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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.
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Keywords:
- spatio-temporal synchronization /
- differential geometry /
- exact linearization /
- parameter mismatch
[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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[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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