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Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems

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Laboratory Modélisation, Analyse et Commande des Systèmes, University of Gabes, Gabes LR16ES22, Tunisia
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Department of Industrial Engineering, College of Engineering, University of Ha’il, Hail 1234, Saudi Arabia
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Department of Electrical Engineering, College of Engineering, University of Ha’il, Hail 1234, Saudi Arabia
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Faculty of Automatics and Computers, University Politehnica of Bucharest, RO-060042 Bucharest, Romania
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Department of Computer Engineering, College of Computer Science and Engineering, University of Ha’il, Hail 1234, Saudi Arabia
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Author to whom correspondence should be addressed.
Electronics 2020, 9(10), 1704; https://doi.org/10.3390/electronics9101704
Received: 8 September 2020 / Revised: 7 October 2020 / Accepted: 11 October 2020 / Published: 16 October 2020
(This article belongs to the Special Issue Control of Nonlinear Systems and Industrial Processes)
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. View Full-Text
Keywords: domain of attraction; polynomial system; chaotic particular swarm optimisation; LMI domain of attraction; polynomial system; chaotic particular swarm optimisation; LMI
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Hamidi, F.; Aloui, M.; Jerbi, H.; Kchaou, M.; Abbassi, R.; Popescu, D.; Ben Aoun, S.; Dimon, C. Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems. Electronics 2020, 9, 1704.

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