Improved Oustaloup approximation of fractional-order operators using adaptive chaotic particle swarm optimization

A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning frequency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization (PSO). The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.