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In this paper, we investigate the signal tracking problem of the uncertain time-varying delay chaotic system with control input nonlinearity and the fuzzy adaptive variable structure control method is proposed. The fuzzy logic system approximates the nonlinearity of the system. The unknown time-varying delay uncertainties are compensated using an appropriate Lyapunov-Krasovskii functional. The proposed controller can make the tracking errors converge to an adjustable region and all signals of the closed system is bounded. The designed control method can have a certain robustness against the disturbance of the system. Finally, taking the simulations on a multi-scroll chaotic system for example, the effectiveness of the proposed method is illustrated.
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Keywords:
- fuzzy system /
- multi scroll chaotic system /
- control input nonlinearity /
- time-varying delay
[1] Rosebium M G, Pikovsky A S, Kurths J 1996 { Phys. Rev. Lett}. 76 1804
[2] Taherrionl S, Lai Y C 1999 { Phys. Rev.} E 59 6247
[3] Zhang P W, Tang G N, Luo X S 2005 Acta Phys. Sin. 54 3497 (in Chinese) [张平伟, 唐国宁, 罗晓曙 2005 物理学报 54 3497]
[4] Wang X Y, Meng J 2008 {Acta Phys. Sin}. 57 726 (in Chinese) [王兴元, 梦娟 2008 物理学报 57 726]
[5] Liu J, Chen S H, Lu J A 2003 {Acta Phys. Sin}. 52 1595 (in Chinese) [刘杰, 陈士华, 陆君安 2003 物理学报 52 1595]
[6] Wang X Y, Wang Y 2007 {Acta Phys. Sin}. 56 2498 (in Chinese) [王兴元, 王勇 2007 物理学报 56 2498]
[7] Wang J A, Liu H P 2010 { Acta Phys. Sin}. 59 2264 (in Chinese) [王建安, 刘贺平 2010 物理学报 59 2264]
[8] Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits Syst. I 40 861
[9] Lü J H, Chen G R, Cheng D Z 2002 Int. J. Bifur. Chaos 12 2917
[10] Lü J H, Chen G R,Yu X H, Leung H 2004 IEEE Trans. Circuits Syst. I 51 2476
[11] Lü J H, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[12] Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I 53 149
[13] Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775
[14] Wang W Y, Leu Y G, Lee T T 2003 { Fuzzy Sets Syst.} 140 341
[15] Zhang W W, Wang J, Wang H, Zhao Y T 2011 { Acta Phys. Sin.} 60 010511 (in Chinese) [张巍巍, 王京, 王惠, 赵云涛 2011 物理学报 60 010511]
[16] Li D, Zhang X H, Yang D, Wang S L 2009 { Acta Phys. Sin.} 58 1433 (in Chinese) [李东, 张小洪, 杨丹, 王时龙 2009 物理学报 58 1433]
[17] Li D, Wang S L, Zhang X H, Yang D 2009 { Acta Phys. Sin.} 58 2940 (in Chinese) [李东, 王时龙, 张小洪, 杨丹 2009 物理学报 58 2940]
[18] Yu J P, Chen B, Yu H S, Gao J W 2011 {Nonlinear Analysis: Real World Applications} 12 671
[19] Li T S, Li R H, Li J F 2011 Neurocomputing 74 2277
[20] Boulroune A, M'Saad M 2011 Expert Systems with Applications 38 14744
[21] Boulroune A, M'Saad M, Farza M 2011 Fuzzy Sets Syst. 164 45
[22] Chen M, Ge S S, Ren B B 2011 {Automatica} 47 452
[23] 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]
[24] Zhang H G, Ma D Z, Wang Z S, Feng J, Wang Y C 2010 Acta Phys. Sin. 59 138 (in Chinese) [张化光, 马大中, 王占山, 冯健, 王迎春 2010 物理学报 59 147]
[25] Boulroune A, Tadjine M, M'Saad M, Farza M 2010 Fuzzy Sets Syst. 161 797
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[1] Rosebium M G, Pikovsky A S, Kurths J 1996 { Phys. Rev. Lett}. 76 1804
[2] Taherrionl S, Lai Y C 1999 { Phys. Rev.} E 59 6247
[3] Zhang P W, Tang G N, Luo X S 2005 Acta Phys. Sin. 54 3497 (in Chinese) [张平伟, 唐国宁, 罗晓曙 2005 物理学报 54 3497]
[4] Wang X Y, Meng J 2008 {Acta Phys. Sin}. 57 726 (in Chinese) [王兴元, 梦娟 2008 物理学报 57 726]
[5] Liu J, Chen S H, Lu J A 2003 {Acta Phys. Sin}. 52 1595 (in Chinese) [刘杰, 陈士华, 陆君安 2003 物理学报 52 1595]
[6] Wang X Y, Wang Y 2007 {Acta Phys. Sin}. 56 2498 (in Chinese) [王兴元, 王勇 2007 物理学报 56 2498]
[7] Wang J A, Liu H P 2010 { Acta Phys. Sin}. 59 2264 (in Chinese) [王建安, 刘贺平 2010 物理学报 59 2264]
[8] Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits Syst. I 40 861
[9] Lü J H, Chen G R, Cheng D Z 2002 Int. J. Bifur. Chaos 12 2917
[10] Lü J H, Chen G R,Yu X H, Leung H 2004 IEEE Trans. Circuits Syst. I 51 2476
[11] Lü J H, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[12] Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I 53 149
[13] Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775
[14] Wang W Y, Leu Y G, Lee T T 2003 { Fuzzy Sets Syst.} 140 341
[15] Zhang W W, Wang J, Wang H, Zhao Y T 2011 { Acta Phys. Sin.} 60 010511 (in Chinese) [张巍巍, 王京, 王惠, 赵云涛 2011 物理学报 60 010511]
[16] Li D, Zhang X H, Yang D, Wang S L 2009 { Acta Phys. Sin.} 58 1433 (in Chinese) [李东, 张小洪, 杨丹, 王时龙 2009 物理学报 58 1433]
[17] Li D, Wang S L, Zhang X H, Yang D 2009 { Acta Phys. Sin.} 58 2940 (in Chinese) [李东, 王时龙, 张小洪, 杨丹 2009 物理学报 58 2940]
[18] Yu J P, Chen B, Yu H S, Gao J W 2011 {Nonlinear Analysis: Real World Applications} 12 671
[19] Li T S, Li R H, Li J F 2011 Neurocomputing 74 2277
[20] Boulroune A, M'Saad M 2011 Expert Systems with Applications 38 14744
[21] Boulroune A, M'Saad M, Farza M 2011 Fuzzy Sets Syst. 164 45
[22] Chen M, Ge S S, Ren B B 2011 {Automatica} 47 452
[23] 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]
[24] Zhang H G, Ma D Z, Wang Z S, Feng J, Wang Y C 2010 Acta Phys. Sin. 59 138 (in Chinese) [张化光, 马大中, 王占山, 冯健, 王迎春 2010 物理学报 59 147]
[25] Boulroune A, Tadjine M, M'Saad M, Farza M 2010 Fuzzy Sets Syst. 161 797
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