Stability Analysis of the Particle Dynamics in
Visakan Kadirkamanathan, Kirusnapillai Selvarajah, Peter John Fleming · 2006
Previous stability analysis of the particle swarm opti- mizer was restricted to the assumption that all parameters are non- random, in effect a deterministic particle swarm optimizer. We an- alyze the stability of the particle dynamics without this restrictive assumption using Lyapunov stability analysis and the concept of passive systems. Sufficient conditions for stability are derived, and an illustrative example is given. Simulation results confirm the pre- diction from theory that stability of the particle dynamics requires increasing the maximum value of the random parameter when the inertia factor is reduced. Index Terms—Absolute stability, circle criterion, Lyapunov sta- bility, particle swarm optimization (PSO), stability analysis.