Stability analysis of a T-S fuzzy stochastic PSO model

Many theoretical and experimental results have appeared recently on the stability of T-S fuzzy systems and the convergence of the Particle Swarm Optimization (PSO) algorithm. In this paper, we present a T-S fuzzy stochastic PSO model in which the PSO algorithm is viewed as a time-invariant linear plant with a time-varying feedback controller that is embedded in the T-S fuzzy state system. The randomly weighted sum of the cognition component and social component is used as the state feedback controller in the local linear state system, and the PSO algorithm is theoretically improved from one that performs single stochastic optimization to one that performs fuzzy stochastic optimization. Conditions for asymptotic stability of the new model are given using the T-S fuzzy stability theory.