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

作　　者：Zhe Gao Xiaozhong Liao 

机构地区：[1]School of Automation, Beijing Institute of Technology, Beijing 100081, P. R. China

出　　处：《Journal of Systems Engineering and Electronics》2012年第1期145-153,共9页系统工程与电子技术（英文版）

基　　金：supported by the National Natural Science Foundation of China (10872030)

摘　　要：A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency 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.A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency 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.

关 键 词：fractional-order calculus rational approximation particle swarm optimization （PSO） tent map. 

分 类 号：O37[理学—流体力学] TP18[理学—力学]