Stability, Convergence of Harmonious Particle Swarm Optimizer and Its Application

Particle swarm optimizer (PSO), a new evolutionary computation algorithm, exhibits good performance for optimization problems, although PSO can not guarantee convergence of a global minimum, even a local minimum. However, there are some adjustable parameters and restrictive conditions which can affect performance of the algorithm. The sufficient conditions for asymptotic stability of an acceleration factor and inertia weight are deduced in this paper. The value of the inertia weight w is enhanced to (-1,1). Furthermore a new adaptive PSO algorithm-harmonious PSO (HPSO) is proposed and proved that HPSO is a global search algorithm. Finally it is focused on a design task of a servo system controller. Considering the existence of model uncertainty and noise from sensors, HPSO are applied to optimize the parameters of fuzzy PID controller. The experiment results demonstrate the efficiency of the methods.