Harmony Gravitational Search Algorithm for Solving the Problem of Parameter Estimation for Fractional-order Chaotic Systems

Abstract

Abstract: Aiming at parameter estimation for fractional-order chaotic systems, a harmony gravitational search algorithm was proposed. The particles, which were updated by gravitational search algorithm, were recreated and searched through memory selections and probability search in harmony search algorithm. At the same times, in order to solve the problem that the speed changed too fast when the particles closed to the optimal solution, the partial adjustment probability was set to non-linearly decrease with the adsorption capacity increasing. Standard test functions were used to test the algorithm, and the test results show that the algorithm has good stability and global search capability. At last, the harmony gravitational search algorithm is applied in the parameter estimation for fractional-order Rӧssler system and fractional-order Lorenz system, and the estimation results show that the algorithm is effective and robust.

Key words: fractional-order chaotic systems, parameter estimation, gravitational search algorithm, harmony search

CLC Number:

TP273

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.

References

[1] 李安平, 刘国荣, 沈细群. 不确定混沌系统用分数阶系统同步与参数辨识[J]. 计算机仿真, 2012, 29(9): 191-194.
[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.
[4] 孙克辉, 杨静利, 丘水生. 分数阶混沌系统的仿真方法研究[J]. 系统仿真学报, 2011, 23(11): 2361-2365.
[5] Li C, Zhou J, Xiao J, et al.Parameters identification of chaotic system by chaotic gravitational search algorithm[J]. Chaos, Solitons & Fractals (S0960-0779), 2012, 45(4): 539-547.
[6] 张宏立, 宋莉莉. 基于量子粒子群算法的混沌系统参数辨识[J]. 物理学报, 2013, 19(62): 106-111.
[7] 李丽香, 彭海朋, 杨义先, 等. 基于混沌蚂蚁群算法的Lorenz混沌系统的参数估计[J]. 物理学报, 2007, 56(1): 51-55.
[8] 曹小群, 宋君强, 张卫民, 等. 基于变分方法的混沌系统参数估计[J]. 物理学报, 2011, 60(7): 129-136.
[9] Li X T, Yin M H.Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method[J]. Chinese Physics B (S1674-1056), 2012, 21(5): 0505071-050576.
[10] Yuan L G, Yang Q G.Parameter identification and synchronization of fractional-order chaotic systems[J]. Communications in Nonlinear Science and Numerical Simulation (S1007-5704), 2012, 17(1): 305-316.
[11] Zhu W, Fang J-a, Tang Y, et al.Identification of fractional-order systems via a switching differential evolution subject to noise perturbations[J]. Phy sics Letters A (S0375-9601) , 2012, 376(45): 3113-3120.
[22] Rashedi E, Nezamabadi-Pour H, Saryazdi S.GSA: a gravitational search algorithm[J]. Information Sciences (S0020-0255), 2009, 179(2009): 2232-2248.
[13] Mondal S, Bhattacharya A, Nee Dey S H. Multi-objective economic emission load dispatch solution using gravitational search algorithm and considering wind power penetration[J]. Inte rnational Journal of Electrical Power & Energy Systems (S0142-0615), 2013, 44(1): 282-292.
[14] Pal K, Saha C, Das S, et al.Dynamic constrained optimization with offspring repair based gravitational search algorithm[C]// Evolutionary Computation (CEC), 2013 IEEE Congress on. USA: IEEE, 2013: 2414-2421.
[15] Duman S, Maden D, Guvenc U. Determination of the PID controller parameters for speed and position control of DC motor using gravitational search algorithm [C]// Electrical and Electronics Engineering (ELECO), 2011 7th International Conference on. USA: IEEE, 2011: I-225-I-229
[16] 戢钢, 王景成, 葛阳, 等. 城市小时级需水量的改进型引力搜索算法-最小二乘支持向量机模型预测[J]. 控制理论与应用, 2014, 31(10): 1377-1382.
[17] Geem Z W.Improved harmony search from ensemble of music players[C]// Knowledge-Based Intelligent Information and Engineering Systems. Germany: Springer, Berlin Heidelberg, 2006: 86-93.
[18] 任子武, 王振华, 孙立宁. 全局和声搜索方法及其在仿人灵巧臂逆运动学求解中的应用[J]. 控制理论与应用, 2012, 29(7): 867-876.
[19] 李若平, 欧阳海滨, 高立群, 等. 学习型和声搜索算法及其在0-1背包问题中的应用[J]. 控制与决策, 2013, 28(2): 205-210.
[20] 欧阳海滨, 高立群, 邹德旋, 等. 和声搜索算法探索能力研究及其修正[J]. 控制理论与应用, 2014, 31(1): 57-65.
[21] 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.
[22] 林剑, 许力. 基于混合生物地理优化的混沌系统参数估计[J]. 物理学报, 2013, 62(3): 0305051-0305057.
[23] Li C, Yan J.The synchronization of three fractional differential systems[J]. Chaos, Solitons & Fractals (S0960-0779), 2007, 32(2): 751-757.

[1]	Xu Shanling, Li Junhong, Liu Mengru, Hua Liang. Chaotic Gravitational Search Iterative Identification for Wiener Systems [J]. Journal of System Simulation, 2021, 33(9): 2138-2146.
[2]	He Yitao, Li Jun, Hao Liyan. Bacterial Foraging Algorithm with Gravitational Mechanism [J]. Journal of System Simulation, 2020, 32(9): 1724-1735.
[3]	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.
[4]	Jiang Li, Zhou Junni, Yang Runling, Liu Li. Parameter Estimation of LFMCW Signals Based on Improved SM Method [J]. Journal of System Simulation, 2018, 30(9): 3283-3287.
[5]	Ge Chenglong, Zhu Yuanchang, Di Yanqiang, Hu Zhiwei, Dong Zhihua. Equipment RUL Prediction Oriented Parallel Simulation Framework [J]. Journal of System Simulation, 2018, 30(6): 2216-2224.
[6]	Wang Yan, Wu Longcheng, Ji Zhicheng, Yan Dahu. Multi-Objective Vulcanization Workshop Scheduling Based on Improved Harmony Search Algorithm [J]. Journal of System Simulation, 2018, 30(1): 139-146.
[7]	Wu Longcheng, Huang Song, Wang Yan, Ji Zhicheng. Improved Harmony Search Algorithm in Application of Vulcanization Workshop Scheduling [J]. Journal of System Simulation, 2017, 29(3): 630-638.
[8]	Ge Yanfeng, Liang Peng, Gao Liqun, Zhai Junchang. Sliding Weighted Least Square Model for Short-term Wind Power Prediction [J]. Journal of System Simulation, 2016, 28(5): 1031-1037.
[9]	Luo Wenmao, Cui Yingliu. Novel Algorithm of High-Speed Target ISAR Imaging Based on Stretch Method [J]. Journal of System Simulation, 2016, 28(4): 851-858.
[10]	Liang Weiping, Wang Jiarong. Mixed H₂/H_∞ Optimal PID Control for Superheated Steam Temperature System [J]. Journal of System Simulation, 2016, 28(3): 661-667.
[11]	Sun Xinxin, Wang Xingwei, Huang Min. Adaptive Harmony PSO Based Trusted QoS Routing Scheme [J]. Journal of System Simulation, 2016, 28(3): 741-748.
[12]	Huang Yu, Wang Jiarong. Optimized Linear Active Disturbance Rejection Controller Design for Hydraulic Turbine Governing Systems [J]. Journal of System Simulation, 2016, 28(12): 3033-3040.