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

Abstract

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.