广义Julia 集的参数辨识

孙洁; 刘树堂; 乔威

doi:10.7498/aps.60.070510

摘要

本文研究了一类相当广泛的复系统Julia 集的参数辨识问题.基于非线性反馈控制器和差分方程稳定性理论, 设计了普遍适用的自适应同步控制器和参数自适应律的解析表达式.理论证明设计的控制器可使得此类广义复系统Julia 集达到同步,并且可以辨识广义Julia 集的未知参数.通过仿真实例验证了该方法的有效性.另外, 本文特别地讨论了最基本的Julia 集的参数辨识问题.

关键词:

Julia集 /
参数辨识 /
同步

In this paper, a class of wide range Julia set of parameter identification problem is investigated. Based on the nonlinear feedback controller and the discretized equation theory, the designed generally applicable adaptive synchronization controller and the parameter adaptive law are obtained, and it is proved that the designed controller of generalized Julia set can achieve the synchronization. Moreover, it can identify the unknown parameters of the generalized Julia set. Particularly, the parameter identification of the basic form of Julia set is discussed in the paper.

Keywords:

作者及机构信息

(1)山东大学控制科学与工程学院, 济南 250061; (2)山东大学控制科学与工程学院, 济南 250061;山东大学威海分校机电与信息工程学院, 威海 264209; (3)山东大学威海分校实验室与设备管理处,威海 264209

基金项目: 国家自然科学基金(批准号:60874009,10971120,61074037)和山东省自然科学基金(批准号:ZR2010FM010)资助的课题.

Authors and contacts

(1)Lab and Equipment Management Office, Shandong University at Weihai, Weihai 264209, China; (2)School of Control Science and Engineering, Shandong University, Jinan 250061, China; (3)School of Control Science and Engineering, Shandong University, Jinan 250061, China;School of Mechanical, Electrical & Information Engineering, Shandong University at Weihai, Weihai 264209, China

参考文献

[1]	Halsey T C, Jensen M H, Kadanoff L P 1986 Phys.Rev.A 33 1141
[2]	Li Y,Kong X M,Huang J Y 2002 Acta Phys. Sin. 51 1346(in Chinese)\[李英、孔祥木、黄家寅 2002 物理学报 51 1346]
[3]	Yu H S,Sun X,Luo S F,Wu Z Q 2002 Acta Phys. Sin. 51 999(in Chinese)\[于会生、孙霞、罗守福、吴自勤 2002 物理学报 51 999]
[4]	He T,Zhou Z O 2007 Acta Phys. Sin. 56 693(in Chinese)\[贺涛、周正欧 2007 物理学报 56 693]
[5]	Sun X,Wu Z Q 2001 Acta Phys. Sin. 50 2126 (in Chinese)\[孙霞、吴自勤 2001 物理学报 50 2126]
[6]	Falconer K 1990 Fractals Geometry Mathematical Foundations and Applications (New York: Wiley)
[7]	Rammal R 1984 J. de Phys. ( Paris: The TeXbook)p191—206.
[8]	Biskup M, Borgs C, Chayes J 2000 Phys. Rev. Lett. 84 4794
[9]	Wang L,Zheng D Z 2000 Control Theory and Applications 17 139(in Chinese)\[王凌、郑大钟 2000 控制理论与应用 17 139]
[10]	Wang X Y,Meng Q Y 2004 Acta Phys. Sin. 53 388 (in Chinese) \[王兴元、孟庆业 2004 物理学报 53 388]
[11]	Li S 2000 In: 5th International conference on signal processing proceeding. (Beijing: Publing House Electronic Industry) p285
[12]	Lakhtakia A 1987 J. Phys A Math. Gen. 20 3533
[13]	Zhang Y P, Liu S T, Shen S L 2009 Chaos Solitons and Fractals 39 1811
[14]	Liu S T, Zhang Y P 2008 Acta Phys. Sin. 57 737(in Chinese)\[刘树堂、张永平 2008 物理学报 57 737]
[15]	Jia Z Q 2001 Higher mathematics(2)(Beijing: Science publisher)p199—200 (inChinese) \[贾启禹 2001 高等数学(下)(北京: 科学出版社)第199—200 页]

施引文献

[1]	Halsey T C, Jensen M H, Kadanoff L P 1986 Phys.Rev.A 33 1141
[2]	Li Y,Kong X M,Huang J Y 2002 Acta Phys. Sin. 51 1346(in Chinese)\[李英、孔祥木、黄家寅 2002 物理学报 51 1346]
[3]	Yu H S,Sun X,Luo S F,Wu Z Q 2002 Acta Phys. Sin. 51 999(in Chinese)\[于会生、孙霞、罗守福、吴自勤 2002 物理学报 51 999]
[4]	He T,Zhou Z O 2007 Acta Phys. Sin. 56 693(in Chinese)\[贺涛、周正欧 2007 物理学报 56 693]
[5]	Sun X,Wu Z Q 2001 Acta Phys. Sin. 50 2126 (in Chinese)\[孙霞、吴自勤 2001 物理学报 50 2126]
[6]	Falconer K 1990 Fractals Geometry Mathematical Foundations and Applications (New York: Wiley)
[7]	Rammal R 1984 J. de Phys. ( Paris: The TeXbook)p191—206.
[8]	Biskup M, Borgs C, Chayes J 2000 Phys. Rev. Lett. 84 4794
[9]	Wang L,Zheng D Z 2000 Control Theory and Applications 17 139(in Chinese)\[王凌、郑大钟 2000 控制理论与应用 17 139]
[10]	Wang X Y,Meng Q Y 2004 Acta Phys. Sin. 53 388 (in Chinese) \[王兴元、孟庆业 2004 物理学报 53 388]
[11]	Li S 2000 In: 5th International conference on signal processing proceeding. (Beijing: Publing House Electronic Industry) p285
[12]	Lakhtakia A 1987 J. Phys A Math. Gen. 20 3533
[13]	Zhang Y P, Liu S T, Shen S L 2009 Chaos Solitons and Fractals 39 1811
[14]	Liu S T, Zhang Y P 2008 Acta Phys. Sin. 57 737(in Chinese)\[刘树堂、张永平 2008 物理学报 57 737]
[15]	Jia Z Q 2001 Higher mathematics(2)(Beijing: Science publisher)p199—200 (inChinese) \[贾启禹 2001 高等数学(下)(北京: 科学出版社)第199—200 页]

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