Parameter selection of a Particle Swarm Optimisation dynamics by closed loop stability analysis

Abstract

The paper addresses the issues of parameter selection of a Particle Swarm Optimisation (PSO) algorithm by a thorough stability analysis of the swarm dynamics. The effectiveness of the work lies in considering the dynamic behaviour of the local best position of a given particle. The behaviour of an individual particle here is modelled as a closed loop control system, where the forward path describes the particle dynamics, and the feedback path adapts the local best position of the particle over the iterations of the algorithm. The stability analysis of the closed loop system is undertaken using Jury's test, and optimal parameter setting of the dynamics is performed by the root locus technique of the classical control theory.