimating and enlarging the domain of attraction for polynomial systems using a deep learning tool Conférence 2023. |
2004 |
Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). |
Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). |