Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems
A novel technique for estimating the asymptotic stability region of nonlinear autonomous polynomial systems is established. The key idea consists of examining the optimal Lyapunov function (LF) level set that is fully included in a region satisfying the negative definiteness of its time derivative....
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/9/10/1704 |
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| author | Faiçal Hamidi Messaoud Aloui Houssem Jerbi Mourad Kchaou Rabeh Abbassi Dumitru Popescu Sondess Ben Aoun Catalin Dimon |
| author_facet | Faiçal Hamidi Messaoud Aloui Houssem Jerbi Mourad Kchaou Rabeh Abbassi Dumitru Popescu Sondess Ben Aoun Catalin Dimon |
| author_sort | Faiçal Hamidi |
| collection | DOAJ |
| description | A novel technique for estimating the asymptotic stability region of nonlinear autonomous polynomial systems is established. The key idea consists of examining the optimal Lyapunov function (LF) level set that is fully included in a region satisfying the negative definiteness of its time derivative. The minor bound of the biggest achievable region, denoted as Largest Estimation Domain of Attraction (LEDA), can be calculated through a Generalised Eigenvalue Problem (GEVP) as a quasi-convex Linear Inequality Matrix (LMI) optimising approach. An iterative procedure is developed to attain the optimal volume or attraction region. Furthermore, a Chaotic Particular Swarm Optimisation (CPSO) efficient technique is suggested to compute the LF coefficients. The implementation of the established scheme was performed using the Matlab software environment. The synthesised methodology is evaluated throughout several benchmark examples and assessed with other results of peer technique in the literature. |
| first_indexed | 2024-03-10T15:33:42Z |
| format | Article |
| id | doaj.art-a357c21cb1994d67b084cf299b461bdc |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T15:33:42Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-a357c21cb1994d67b084cf299b461bdc2023-11-20T17:27:05ZengMDPI AGElectronics2079-92922020-10-01910170410.3390/electronics9101704Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear SystemsFaiçal Hamidi0Messaoud Aloui1Houssem Jerbi2Mourad Kchaou3Rabeh Abbassi4Dumitru Popescu5Sondess Ben Aoun6Catalin Dimon7Laboratory Modélisation, Analyse et Commande des Systèmes, University of Gabes, Gabes LR16ES22, TunisiaLaboratory Modélisation, Analyse et Commande des Systèmes, University of Gabes, Gabes LR16ES22, TunisiaDepartment of Industrial Engineering, College of Engineering, University of Ha’il, Hail 1234, Saudi ArabiaDepartment of Electrical Engineering, College of Engineering, University of Ha’il, Hail 1234, Saudi ArabiaDepartment of Electrical Engineering, College of Engineering, University of Ha’il, Hail 1234, Saudi ArabiaFaculty of Automatics and Computers, University Politehnica of Bucharest, RO-060042 Bucharest, RomaniaDepartment of Computer Engineering, College of Computer Science and Engineering, University of Ha’il, Hail 1234, Saudi ArabiaFaculty of Automatics and Computers, University Politehnica of Bucharest, RO-060042 Bucharest, RomaniaA novel technique for estimating the asymptotic stability region of nonlinear autonomous polynomial systems is established. The key idea consists of examining the optimal Lyapunov function (LF) level set that is fully included in a region satisfying the negative definiteness of its time derivative. The minor bound of the biggest achievable region, denoted as Largest Estimation Domain of Attraction (LEDA), can be calculated through a Generalised Eigenvalue Problem (GEVP) as a quasi-convex Linear Inequality Matrix (LMI) optimising approach. An iterative procedure is developed to attain the optimal volume or attraction region. Furthermore, a Chaotic Particular Swarm Optimisation (CPSO) efficient technique is suggested to compute the LF coefficients. The implementation of the established scheme was performed using the Matlab software environment. The synthesised methodology is evaluated throughout several benchmark examples and assessed with other results of peer technique in the literature.https://www.mdpi.com/2079-9292/9/10/1704domain of attractionpolynomial systemchaotic particular swarm optimisationLMI |
| spellingShingle | Faiçal Hamidi Messaoud Aloui Houssem Jerbi Mourad Kchaou Rabeh Abbassi Dumitru Popescu Sondess Ben Aoun Catalin Dimon Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems Electronics domain of attraction polynomial system chaotic particular swarm optimisation LMI |
| title | Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems |
| title_full | Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems |
| title_fullStr | Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems |
| title_full_unstemmed | Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems |
| title_short | Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems |
| title_sort | chaotic particle swarm optimisation for enlarging the domain of attraction of polynomial nonlinear systems |
| topic | domain of attraction polynomial system chaotic particular swarm optimisation LMI |
| url | https://www.mdpi.com/2079-9292/9/10/1704 |
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