A closed loop stability analysis and parameter selection of the Particle Swarm Optimization dynamics for faster convergence

This paper presents an alternative formulation of the PSO dynamics by a closed loop control system, and analyzes the stability behavior of the system by using Jury´s test and root locus technique. Previous stability analysis of the PSO dynamics was restricted because of no explicit modeling of the non-linear element in the feedback path. In the present analysis, the nonlinear element model of the non-linear element is considered for closed loop stability analysis. Unlike the previous works on stability analysis, where the acceleration coefficients have been combined into a single term, this paper considered their separate existence for determining their suitable range to ensure stability of the dynamics. The range of parameters of the PSO dynamics, obtained by Jury´s test and root locus technique were also confirmed by computer simulation of the PSO algorithm.