|
|
论文:2017,Vol:35,Issue(6):1079-1082 |
|
|
引用本文： |
|
|
周敏, 刘振亚, 徐宇宏, 梁安祺, 王鹏飞. 速度可控的Julia集的同步与参数辨识[J]. 西北工业大学学报 |
|
|
Zhou Min, Liu Zhenya, Xu Yuhong, Liang Anqi, Wang Pengfei. Speed Controllable Synchronization and Parameter Identification of Julia Set[J]. Northwestern polytechnical university |
|
|
|
|
|
|
|
| 速度可控的Julia集的同步与参数辨识 |
|
| 周敏, 刘振亚, 徐宇宏, 梁安祺, 王鹏飞 |
|
| 西北工业大学 理学院, 陕西 西安 710072 |
| 摘要: |
| Julia集是分形理论中最重要的分形集之一，有着大量的应用。研究了Julia集的速度可控的同步与参数辨识。基于一阶线性差分方程的稳定性理论，针对响应系统，设计了同步控制器与参数辨识器，并运用极限理论在所设计的同步控制器与参数辨识器上加入了速度控制项，通过调整速度控制项来控制两系统间的同步速度以及驱动系统中所含未知参数的辨识速度。同步控制器控制驱动系统与响应系统达到渐进同步，参数辨识器则控制在驱动系统与响应系统达到渐进同步的过程中辨识出驱动系统中所含的未知参数，从而在驱动系统含有未知参数的情况下，实现两系统间的同步控制。最后，仿真实例表明了方法的有效性和速度可控性。 |
| 关键词:
Julia集
同步控制
参数辨识
速度可控
控制器
线性反馈
|
|
| Speed Controllable Synchronization and Parameter Identification of Julia Set |
|
| Zhou Min, Liu Zhenya, Xu Yuhong, Liang Anqi, Wang Pengfei |
|
| School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi'an 710072, China |
| Abstract: |
| Julia set is a set of great importance in fractal theory, and has been widely applied. In this paper, speed controllable synchronization and parameter identification of Julia set are researched. Based on the nonlinear feedback controller and the stability theory of first-order linear difference equation, the designs for a generally applicable adaptive synchronization controller and the parameter identifier are obtained. It is proved that the design of the controller for the generalized Julia set achieves the synchronization and unknown parameters of the generalized Julia set can be identified. Meanwhile, the synchronization controller and the parameter identifier are designed with the speed control item which makes the synchronization of drive system and response system and the identification of unknown parameters in the drive system achieve faster. Finally, the simulation examples demonstrate the effectiveness of the methods provided in this paper. |
| Key words:
Julia set
synchronization
parameter identification
speed controllable
controller
nonlinear feedback
|
|
| 收稿日期: 2017-02-01
修回日期:
|
| DOI: |
| 基金项目: 陕西省自然科学基础研究计划（2015JM6296）、国家自然科学基金（61070233）与国家级大学生创新训练项目（201610699017）资助 |
| 通讯作者:
Email： |
| 作者简介: 周敏(1966-),女,西北工业大学副教授、博士,主要从事计算机辅助几何设计、细分与分形图形图像处理研究。
|
|
|
|
|
|
|
|
参考文献: |
|
|
[1] Beardon A F. Symmetries of Julia Sets[J]. The Mathematical Intelligencer, 1996, 18(1):43-44
[2] Zhang Y P, Fan Y J. Generalized Synchronization of Julia Sets[J]. Control Theory & Applications, 2009, 26(4):463-467
[3] Zhang Y P, Sun W H, Liu C A. Control and Synchronization of Second Julia Sets[J]. Chinese Physics B, 2010, 19(5):050512
[4] Zhang Y P. Control and Synchronization of Julia Sets of the Complex Perturbed Rational Maps[J]. Journal of Bifurcation and Chaos, 2013, 23(5):1350083
[5] 梁峰. 一类有理分形的控制[D]. 山东:山东大学, 2011 Liang Feng. A Kind of Rational Fractal in Control[D]. Shandong, Shandong University, 2011
[6] Liu P, Liu C. Linear Generalized Synchronization of Spatial Julia Sets[J]. International Journal of Bifurcation and Chaos, 2011, 21(5):1281-1291
[7] Liu P, Hou J. Generalized Julia Set in Coupled Map Lattice and Its Coupling and Synchronization[J]. International Journal of Computer Mathematics, 2015, 92(7):1329-1344
[8] Sun J, Liu S T. A New Identification Control for Generalized Julia Sets[J]. Chinese Physics B, 2013, 22(5):050505 |
|
|
|
|
|
|
|
