Differential Evolution Quantum Particle Swarm Optimization for Parameter Estimation of Fractional-order Chaotic System

doi:10.16182/j.issn1004731x.joss.17-0265

Abstract

Abstract: In order to accurately estimate the unknown parameters for fractional order chaotic systems, a quantum particle swarm optimization algorithm based on differential quantum properties is proposed. On the basis of quantum behaved particle swarm optimization, variation, crossover and selection operation are utilized by particles, which can better keep the diversity of the particles in the population, avoiding the local optimum in the later phase of the iteration. The multi-neighborhood local search strategy is used for particles’ local search to improve search precision. Standard test functions are used to test the algorithm, and the test results show that the algorithm has good global search capability. At last, the proposed algorithm is applied in the parameter estimation for fractional-order Lorenz system and fractional-order Chen system, and the estimation results demonstrate that the algorithm is effective and robust.

Key words: fractional-order chaotic systems, parameter estimation, quantum particle swarm optimization, differential evolution, multi-neighborhood search

CLC Number:

TP273

Dong Ze, Ma Ning. Differential Evolution Quantum Particle Swarm Optimization for Parameter Estimation of Fractional-order Chaotic System[J]. Journal of System Simulation, 2019, 31(8): 1664-1673.

References

[1] 黄宇, 王佳荣, 梁伟平. 求解分数阶混沌系统参数估计问题的和声引力搜索算法[J]. 系统仿真学报, 2016, 28(5): 1045-1053.
Huang Yu, Wang Jiarong, Liang Weiping.Harmony Gravitational Search Algorithm for Solving the Problem of Parameter Estimation for Fractional-order Chaotic Systems[J]. Journal of System Simulation, 2016, 28(5), 1045-1053.
[2] Gandomi A H, Yun G J, Yang X S, et al.Chaos-enhanced accelerated particle swarm optimization[J]. Communications in Nonlinear Science and Numerical Simulation (S1007-5704), 2013, 18(2): 327-340.
[3] 黄丽莲, 辛方, 王霖郁. 新分数阶混沌系统的异结构同步及其电路仿真[J]. 系统仿真学报, 2012, 24(7): 1479-1484.
Huang Lilian, Xin Fang, Wang Linyu.Circuit Simulation and Synchronization of New Fractional-order Chaotic System[J]. Journal of System Simulation, 2012, 24(7): 1479-1484.
[4] Gu W, Yu Y, Hu W.Parameter estimation of unknow fractional-order memristor-based chaotic systems by a hybrid artificial bee colony algorithm combined with differential evolution[J]. Nonliner Dynamics (S0924-090X), 2016, 84(2) 779-795.
[5] Gao F, Teng L, Cao W, et al.Self-evolution of hyper fractional order chaos driven by a novel approach through genetic programming[J]. Expert Systems with Application (S0957-4174), 2016, 84: 1-15.
[6] Liu F, Li X, Liu X, et al Parameter identification of fractionai-order chaotic system with time delay via multi-selection differential evolution[J]. Systems Science& Control Engineering (S2164-2583), 2017, 5(1): 42-48.
[7] Wei D, Miao Q Y, Tong L, et al.Identification of fractional-order systems with unknow initial values and structure[J]. Physics Letters A (S0375-9601), 2017, 381(23): 1943-1949.
[8] 王柳, 何文平, 万仕全, 等. 混沌系统中参数估计的演化建模方法[J]. 物理学报, 2014, 63(1): 109203.
Wang Liu, He Wenping, Wan Shiquan, et al.Evolutionary modeling for parameter estimation for chaotic system[J]. Acta Physica Sinica, 2014, 63(1): 109203.
