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

Faiçal Hamidi, Houssem Jerbi, Hadeel Alharbi, Víctor Leiva, Dumitru Popescu, Wajdi Rajhi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number78
JournalFractal and Fractional
Volume7
Issue number1
DOIs
StatePublished - Jan 2023

Keywords

  • Jaya algorithm
  • Lyapunov theory
  • fractional differential equations
  • fractional systems
  • heuristic algorithms
  • linear matrix inequalities
  • nonlinear systems
  • optimization methods
  • stability

Fingerprint

Dive into the research topics of 'Metaheuristic Solution for Stability Analysis of Nonlinear Systems Using an Intelligent Algorithm with Potential Applications'. Together they form a unique fingerprint.

Cite this