基于微分几何理论的参数失配系统时空同步研究

谭平安; 杨磊; 张波

doi:10.7498/aps.62.230507

摘要

本文采用状态反馈精确线性化方法，实现了参数失配系统的时空同步控制. 引入微分几何理论，首先采用李导数判定了参数失配系统的仿射模型是否满足状态精确线性化的充要条件，通过非线性坐标变换得到了其线性解耦系统，并结合线性最优控制理论确定了同步控制律，数值仿真证实了该控制方法的有效性，从非线性控制角度探索了混沌系统时空同步的新方法.

关键词:

A new nonlinear synchronization control strategy for a parameter mismatch system based on exact linearization via feedback is presented. First, a nonlinear affine model of parameter mismatch system is established, and the precondition of exact linearization is verified based on the differential geometry theory. Through the nonlinear coordinate transformation, the linear decoupling system is obtained, so the state feedback control law can be determined by the linear optimal control theory. It is found by simulation results that the proposed synchronization method based on exact linearization via feedback can ensure the successful control of the parameter mismatch system.

Keywords:

作者及机构信息

1.
湘潭大学信息工程学院, 湘潭 411105;

2.
华南理工大学电力学院, 广州 510640

基金项目: 国家自然科学基金（批准号：51207134）、国家自然科学基金重点项目（批准号：50937001）和湖南省重点学科建设项目资助的课题.

Authors and contacts

1.
College of Information Engineering, Xiangtan University, Xiangtan 411105, China;

2.
College of Electric Power, South China University of Technology, Guangzhou 510640, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51207134), the Key Program of the National Natural Science Foundation of China (Grant No. 50937001), and the Construct Program of the Key Discipline of Hunan Province, China.

参考文献

[1]	L L, Shang J Y, Zhu J B, Shen N, Liu S, Zhang X 2012 Acta Phys. Sin. 61 140504 (in Chinese) [吕翎, 商锦玉, 朱佳博, 沈娜, 柳爽, 张新 2012 61 140504]
[2]	Zhao Y B, Luo X S 2007 Acta Phys. Sin. 56 6258 (in Chinese) [赵益波, 罗晓曙 2007 56 6258]
[3]	Yamada T, Graham R 1980 Phys. Rev. Lett. 45 1322
[4]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[5]	Brandt S F, Dellen B K, Wessel R 2006 Phys. Rev. Lett. 96 034104
[6]	Pyragas K 2006 Philos. T R Soc. A 364 2309
[7]	Unkelbach J, Amann A, Just W, Schöll E 2003 Phys. Rev. E 68 026204
[8]	Beck O, Amann A, Schöll E, Socolar J E, Just W 2002 Phys. Rev. E 66 016213
[9]	Vasegh N, Khellat F 2009 Chaos Solitons and Fractals 42 1054
[10]	Guan X P, He Y H 2004 Chin. Phys. Lett. 21 227
[11]	Li H Y, Hu Y A 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3904
[12]	Han C Z, Li Z 2002 Chin. Phys. 11 666
[13]	Zhou T S, L J H, Zhang S C 2002 Chin. Phys. 11 12
[14]	Wang Z, Zhao P D, Zhang X D 2008 Chin. Phys. Lett. 25 397
[15]	Suykens J A K, Curran P F, Chua L O 1999 IEEE Trans. Circ. Syst. I 46 841
[16]	Wu X F, Cai J P, Zhao Y 2005 IEEE Trans. Circ. Syst. II 52 429
[17]	Wang J G, Cai J P, Ma M H 2008 Acta Phys. Sin. 57 3367 (in Chinese) [王建根, 蔡建平, 马米花 2008 57 3367]
[18]	Li D P 2006 Nonlinear control systems theory (Harbin: Harbin engineering university press) p249 (in Chinese) [李殿璞 2006 非线性控制系统理论基础 (哈尔滨: 哈尔滨工程大学出版社) 第249页]
[19]	Hu Y M 2005 Nonlinear control systems theory and applications (Beijing: National defense industry press) p21 (in Chinese) [胡跃明 2005 非线性控制系统理论与应用 (北京: 国防工业出版社) 第21页]
[20]	Tan P A, Zhang B, Qiu D Y 2010 Acta Phys. Sin. 59 5299 (in Chinese) [谭平安, 张波, 丘东元 2010 59 5299]

施引文献

[1]	L L, Shang J Y, Zhu J B, Shen N, Liu S, Zhang X 2012 Acta Phys. Sin. 61 140504 (in Chinese) [吕翎, 商锦玉, 朱佳博, 沈娜, 柳爽, 张新 2012 61 140504]
[2]	Zhao Y B, Luo X S 2007 Acta Phys. Sin. 56 6258 (in Chinese) [赵益波, 罗晓曙 2007 56 6258]
[3]	Yamada T, Graham R 1980 Phys. Rev. Lett. 45 1322
[4]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[5]	Brandt S F, Dellen B K, Wessel R 2006 Phys. Rev. Lett. 96 034104
[6]	Pyragas K 2006 Philos. T R Soc. A 364 2309
[7]	Unkelbach J, Amann A, Just W, Schöll E 2003 Phys. Rev. E 68 026204
[8]	Beck O, Amann A, Schöll E, Socolar J E, Just W 2002 Phys. Rev. E 66 016213
[9]	Vasegh N, Khellat F 2009 Chaos Solitons and Fractals 42 1054
[10]	Guan X P, He Y H 2004 Chin. Phys. Lett. 21 227
[11]	Li H Y, Hu Y A 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3904
[12]	Han C Z, Li Z 2002 Chin. Phys. 11 666
[13]	Zhou T S, L J H, Zhang S C 2002 Chin. Phys. 11 12
[14]	Wang Z, Zhao P D, Zhang X D 2008 Chin. Phys. Lett. 25 397
[15]	Suykens J A K, Curran P F, Chua L O 1999 IEEE Trans. Circ. Syst. I 46 841
[16]	Wu X F, Cai J P, Zhao Y 2005 IEEE Trans. Circ. Syst. II 52 429
[17]	Wang J G, Cai J P, Ma M H 2008 Acta Phys. Sin. 57 3367 (in Chinese) [王建根, 蔡建平, 马米花 2008 57 3367]
[18]	Li D P 2006 Nonlinear control systems theory (Harbin: Harbin engineering university press) p249 (in Chinese) [李殿璞 2006 非线性控制系统理论基础 (哈尔滨: 哈尔滨工程大学出版社) 第249页]
[19]	Hu Y M 2005 Nonlinear control systems theory and applications (Beijing: National defense industry press) p21 (in Chinese) [胡跃明 2005 非线性控制系统理论与应用 (北京: 国防工业出版社) 第21页]
[20]	Tan P A, Zhang B, Qiu D Y 2010 Acta Phys. Sin. 59 5299 (in Chinese) [谭平安, 张波, 丘东元 2010 59 5299]

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