A hybrid particle swarm optimization and vector fitting based identification algorithm in a time-delayed systems

An exact knowledge of delay is crucial to control and synchronize a time-delayed system. In this paper, a least square based so-called Vector Fitting method is developed to identify parameters of a time-delayed system. The Vector Fitting (V.F.) algorithm efficiently directs evolution of parameters of a model towards their optimal values, iteratively. During each iteration poles of the model are calculated and replaced as starting poles for the next generation. The proposed algorithm is then combined with a heuristic optimization method, i.e. Particle Swarm Optimization (PSO) to provide a hybrid technique, leading to identify delay time (r) of the system. The hybrid algorithm works in two stages; primarily the delay parameter is estimated using particle swarm optimization. The Vector fitting algorithm identifies the remaining parameters in the second stage. These two stages will be performed iteratively until the termination criterion is reached. Illustrative cases especially in presence of white noisy data are given to show the validity and the significance of the proposed method.