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提出一种混合交叉进化算法 来估计混沌系统的未知参数. 首先通过构造一个适当的适应度函数, 将混沌系统的参数估计问题转化为一个多维的优化问题. 在混合交叉进化算法中, 利用佳点集方法初始化种群, 增加了算法的稳定性和全局搜索能力. 在进化过程中, 混合交叉操作既能指导种群个体向最优解子空间靠近, 又能提高算法跳出局部最优的能力, 从而协调了算法的勘探和开采能力. 以几个标准测试函数和典型的Lorenz混沌系统为例进行仿真实验, 结果表明了该方法的有效性.
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关键词:
- Lorenz混沌系统 /
- 参数估计 /
- 混合交叉 /
- 进化算法
A hybrid-crossover-based evolution algorithm is proposed to estimate the parameters of chaotic system. Through establishing an appropriate fitness function, the parameter estimation problem is coverted into a multi-dimensional functional optimization problem. In this approach, the individual generation based on good-point-set method is introduced into the evolutionary algorithm initial step, which reinforces the stability and global exploration ability of the evolutionary algorithm. In the evolution process, it not only can be explored to induce the new individuals generated by stochastic hybrid crossover operation to fly into the better subspace, but also can avoid the premature convergence and speed up the convergence. It coordinates the exploitation ability and the exploration ability of algorithm. Numerical simulations on the benchmark function and the Lorenz system are conducted. The results demonstrate the effectiveness of the proposed algorithm, which is shown to be an effective method of parameter estimation for chaotic systems.-
Keywords:
- Lorenz chaotic system /
- parameter estimation /
- hybrid crossover /
- evolution algorithm
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[16] Kusum D, Manoj T 2007 Appl. Math. Comput. 188 895
[17] Liang X M, Xiao W, Long W, Qin H Y 2010 J. Comput. Appl. 30 2582 (in Chinese) [梁昔明, 肖伟, 龙文, 秦浩宇 2010 计算机应用 30 2582]
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[1] Park J H 2005 Chaos Soliton. Fract. 23 503
[2] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[3] Duchateau A, Bradshawn P, Beraini H 1999 Int. J. Control 72 727
[4] Maybhate A, Amritkar R E 1999 Phys. Rev. E 59 284
[5] Parlitz U 1996 Phys. Rev. Lett. 76 1232
[6] Cao X Q, Song J Q, Zhang W M, Zhao J, Zhang L L 2011 Acta Phys.Sin. 60 070511 (in Chinese) [曹小群, 宋君强, 张卫民, 赵军, 张理论 2011 物理学报 60 070511]
[7] Wang S M, Yue C Y, Luo H G 2007 J. Huazhong Univ. Sci. Technol. 35 121 (in Chinese) [王绍明, 岳超源, 罗海庚 2007 华中科技大学学报 35 121]
[8] Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 物理学报 51 2459]
[9] Gao F, Tong H Q 2006 Acta Phys. Sin. 55 577 (in Chinese) [高飞, 童恒庆 2006 物理学报 55 577]
[10] Li L X, Peng H P, Yang Y X, Wang X D 2007 Acta Phys. Sin. 56 51 (in Chinese) [李丽香, 彭海朋, 杨义先, 王向东 2007 物理学报 56 51]
[11] Wang J Y, Huang D X 2008 Acta Phys. Sin. 57 2755 (in Chinese) [王钧炎, 黄德先 2008 物理学报 57 2755]
[12] Ren Z W, Xiong R 2010 Control Theory Appl. 27 1448 (in Chinese) [任子武, 熊蓉 2010 控制理论与应用 27 1448]
[13] Leung Y W, Wang Y P 2000 IEEE Trans. Evolu. Comp. 4 41
[14] Zhang L, Zhang B 2001 Chin. J. Comput. 24 917 (in Chinese) [张铃, 张钹 2001 计算机学报 24 917]
[15] Gen M, Cheng R W 1997 Genetic Algorithm+Data Structure = Evolutionary Programs (New York: John Wiley and Sons Press) p29
[16] Kusum D, Manoj T 2007 Appl. Math. Comput. 188 895
[17] Liang X M, Xiao W, Long W, Qin H Y 2010 J. Comput. Appl. 30 2582 (in Chinese) [梁昔明, 肖伟, 龙文, 秦浩宇 2010 计算机应用 30 2582]
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