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Based on sliding mode control theory and adaptive control theory, this paper investigates the synchronization of three-dimensional chaotic systems, designs a fractional order proportional integral switching surface, and proposes a single adaptive-feedback controller for fractional-order chaos synchronization. Simulation results for fractional-order unified chaotic system and Arneodo chaotic systems are provided to illustrate the effectiveness of the proposed scheme.
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Keywords:
- sliding mode control /
- fractional-order chaotic system /
- single controller /
- adaptive synchronization
[1] Hartly T T, Lorenzo C F, Qammer H K 1995 IEEE Trans CAI 42 485.
[2] Grigorenko I, Grigorenko E 2003 Phys.Rev. Lett. 91 034101
[3] Li C P, Peng G J 2004 Chaos, Solitons & Fractals 22 443
[4] Li C G, Chen G R 2004 Chaos, Solitons & Fractals 22 549
[5] Lu J G, Chen G R 2006 Chaos, Solitons & Fractals 27 685
[6] Deng W H, Li C P 2005 Physica A 353 61
[7] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922(in Chinese)[王发强、刘崇新 2006 55 3922]
[8] Chen X R, Liu C X, Wang F Q,Li Y X 2008 Acta Phys. Sin. 57 1416(in Chinese)[陈向荣、刘崇新、刘发强、李永勋 2008 57 1416]
[9] Liu C X, Liu T, Liu L and Liu K 2004 Chaos, Solitions & Fractals 22 1031
[10] Gao X, Yu J B 2005 Chaos, Solitons & Fractals 24 1097
[11] Ahamd W M, Sprott J C 2003 Chaos, Solitons & Fractals 16 339
[12] Gao X, Yu J B 2005 Chin. Phys. 14 908
[13] Li C G, Chen G R 2004 Physica A 341 55
[14] Liu C X 2007 Acta Phys. Sin. 56 6865(in Chinese)[刘崇新 2007 56 6865]
[15] Arman Kiani-B, Kia Fallahi, Naser Pariz, Henry Leung 2009 Commun. Nonlinear Sci. Numer. Simul. 14 863
[16] Li C P, Deng W H 2006 Int. J. Modern Phys. B 20 791
[17] Mohammad Saleh Tavazoei, Mohammad Haeri 2008 Physica A 387 57
[18] Hu J B, H Y, Zhao L D 2008 Acta Phys. Sin. 57 7522 (in Chinese)[胡建兵、韩 焱、赵灵冬 2008 57 7522]
[19] Zhang R X, Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6309 (in Chinese)[张若洵、杨世平 2009 58 6309]
[20] Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510
[21] Wang X Y, Song J M 2009 Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2009.01.010
[22] Zhang R X, Yang S P 2008 Acta Phys. Sin. 57 6837 (in Chinese)[张若洵、 杨世平 2008 57 6837]
[23] Deng W H 2007 Phys. Rev. E 75 056201
[24] Wang X J, Li J, Chen G R 2008 J. of the Franklin Institute 345 392
[25] Ahmad W M, Sprott J C 2003 Chaos, Solitons & Fractals 16 339
[26] Sun K H, Re J, Shang F 2008 Computer Simulation 25 312
[27] Lu J G 2005 Chaos, Solitions & Fractals 26 1125
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[1] Hartly T T, Lorenzo C F, Qammer H K 1995 IEEE Trans CAI 42 485.
[2] Grigorenko I, Grigorenko E 2003 Phys.Rev. Lett. 91 034101
[3] Li C P, Peng G J 2004 Chaos, Solitons & Fractals 22 443
[4] Li C G, Chen G R 2004 Chaos, Solitons & Fractals 22 549
[5] Lu J G, Chen G R 2006 Chaos, Solitons & Fractals 27 685
[6] Deng W H, Li C P 2005 Physica A 353 61
[7] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922(in Chinese)[王发强、刘崇新 2006 55 3922]
[8] Chen X R, Liu C X, Wang F Q,Li Y X 2008 Acta Phys. Sin. 57 1416(in Chinese)[陈向荣、刘崇新、刘发强、李永勋 2008 57 1416]
[9] Liu C X, Liu T, Liu L and Liu K 2004 Chaos, Solitions & Fractals 22 1031
[10] Gao X, Yu J B 2005 Chaos, Solitons & Fractals 24 1097
[11] Ahamd W M, Sprott J C 2003 Chaos, Solitons & Fractals 16 339
[12] Gao X, Yu J B 2005 Chin. Phys. 14 908
[13] Li C G, Chen G R 2004 Physica A 341 55
[14] Liu C X 2007 Acta Phys. Sin. 56 6865(in Chinese)[刘崇新 2007 56 6865]
[15] Arman Kiani-B, Kia Fallahi, Naser Pariz, Henry Leung 2009 Commun. Nonlinear Sci. Numer. Simul. 14 863
[16] Li C P, Deng W H 2006 Int. J. Modern Phys. B 20 791
[17] Mohammad Saleh Tavazoei, Mohammad Haeri 2008 Physica A 387 57
[18] Hu J B, H Y, Zhao L D 2008 Acta Phys. Sin. 57 7522 (in Chinese)[胡建兵、韩 焱、赵灵冬 2008 57 7522]
[19] Zhang R X, Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6309 (in Chinese)[张若洵、杨世平 2009 58 6309]
[20] Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510
[21] Wang X Y, Song J M 2009 Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2009.01.010
[22] Zhang R X, Yang S P 2008 Acta Phys. Sin. 57 6837 (in Chinese)[张若洵、 杨世平 2008 57 6837]
[23] Deng W H 2007 Phys. Rev. E 75 056201
[24] Wang X J, Li J, Chen G R 2008 J. of the Franklin Institute 345 392
[25] Ahmad W M, Sprott J C 2003 Chaos, Solitons & Fractals 16 339
[26] Sun K H, Re J, Shang F 2008 Computer Simulation 25 312
[27] Lu J G 2005 Chaos, Solitions & Fractals 26 1125
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