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Active radial basis function sliding mode controller for unified chaotic system with disturbance and uncertainties

Guo Hui-Jun Liu Ding Zhao Guang-Zhou

Active radial basis function sliding mode controller for unified chaotic system with disturbance and uncertainties

Guo Hui-Jun, Liu Ding, Zhao Guang-Zhou
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  • An adaptive active radial basis function (RBF) sliding mode controller is designed to control a unified chaotic system with parametric uncertainties under external disturbance. The controlled system is divided into a controllable subsystem and a free subsystem. Based on the controllable canonical form of controllable sub-systems state errors at the target points, a sliding surface is defined as the only input to the RBF controller. The weight of the controller is tuned on-line based on the sliding mode reaching law. The simulation results show that this method is applicable and effective, and the robustness to parametric uncertainties and external disturbance is provided. And the chattering of conventional sliding controls doesn’t occur.
    • Funds:
    [1]

    Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196

    [2]

    Chen G, Dong X 1993 Int. J. Bifur. Chaos. 3 1363

    [3]

    Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1

    [4]

    Li D, Wang S L,Yang D, Zhang X H 2009 Acta Phys. Sin. 58 1432 (in Chinese)[李 东、王时龙、杨 丹、张小洪 2009 物理学报 58 1432]

    [5]

    Yang J, Qi D L 2010 Chin. Phys. B 19 020508-1

    [6]

    Hao J H, Wu S H, Xu H B 2010 Chin. Phys. B. 19 020509-1

    [7]

    Cai G L, Miao S T, Li X, Wang H X 2010 Chin. Phys. B 19 030509-1

    [8]

    Liu C X, Xu Z, Yang T 2010 Acta Phys. Sin. 59 1524(in Chinese)[刘崇新、许 喆、杨 韬 2010 物理学报 59 1524]

    [9]

    Lai X Q, Li Z H, Wang H, Ye Q, Yuan B, Zhao Y R 2010 Acta Phys. Sin. 59 2256(in Chinese) [来新泉、李祖贺、王 慧、叶 强、袁 冰、赵永瑞 2010 物理学报 59 2256]

    [10]

    Tang G N, Yang C Y 2009 Acta Phys. Sin. 58 143(in Chinese) [唐国宁、杨朝羽 2009 物理学报 58 143]

    [11]

    Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969

    [12]

    Ma W Q, Niu Y D, Wang R 2009 Acta Phys. Sin. 58 2934(in Chinese) [马文强、牛永迪、王 荣 2009 物理学报 58 2934]

    [13]

    Tong W J, Yu H J 2009 Acta Phys. Sin. 58 2977 (in Chinese) [童伟君、于洪洁、2009 物理学报 58 2977]

    [14]

    Gao J H, Peng J H, Xie L L 2009 Acta Phys. Sin. 58 5218(in Chinese) [高继华、彭建华、谢玲玲 2009 物理学报 58 5218]

    [15]

    Luo X S, Qiu D Y, Wei D Q, Zhang B 2009 Acta Phys. Sin. 58 6026 (in Chinese) [罗晓曙、丘东元、韦笃取、张 波 2009 物理学报 58 6026]

    [16]

    Chen Q H, Li H Q, Luo X H 2009 Acta Phys. Sin. 58 7532(in Chinese) [陈秋华、李华青、罗小华 2009 物理学报 58 7532]

    [17]

    Zhou J H, Deng M Y, Tang G N, Kong L J, Liu M R 2009 Acta Phys. Sin. 58 6828 (in Chinese)

    [18]

    Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 140 (in Chinese) [行鸿彦、金天力 2010物理学报 59 140]

    [19]

    Wang X F, Xue H J, Shi S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) [王校锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3279]

    [20]

    Li L X, Peng H P, Yang Y X 2008 Acta Phys. Sin. 57 703 (in Chinese)[李丽香、彭海朋、杨义先 2008 物理学报 57 703]

    [21]

    Wang G L, Yang P C, Mao Y Q 2008 Acta Phys. Sin. 57 714 (in Chinese)[王革丽、杨培才、毛宇清 2008 物理学报 57 714]

    [22]

    Zhang J F, Hu S S 2007 Acta Phys. Sin. 56 713 (in Chinese) [张军峰、胡寿松 2007 物理学报 56 713]

    [23]

    Niu P F, Zhang J, Guan X P 2007 Acta Phys. Sin. 56 2493 (in Chinese) [牛培峰、张 君、关新平 2007 物理学报 56 2493]

    [24]

    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]

    [25]

    Ye M Y 2005 Acta Phys. Sin. 54 30 (in Chinese) [叶美盈 2005 物理学报 54 30]

