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For a class of cross-strict feedback hyperchaotic systems with unmatched uncertainties, a multilayer neural network (MNN) based adaptive backstepping design method is proposed. An MNN is introduced to estimate the uncertainties in systems. Sliding mode and adaptive backstepping control are used to deal with the unmatched uncertainties and the MNN approximation errors. If the virtual control coefficients do not pass through zeros, the proposed method guarantees that the synchronization errors of the systems approach zeros. If the virtual control coefficients pass through zeros, the proposed method guarantees that the synchronization errors of the systems are bounded. Numerical simulations are given to demonstrate the efficiency of the proposed control scheme.
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Keywords:
- hyper-chaos synchronization /
- cross-strict feedback system /
- backstepping /
- MNN
[1] Wu T, Chen M S 2002 Physica D 164 53
[2] Harb A, Abedl-Jabbar N 2003 Chaos, Solitons and Fractals 18 1055
[3] Chen G 1999 Controlling Chaos and Bifurcations in Engineering Systems (1st Ed.) (Boca Raton: CRC Press) p10
[4] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[5] Zhu C X 2009 Appl. Math. Comput. 215 557
[6] Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1
[7] Yan Z 2005 Appl. Math. Comput. 168 1239
[8] Wang F, Liu C 2006 Phys. Lett. A 360 274
[9] Wu X Y, Zhang H M 2009 Chaos, Solitons and Fractals 39 2268
[10] Jia Q 2007 Phys. Lett. A 362 424
[11] Zhou X B, Wu Y, Li Y, Xue H Q 2009 Chaos, Solitons and Fractals 39 2477
[12] Wang J, Gao J F, Ma X K 2007 Phys. Lett. A 369 452
[13] Zhang H, Ma X K, Li M, Zou J L 2005 Chaos, Solitons and Fractals 26 353
[14] Yu Y G, Zhang S C 2004 Chaos, Solitons and Fractals 21 643
[15] Tan X H, Zhang J Y, Yang Y R 2003 Chaos, Solitons and Fractals 16 37
[16] Wang C, Ge S S 2001 Int. J. Bifur. Chaos 11 1743
[17] Bowong S, Kakmeni F M M 2004 Chaos, Solitons and Fractals 21 999
[18] Kittel A, Parisi J, Pyragas K 1995 Phys. Lett. A 198 433
[19] Chen F X, Wang W, Chen L, Zhang W D 2007 Phys. Scr. 75 285
[20] Haeri M, Emadzadeh A A 2007 Chaos, Solitons and Fractals 31 119
[21] Yan J J, Hung M L, Chiang T Y, Yang Y S 2006 Phys. Lett. A 356 220
[22] Roopaei M, Sahraei B R, Lin T C 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 4158
[23] Yau H T 2008 Mech. Syst. Signal Process 22 408
[24] Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2728
[25] Xiang W, Huangpu Y G 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3241
[26] Guo H J, Lin S F, Liu J H 2006 Phys. Lett. A 351 257
[27] Lu Z, Shieh L S, Chen G R, Coleman N P 2006 Inf. Sci. 176 2337
[28] Zhang N N , Zhang D J, Feng Y 2007 Control and Decis. 22 1143 (in Chinese) [张袅娜, 张德江, 冯勇 2007 控制与决策 22 1143]
[29] Guo H J, Liu D, Zhao G Z 2011 Acta Phys. Sin. 60 010510 (in Chinese) [郭会军, 刘丁, 赵光宙 2011 物理学报 60 010510]
[30] Krstic M, Kanellakopoulos I, Kokotovic P 1995 Nonlinear and Adaptive Control Design (New York: Wiley) p1
[31] Li G H, Zhou S P, Yang K 2006 Phys. Lett. A 355 326
[32] Li H Y, Hu Y A 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3904
[33] Li Y, Tang W K S, Chen G R 2005 Int. J. Bifur. Chaos 15 3367
[34] Wu X Y, Guan Z H, Wu Z P 2008 Nonlinear Anal. 68 1346
[35] Zhang T, Ge S S, Hang C C 1999 Automatica 35 1809
[36] Sun Y J, Lien C H, Hsieh J G 1998 IEEE Trans. Autom. Control. 43 674
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[1] Wu T, Chen M S 2002 Physica D 164 53
[2] Harb A, Abedl-Jabbar N 2003 Chaos, Solitons and Fractals 18 1055
[3] Chen G 1999 Controlling Chaos and Bifurcations in Engineering Systems (1st Ed.) (Boca Raton: CRC Press) p10
[4] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[5] Zhu C X 2009 Appl. Math. Comput. 215 557
[6] Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1
[7] Yan Z 2005 Appl. Math. Comput. 168 1239
[8] Wang F, Liu C 2006 Phys. Lett. A 360 274
[9] Wu X Y, Zhang H M 2009 Chaos, Solitons and Fractals 39 2268
[10] Jia Q 2007 Phys. Lett. A 362 424
[11] Zhou X B, Wu Y, Li Y, Xue H Q 2009 Chaos, Solitons and Fractals 39 2477
[12] Wang J, Gao J F, Ma X K 2007 Phys. Lett. A 369 452
[13] Zhang H, Ma X K, Li M, Zou J L 2005 Chaos, Solitons and Fractals 26 353
[14] Yu Y G, Zhang S C 2004 Chaos, Solitons and Fractals 21 643
[15] Tan X H, Zhang J Y, Yang Y R 2003 Chaos, Solitons and Fractals 16 37
[16] Wang C, Ge S S 2001 Int. J. Bifur. Chaos 11 1743
[17] Bowong S, Kakmeni F M M 2004 Chaos, Solitons and Fractals 21 999
[18] Kittel A, Parisi J, Pyragas K 1995 Phys. Lett. A 198 433
[19] Chen F X, Wang W, Chen L, Zhang W D 2007 Phys. Scr. 75 285
[20] Haeri M, Emadzadeh A A 2007 Chaos, Solitons and Fractals 31 119
[21] Yan J J, Hung M L, Chiang T Y, Yang Y S 2006 Phys. Lett. A 356 220
[22] Roopaei M, Sahraei B R, Lin T C 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 4158
[23] Yau H T 2008 Mech. Syst. Signal Process 22 408
[24] Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2728
[25] Xiang W, Huangpu Y G 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3241
[26] Guo H J, Lin S F, Liu J H 2006 Phys. Lett. A 351 257
[27] Lu Z, Shieh L S, Chen G R, Coleman N P 2006 Inf. Sci. 176 2337
[28] Zhang N N , Zhang D J, Feng Y 2007 Control and Decis. 22 1143 (in Chinese) [张袅娜, 张德江, 冯勇 2007 控制与决策 22 1143]
[29] Guo H J, Liu D, Zhao G Z 2011 Acta Phys. Sin. 60 010510 (in Chinese) [郭会军, 刘丁, 赵光宙 2011 物理学报 60 010510]
[30] Krstic M, Kanellakopoulos I, Kokotovic P 1995 Nonlinear and Adaptive Control Design (New York: Wiley) p1
[31] Li G H, Zhou S P, Yang K 2006 Phys. Lett. A 355 326
[32] Li H Y, Hu Y A 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3904
[33] Li Y, Tang W K S, Chen G R 2005 Int. J. Bifur. Chaos 15 3367
[34] Wu X Y, Guan Z H, Wu Z P 2008 Nonlinear Anal. 68 1346
[35] Zhang T, Ge S S, Hang C C 1999 Automatica 35 1809
[36] Sun Y J, Lien C H, Hsieh J G 1998 IEEE Trans. Autom. Control. 43 674
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