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Chin. Phys. B, 2013, Vol. 22(5): 050505    DOI: 10.1088/1674-1056/22/5/050505
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A new identification control for generalized Julia sets

Sun Jie (孙洁)a b, Liu Shu-Tang (刘树堂)a
a College of Control Science and Engineering, Shandong University, Jinan 250061, China;
b School of Mechanical, Electrical and Information Engineering, Shandong University at Weihai, Weihai 264209, China
Abstract  In this paper, we propose a new method to realize drive-response system synchronization control and parameter identification for a class of generalized Julia sets. By means of this method, the zero asymptotic sliding variables are applied to control the fractal identification. Furthermore, the problems of synchronization control are solved in the case of a drive system with unknown parameters, and the unknown parameters of the drive system can be identified in the asymptotic synchronization process. The results of simulation examples demonstrate the effectiveness of this new method. Particularly, the basic Julia set is also discussed.
Keywords:  Julia set      synchronization      parameter identification  
Received:  13 October 2012      Revised:  10 December 2012      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  
  47.53.+n (Fractals in fluid dynamics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61273088 and 11271194), the National Excellent Doctoral Dissertation of China (Grant No. 200444), and the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2010FM010 and ZR2011FQ035).
Corresponding Authors:  Sun Jie     E-mail:  sunj@sdu.edu.cn

Cite this article: 

Sun Jie (孙洁), Liu Shu-Tang (刘树堂) A new identification control for generalized Julia sets 2013 Chin. Phys. B 22 050505

[1] Mandelbrot B B 1977 Fractal: Form, Chance and Dimension (San Francisco: Freeman)
[2] Mandelbrot B B 1982 The Fractal Geometry of Nature (San Francisco: Freeman)
[3] Isvoran A, Pitulice L and Creascu C T 2008 Chaos Soliton. Fract. 35 960
[4] Mobahed M S and Hermanis E 2008 Physica A 387 915
[5] Wang L, Zheng D Z and Lin Q S 2001 Computing Technology and Automation 20 1
[6] Wang X Y, Xie Y X and Qin X 2012 Chin. Phys. B 21 040504
[7] Wang X Y and He G X 2012 Chin. Phys. B 21 060502
[8] Wang X Y and Wang M J 2008 Acta Phys. Sin. 57 731 (in Chinese)
[9] Wang X Y and Meng Q Y 2004 Acta Phys. Sin. 53 388 (in Chinese)
[10] Wang X Y, Liu W and Yu X J 2007 Modern Physics Letters B 21 1321
[11] Wang L and Zheng D Z 2000 Control Theory and Applications 17 139
[12] Rani M and Negi A 2008 Chaos Soliton. Fract. 36 226
[13] Gao J Y 2011 Chaos Soliton. Fract. 44 871
[14] Wang X Y and Sun Y Y 2007 Computers and Mathematics with Applications 53 1718
[15] Wang X Y and Shi Q J 2006 Applied Mathematics and Computation 181 816
[16] Wang X Y and Yu X J 2007 Applied Mathematics and Computation 189 1186
[17] Yang W F 2010 Applied Mathematics and Computation 217 2490
[18] Argyris J, Karakasidis T E and Andreadis I 2000 Chaos Solitons. Fract. 11 2067
[19] Zhang Y P, Liu S T and Shen S L 2009 Chaos Solitons. Fract. 39 1811
[20] Liu P and Liu S T 2011 Communications in Nonlinear Science and Numerical Simulation 16 3344
[21] Zhang Y P, Sun W H and Liu S T 2009 Chaos Solitons. Fract. 42 1738
[22] Furuta K 1990 Syst. Cont. Lett. 14 145
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