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In this paper, we present a novel impulsive control method based on polynomial model for a large class of chaotic systems. First, the polynomial model is used to model the chaotic system, in which the state equation of the system is composed of the polynomial matrix of the system and the column vector of monomials in state. Compared with others modeling methods, any pre-defined hypothesis is removed. Next, a sum-of-square (SOS)-based impulsive control method is investigated to guarantee that the chaotic system is asymptotically stable. It can obtain larger impulsive interval using SOS-based optimization algorithm over linear matrix inequality technique, which means the same control performance can be realized by less control action. Finally, the simulation is provided to demonstrate the effectiveness of the proposed method.
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Keywords:
- chaos control /
- polynomial model /
- sum-of-square algorithm /
- impulsive control
[1] Li W, Wang X 2009 Techniques of Automation and Applications 28 1 (in Chinese) [李卫东, 王秀岩 2009 自动化技术与应用 28 1]
[2] Jackson E A 1991 Physical D 50 247
[3] Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 物理学报 54 3502]
[4] Zhang X, Khadra A, Yang D, Li D 2010 Commun. Nonlinear Sci. Numer. Simulat 15 105
[5] Liu X 2009 Nonlinear Analysis 71 e1320
[6] Yang D S, Zhang H G, Zhao Y, Song C H, Wang Y C 2010 Acta Phys. Sin. 59 1562 (in Chinese) [杨东升, 张化光, 赵琰, 宋崇辉, 王迎春 2010 物理学报 59 1562]
[7] Lam H K 2009 Chaos Soliton. Fract. 41 2624
[8] Tanaka K, Ikeda T, Wang H O 1998 IEEE Trans. Circuits Syst. I: Fundam. Appl. 45 1021
[9] Lian K Y, Liu P, Wu T C, Lin W C 2002 Int. J. Bifurcation Chaos 12 1827
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[1] Li W, Wang X 2009 Techniques of Automation and Applications 28 1 (in Chinese) [李卫东, 王秀岩 2009 自动化技术与应用 28 1]
[2] Jackson E A 1991 Physical D 50 247
[3] Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 物理学报 54 3502]
[4] Zhang X, Khadra A, Yang D, Li D 2010 Commun. Nonlinear Sci. Numer. Simulat 15 105
[5] Liu X 2009 Nonlinear Analysis 71 e1320
[6] Yang D S, Zhang H G, Zhao Y, Song C H, Wang Y C 2010 Acta Phys. Sin. 59 1562 (in Chinese) [杨东升, 张化光, 赵琰, 宋崇辉, 王迎春 2010 物理学报 59 1562]
[7] Lam H K 2009 Chaos Soliton. Fract. 41 2624
[8] Tanaka K, Ikeda T, Wang H O 1998 IEEE Trans. Circuits Syst. I: Fundam. Appl. 45 1021
[9] Lian K Y, Liu P, Wu T C, Lin W C 2002 Int. J. Bifurcation Chaos 12 1827
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