    [26]

    Wang D F 2005 Acta Phys. Sin. 54 1495 (in Chinese) [王东风 2005 物理学报 54 1495]

    [27]

    Yang G L, Li H G 2009 Acta Phys. Sin. 58 7552 (in Chinese) [杨国良、李惠光 2009 物理学报 58 7552]

    [28]

    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]

    [29]

    Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才、宋佳秋 2008 物理学报 57 4729]

    [30]

    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]

    [31]

    Lü J, Chen G R, Zhang D Z, Celikovsky S 2002 Int. J. Bifurcat. Chaos 12 2917

    [32]

    Yang S K, Chen S L, Yau H T 2002 Chaos, Solitons and Fractals 13 767

    [33]

    Yassen M T 2005 Chaos, Solitons and Fractals 23 1245

    [34]

    Broomhead D S, Low D 1998 Complex Systems 2 321

    [35]

    Powell M J D 1992 Advances in Numerical Analysis (Oxford: Oxford Univ. Press) p 46

    [36]

    Edwards Ch, Spurgeon S K 1998 Sliding mode control-theory and applications (London, Bristol: Taylor & Francis) p121

  • [1]

    Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196

    [2]

    Chen G, Dong X 1993 Int. J. Bifur. Chaos. 3 1363

    [3]

    Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1

    [4]

    Li D, Wang S L,Yang D, Zhang X H 2009 Acta Phys. Sin. 58 1432 (in Chinese)[李 东、王时龙、杨 丹、张小洪 2009 物理学报 58 1432]

    [5]

    Yang J, Qi D L 2010 Chin. Phys. B 19 020508-1

    [6]

    Hao J H, Wu S H, Xu H B 2010 Chin. Phys. B. 19 020509-1

    [7]

    Cai G L, Miao S T, Li X, Wang H X 2010 Chin. Phys. B 19 030509-1

    [8]

    Liu C X, Xu Z, Yang T 2010 Acta Phys. Sin. 59 1524(in Chinese)[刘崇新、许 喆、杨 韬 2010 物理学报 59 1524]

    [9]

    Lai X Q, Li Z H, Wang H, Ye Q, Yuan B, Zhao Y R 2010 Acta Phys. Sin. 59 2256(in Chinese) [来新泉、李祖贺、王 慧、叶 强、袁 冰、赵永瑞 2010 物理学报 59 2256]

    [10]

    Tang G N, Yang C Y 2009 Acta Phys. Sin. 58 143(in Chinese) [唐国宁、杨朝羽 2009 物理学报 58 143]

    [11]

    Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969

    [12]

    Ma W Q, Niu Y D, Wang R 2009 Acta Phys. Sin. 58 2934(in Chinese) [马文强、牛永迪、王 荣 2009 物理学报 58 2934]

    [13]

    Tong W J, Yu H J 2009 Acta Phys. Sin. 58 2977 (in Chinese) [童伟君、于洪洁、2009 物理学报 58 2977]

    [14]

    Gao J H, Peng J H, Xie L L 2009 Acta Phys. Sin. 58 5218(in Chinese) [高继华、彭建华、谢玲玲 2009 物理学报 58 5218]

    [15]

    Luo X S, Qiu D Y, Wei D Q, Zhang B 2009 Acta Phys. Sin. 58 6026 (in Chinese) [罗晓曙、丘东元、韦笃取、张 波 2009 物理学报 58 6026]

    [16]

    Chen Q H, Li H Q, Luo X H 2009 Acta Phys. Sin. 58 7532(in Chinese) [陈秋华、李华青、罗小华 2009 物理学报 58 7532]

    [17]

    Zhou J H, Deng M Y, Tang G N, Kong L J, Liu M R 2009 Acta Phys. Sin. 58 6828 (in Chinese)

    [18]

    Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 140 (in Chinese) [行鸿彦、金天力 2010物理学报 59 140]

    [19]

    Wang X F, Xue H J, Shi S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) [王校锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3279]

    [20]

    Li L X, Peng H P, Yang Y X 2008 Acta Phys. Sin. 57 703 (in Chinese)[李丽香、彭海朋、杨义先 2008 物理学报 57 703]

    [21]

    Wang G L, Yang P C, Mao Y Q 2008 Acta Phys. Sin. 57 714 (in Chinese)[王革丽、杨培才、毛宇清 2008 物理学报 57 714]

    [22]

    Zhang J F, Hu S S 2007 Acta Phys. Sin. 56 713 (in Chinese) [张军峰、胡寿松 2007 物理学报 56 713]

    [23]

    Niu P F, Zhang J, Guan X P 2007 Acta Phys. Sin. 56 2493 (in Chinese) [牛培峰、张 君、关新平 2007 物理学报 56 2493]

