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An active adaptive fuzzy integral sliding mode controller is proposed for a unified chaotic system with parametric uncertainties under external perturbation. An improved control method is designed to guarantee the stability, while maintaining the transient performances of the original nonlinear integral sliding mode control. The proposed method reduces the effects of both the uncontrollable state of unified chaotic system and approximation error of adaptive fuzzy compensator on system state error. The stability of the controller is analyzed by Lyapunov stability theorem. The simulation results show that the system states can be controlled to target points with parametric uncertainties under external perturbation. The effectiveness of this method is illustrated by the numerical simulation.
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Keywords:
- unified chaotic system /
- active control /
- sliding mode control /
- adaptive fuzzy compensator
[1] Li N, Li J F 2008 Acta Phys. Sin. 57 6098 (in Chinese) [李农, 李建芬 2008 物理学报 57 6098]
[2] Yu Y, Mi Z Q, Liu X J 2011 Acta Phys. Sin. 60 070509 (in Chinese) [余洋, 米增强, 刘兴杰 2011 物理学报 60 070509]
[3] Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 100504 (in Chinese) [邝玉兰, 唐国宁 2012 物理学报 61 100504]
[4] Tao C H, Lu J A 2003 Acta Phys. Sin. 52 281 (in Chinese) [陶朝海, 陆君安 2003 物理学报 52 281]
[5] Wang D F 2005 Acta Phys. Sin. 54 1495 (in Chinese) [王东风 2005 物理学报 54 1495]
[6] Gao X, Liu X W 2007 Acta Phys. Sin. 56 84 (in Chinese) [高心, 刘兴文 2007 物理学报 56 84]
[7] Li W L, Chen X Q, Shen Z P 2008 Chin. Phys. B 17 87
[8] Yu D C, Wu A G, Wang D Q 2006 Chin. Phys. 15 306
[9] Wei W, Li D H, Wang J 2011 Chin. Phys. B 20 040510
[10] Guo H J, Liu D, Zhao G Y 2011 Acta Phys. Sin. 60 010510 (in Chinese) [郭会军, 刘丁, 赵光宙 2011 物理学报 60 010510]
[11] Li M, Liu C X 2010 Chin. Phys. B 19 100504
[12] Li W L, Chang K M 2009 Chaos, Solitons and Fractals 39 2086
[13] Lou X Y, Cui B T 2008 Chin. Phys. B 17 4434
[14] Li X C, Xu W, Xiao Y Z 2008 Acta Phys. Sin. 57 4721 (in Chinese) [李秀春, 徐伟, 肖玉柱 2008 物理学报 57 4721]
[15] Li P, Ma J J, Li W Q, Zheng Z Q 2009 Control and Decision 24 1463 (in Chinese) [李鹏, 马建军, 李文强, 郑志强 2009 控制与决策 24 1463]
[16] Peng Y, Vrancic D, Hanus R 1996 IEEE Contr. Syst. Mag. 16 48
[17] Tong S C, Li Y M, Shi Peng 2009 Infor. Sci. 179 1319
[18] Tan W, Wang Y N 2004 Acta Phys. Sin. 53 4087 (in Chinese) [谭文, 王耀南 2004 物理学报 53 4087]
[19] Guan X P, Chen C L, Fan Z P 2002 Acta Phys. Sin. 51 07531 (in Chinese) [关新平, 陈彩莲, 范正平 2002 物理学报 51 07531]
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[1] Li N, Li J F 2008 Acta Phys. Sin. 57 6098 (in Chinese) [李农, 李建芬 2008 物理学报 57 6098]
[2] Yu Y, Mi Z Q, Liu X J 2011 Acta Phys. Sin. 60 070509 (in Chinese) [余洋, 米增强, 刘兴杰 2011 物理学报 60 070509]
[3] Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 100504 (in Chinese) [邝玉兰, 唐国宁 2012 物理学报 61 100504]
[4] Tao C H, Lu J A 2003 Acta Phys. Sin. 52 281 (in Chinese) [陶朝海, 陆君安 2003 物理学报 52 281]
[5] Wang D F 2005 Acta Phys. Sin. 54 1495 (in Chinese) [王东风 2005 物理学报 54 1495]
[6] Gao X, Liu X W 2007 Acta Phys. Sin. 56 84 (in Chinese) [高心, 刘兴文 2007 物理学报 56 84]
[7] Li W L, Chen X Q, Shen Z P 2008 Chin. Phys. B 17 87
[8] Yu D C, Wu A G, Wang D Q 2006 Chin. Phys. 15 306
[9] Wei W, Li D H, Wang J 2011 Chin. Phys. B 20 040510
[10] Guo H J, Liu D, Zhao G Y 2011 Acta Phys. Sin. 60 010510 (in Chinese) [郭会军, 刘丁, 赵光宙 2011 物理学报 60 010510]
[11] Li M, Liu C X 2010 Chin. Phys. B 19 100504
[12] Li W L, Chang K M 2009 Chaos, Solitons and Fractals 39 2086
[13] Lou X Y, Cui B T 2008 Chin. Phys. B 17 4434
[14] Li X C, Xu W, Xiao Y Z 2008 Acta Phys. Sin. 57 4721 (in Chinese) [李秀春, 徐伟, 肖玉柱 2008 物理学报 57 4721]
[15] Li P, Ma J J, Li W Q, Zheng Z Q 2009 Control and Decision 24 1463 (in Chinese) [李鹏, 马建军, 李文强, 郑志强 2009 控制与决策 24 1463]
[16] Peng Y, Vrancic D, Hanus R 1996 IEEE Contr. Syst. Mag. 16 48
[17] Tong S C, Li Y M, Shi Peng 2009 Infor. Sci. 179 1319
[18] Tan W, Wang Y N 2004 Acta Phys. Sin. 53 4087 (in Chinese) [谭文, 王耀南 2004 物理学报 53 4087]
[19] Guan X P, Chen C L, Fan Z P 2002 Acta Phys. Sin. 51 07531 (in Chinese) [关新平, 陈彩莲, 范正平 2002 物理学报 51 07531]
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