[9] Shirin P, Sajad J, Pham V T, et al.Parameter Identification of a Chaotic Circuit with a Hidden Attractor Using Krill Herd Optimization[J]. International Journal of Bifurcation and Chaos (S0218-1274), 2016, 26: 1650221.
[10] 任开军, 邓科峰, 宋少伟, 等. 自适应人工蜂群优化的混沌系统参数估计[J]. 国防科技大学学报, 2015, 37(5): 135-140.
Ren Kaijun, Deng Kefeng, Song Shaowei, et al.Adaptive artificial bee colony optimization for parameter estimation of chaotic systems[J]. Journal of National University of Defense Technology, 2015, 37(5): 135-140.
[11] 胡文斌, 王欢, 严丽平, 等. 混合指标量子群智能社会网络事件检测方法[J]. 软件学报, 2016, 27(11): 2747-2762.
Hu Wenbin, Wang Huan, Yan Liping, et al.Hybrid Quantum Swarm Intelligence Indexing for Event Detection in Social Networks[J]. Journal of Software, 2016, 27(11): 2747-2762.
[12] Xie X, Jiang W, He N, et al.Empirical Study on How to Set Prices for Cruise Cabins Based on Improved Quantum Partice Swarm Optimization[J]. Computer and Information Science (S1820-0214), 2016, 9(2): 82-90.
[13] He Z, Qi H, Chen Q, et al.Retrieval of aerosol size distribution using improved quantum-behaved particle swarm optimization on spectral extinction measurements[J]. Particuology (S1674-2001), 2016, 28: 6-14.
[14] 王凌, 钱斌. 混合差分进化与调度算法[M]. 北京: 清华大学出版社, 2012.
Wang Ling, Qian Bin.Hybrid differential evolution and scheduling algorithm[M]. Beijing: Tsinghua University Press, 2012.
[15] Sun J, Fang B, Wu X.Particle swarm optimization algorithm with particles having quantum behavior[C]. Proceedings of Congress Evolutionary Computation, IEEE Press, Portland, USA, 2004: 325-331.
[16] Sun J, Fang W, Wu X.Quantum-behaved particle swarm optimization: analysis of the individual particle's behavior and parameter selection[J]. Evolutionary Computation (S1530-9304), 2012, 20(3): 349-393.
[17] Nickabadi A, Ebadzadeh M, Safabakhsh R.A novel particle swarm optimization algorithm with adaptive inertia weight[J]. Applied Soft Computing (S1568-4946), 2011, 11(4): 3658-3670.
[18] Tian N, Lai C, Pericleous K.Contraction-expansion coefficient learning in quantum-behaved particle swarm optimization [C]. 10th International Symposium on Distributed and Applications to Business, Engineering and Science, Wuxi, China. USA: IEEE Press, 2011: 304-308.
[19] Price K, Storn R M, Lampinen J A.Differential evolution: A practical approach to global optimization[M]. Germany: Springer Verlag, 2005.
[20] 徐遥, 王士同. 引力搜索算法的改进[J]. 计算机工程与应用, 2012, 47(35): 188-192.
Xu Yao, Wang Shitong.Enhanced version of gravitational search algorithm: weighted GSA[J]. Computer Engineering and Applications, 2012, 47(35): 188-192.
[21] Rashedi E, Nezamabadi-Pour H, Saryazdi S.GSA: a gravitational search algorithm[J]. Information Science (S0020-0255), 2009, 179(13): 2232-2248.
[22] 黄宇, 刘玉峰, 彭志敏, 等. 基于量子并行粒子群优化算法的分数阶混沌系统参数估计[J]. 物理学报, 2015, 64(3): 030505.
Huang Yu, Liu Yunfeng, Peng Zhimin, et al.Research on particle swarm optimization algorithm with characteristic of quantum parallel and its application inparameter estimation for fractional-order chaotic systems[J]. Acta Physica Sinica, 2015, 64(3): 030505.
[23] Yuan L, Yang Q.Parameter identification and synchronization of fractional-order chaotic systems[J]. Communications in Nonlinear Science and Numerical Simulation (S1007-5704), 2012, 17: 305-316.