Metaheuristic Solution for Stability Analysis of Nonlinear Systems Using an Intelligent Algorithm with Potential Applications

被引:8
|
作者
Hamidi, Faical [1 ]
Jerbi, Houssem [2 ]
Alharbi, Hadeel [3 ]
Leiva, Victor [4 ]
Popescu, Dumitru [5 ]
Rajhi, Wajdi [6 ]
机构
[1] Univ Gabes, Lab Modelisat Anal & Commande Syst, Gabes LR16ES22, Gabes, Tunisia
[2] Univ Hail, Coll Engn, Dept Ind Engn, Hail 2440, Saudi Arabia
[3] Univ Hail, Coll Comp Sci & Engn, Dept Informat & Comp Sci, Hail 2440, Saudi Arabia
[4] Pontificia Univ Catolica Valparaiso, Sch Ind Engn, Valparaiso 2362807, Chile
[5] Univ Politehn Bucuresti, Fac Automatic Control & Comp Sci, RO-060042 Bucharest, Romania
[6] Univ Hail, Coll Engn, Dept Mech Engn, Hail, Saudi Arabia
关键词
fractional differential equations; fractional systems; heuristic algorithms; Jaya algorithm; linear matrix inequalities; Lyapunov theory; nonlinear systems; optimization methods; stability; LYAPUNOV FUNCTIONS; EPIDEMIC MODEL; ATTRACTION; DOMAIN; STABILIZATION; OPTIMIZATION; DYNAMICS; SUBJECT; DESIGN; SOS;
D O I
10.3390/fractalfract7010078
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this article, we provide a metaheuristic-based solution for stability analysis of nonlinear systems. We identify the optimal level set in the state space of these systems by combining two optimization phases. This set is in a definite negative region of the time derivative for a polynomial Lyapunov function (LF). Then, we consider a global optimization problem stated in two phases. The first phase is an external optimization to search for a definite positive LF, whose derivative is definite negative under linear matrix inequalities. The candidate LF coefficients are adjusted using a Jaya metaheuristic optimization algorithm. The second phase is an internal optimization to ensure an accurate estimate of the attraction region for each candidate LF that is optimized externally. The key idea of the algorithm is based mainly on a Jaya optimization, which provides an efficient way to characterize accurately the volume and shape of the maximal attraction domains. We conduct numerical experiments to validate the proposed approach. Two potential real-world applications are proposed.
引用
收藏
页数:25
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