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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.
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Keywords:
- Lorenz chaotic system /
- parameter estimation /
- hybrid crossover /
- evolution algorithm
[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 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 51 2459]
[9] Gao F, Tong H Q 2006 Acta Phys. Sin. 55 577 (in Chinese) [高飞, 童恒庆 2006 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 56 51]
[11] Wang J Y, Huang D X 2008 Acta Phys. Sin. 57 2755 (in Chinese) [王钧炎, 黄德先 2008 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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[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 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 51 2459]
[9] Gao F, Tong H Q 2006 Acta Phys. Sin. 55 577 (in Chinese) [高飞, 童恒庆 2006 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 56 51]
[11] Wang J Y, Huang D X 2008 Acta Phys. Sin. 57 2755 (in Chinese) [王钧炎, 黄德先 2008 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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