A closed loop stability analysis for the Particle Swarm Optimization dynamics

The 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 model of the nonlinear 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, we in this paper consider their separate existence to determine 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 are also confirmed by computer simulation of the PSO algorithm.