    [24]

    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]

    [25]

    Ye M Y 2005 Acta Phys. Sin. 54 30 (in Chinese) [叶美盈 2005 物理学报 54 30]

    [26]

    Wang D F 2005 Acta Phys. Sin. 54 1495 (in Chinese) [王东风 2005 物理学报 54 1495]

    [27]

    Yang G L, Li H G 2009 Acta Phys. Sin. 58 7552 (in Chinese) [杨国良、李惠光 2009 物理学报 58 7552]

    [28]

    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]

    [29]

    Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才、宋佳秋 2008 物理学报 57 4729]

    [30]

    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]

    [31]

    Lü J, Chen G R, Zhang D Z, Celikovsky S 2002 Int. J. Bifurcat. Chaos 12 2917

    [32]

    Yang S K, Chen S L, Yau H T 2002 Chaos, Solitons and Fractals 13 767

    [33]

    Yassen M T 2005 Chaos, Solitons and Fractals 23 1245

    [34]

    Broomhead D S, Low D 1998 Complex Systems 2 321

    [35]

    Powell M J D 1992 Advances in Numerical Analysis (Oxford: Oxford Univ. Press) p 46

    [36]

    Edwards Ch, Spurgeon S K 1998 Sliding mode control-theory and applications (London, Bristol: Taylor & Francis) p121

  • [1] Lu Yong-Kun. Active adaptive fuzzy integral sliding mode control for unified chaotic system with uncertainties and disturbance. Acta Physica Sinica, 2012, 61(22): 220504. doi: 10.7498/aps.61.220504
    [2] Liu Fu-Cai, Song Jia-Qiu. Anti-synchronizing different chaotic systems using active sliding mode control. Acta Physica Sinica, 2008, 57(8): 4729-4737. doi: 10.7498/aps.57.4729
    [3] Li Yu-San, Wei Lin-Ling, Yu Miao, Zhang Meng. Chaos synchronization of regular network based on sliding mode control. Acta Physica Sinica, 2012, 61(12): 120504. doi: 10.7498/aps.61.120504
    [4] Li Hua-Qing, Liao Xiao-Feng, Huang Hong-Yu. Synchronization of uncertain chaotic systems based on neural network and sliding mode control. Acta Physica Sinica, 2011, 60(2): 020512. doi: 10.7498/aps.60.020512
    [5] Tao Chao-Hai, Lu Jun-An. Control of a unified chaotic system. Acta Physica Sinica, 2003, 52(2): 281-284. doi: 10.7498/aps.52.281
    [6] Gao Xin, Liu Xing-Wen. Delayed fuzzy control of a unified chaotic system. Acta Physica Sinica, 2007, 56(1): 84-90. doi: 10.7498/aps.56.84
    [7] Chen Shi-Hua, Lu Jun-An, Liu Jie. Projective synchronization in a unified chaotic system and its control. Acta Physica Sinica, 2003, 52(7): 1595-1599. doi: 10.7498/aps.52.1595
    [8] Wang Dong-Feng. Genetic algorithm optimization based proportional-integral-derivative controller for unified chaotic system. Acta Physica Sinica, 2005, 54(4): 1495-1499. doi: 10.7498/aps.54.1495
    [9] Lu Yong-Kun. Robust fractional-order proportional-derivative control of unified chaotic systems with parametric uncertainties. Acta Physica Sinica, 2015, 64(5): 050503. doi: 10.7498/aps.64.050503
    [10] Zhang Ruo-Xun, Cao He-Fei. Adaptive synchronization of fractional-order chaotic system via sliding mode control. Acta Physica Sinica, 2011, 60(5): 050510. doi: 10.7498/aps.60.050510
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  • Received Date:  06 March 2010
  • Accepted Date:  04 May 2010
  • Published Online:  15 January 2011

Active radial basis function sliding mode controller for unified chaotic system with disturbance and uncertainties

  • 1. (1)Department of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China; (2)Department of System Science and Engineering, Zhejiang University,Hangzhou 310027, China

Abstract: An adaptive active radial basis function (RBF) sliding mode controller is designed to control a unified chaotic system with parametric uncertainties under external disturbance. The controlled system is divided into a controllable subsystem and a free subsystem. Based on the controllable canonical form of controllable sub-systems state errors at the target points, a sliding surface is defined as the only input to the RBF controller. The weight of the controller is tuned on-line based on the sliding mode reaching law. The simulation results show that this method is applicable and effective, and the robustness to parametric uncertainties and external disturbance is provided. And the chattering of conventional sliding controls doesn’t occur.

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