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This paper designs an adaptive and robustness backstepping control law to realize the control of Rossler-like systems of uncertainties. First, a wavelet network is used for the identification the nonlinear part of the system to change it into parametric model with parametric and structural uncertainties; Then, for the parameter uncertainties, an adaptive control law is designed to online estimate the unknown parameters; for the structural uncertainties, a robust control law is designed to make the system robustness. Finally, The effective of this methodology is illustrated by the simulation results.
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Keywords:
- adaptive backstepping /
- chaos control /
- wavelet network /
- robustness
[1] Krstic M, Kanellakopoulos I, Kokotovic P 1995 Nonlinear and Adaptive Control Design (New York: Wiley)pp124—183
[2] Cai G L, Tan Z M, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese)[蔡国梁,谭振梅, 周维怀, 涂文桃 2007 物理学报 56 6230]
[3] Zheng J F, Feng Y, Zheng X M, Yang X Q 2009 Control Theory & Applications 26 410 (in Chinese)[郑剑飞, 冯勇, 郑雪梅,杨旭强 2009 控制理论与应用 26 410]
[4] Zhang T, Ge S S, Hang C C 2000 Automatica 36 1835
[5] Li Y H, Sheng Q, Zhuang X Y, Kaynak O 2004 IEEE Trans. Neural Networks 15 693
[6] Kwan C M, Lewis F L 2004 IEEE Trans. Neural Networks 11 1178
[7] Peng Y F, Hsu C F 2009 Chaos, Solitons and Fractals 41 1377
[8] Hsu C F, Lin C M 2005 Fuzzy Set Syst. 151 43
[9] Zhang Q, Benveniste A 1992 IEEE Trans. Neural Networks 3 889
[10] Zhang Q 1997 IEEE Trans. Neural Networks 8 227
[11] zhang Q 1992 Technical Report LITH-ISY-I-1423 (Linkoping University)
[12] Hsu C F, Lin C M, Lee T T 2006 IEEE Trans. Neural Networks 7 1175
[13] Wai R J, Chang H H 2004 IEEE Trans. Neural Networks 5 367
[14] Lin F J, Shieh H J, Huang P K 2006 IEEE Trans. Neural Networks 17 432
[15] Wang H O, Tanaka K 1996 IEEE Trans. Fuzz. Syst. 3 1433
[16] Miao Z Q, Wang Y N 2010 J. Dynamics & Control 8 229 (in Chinese)[缪志强, 王耀南 2010 动力学与控制学报 8 229]
[17] Thomas R 1999 Int. J. Bifur. Chaos 9 1889 030503-6
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[1] Krstic M, Kanellakopoulos I, Kokotovic P 1995 Nonlinear and Adaptive Control Design (New York: Wiley)pp124—183
[2] Cai G L, Tan Z M, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese)[蔡国梁,谭振梅, 周维怀, 涂文桃 2007 物理学报 56 6230]
[3] Zheng J F, Feng Y, Zheng X M, Yang X Q 2009 Control Theory & Applications 26 410 (in Chinese)[郑剑飞, 冯勇, 郑雪梅,杨旭强 2009 控制理论与应用 26 410]
[4] Zhang T, Ge S S, Hang C C 2000 Automatica 36 1835
[5] Li Y H, Sheng Q, Zhuang X Y, Kaynak O 2004 IEEE Trans. Neural Networks 15 693
[6] Kwan C M, Lewis F L 2004 IEEE Trans. Neural Networks 11 1178
[7] Peng Y F, Hsu C F 2009 Chaos, Solitons and Fractals 41 1377
[8] Hsu C F, Lin C M 2005 Fuzzy Set Syst. 151 43
[9] Zhang Q, Benveniste A 1992 IEEE Trans. Neural Networks 3 889
[10] Zhang Q 1997 IEEE Trans. Neural Networks 8 227
[11] zhang Q 1992 Technical Report LITH-ISY-I-1423 (Linkoping University)
[12] Hsu C F, Lin C M, Lee T T 2006 IEEE Trans. Neural Networks 7 1175
[13] Wai R J, Chang H H 2004 IEEE Trans. Neural Networks 5 367
[14] Lin F J, Shieh H J, Huang P K 2006 IEEE Trans. Neural Networks 17 432
[15] Wang H O, Tanaka K 1996 IEEE Trans. Fuzz. Syst. 3 1433
[16] Miao Z Q, Wang Y N 2010 J. Dynamics & Control 8 229 (in Chinese)[缪志强, 王耀南 2010 动力学与控制学报 8 229]
[17] Thomas R 1999 Int. J. Bifur. Chaos 9 1889 030503-6
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