Lorenz混沌系统的近似有限时间稳定控制

赵建利; 王京; 魏伟

doi:10.7498/aps.60.100203

摘要

针对Lorenz混沌系统,研究其有限时间稳定控制问题.考虑系统存在不确定非线性,提出一种可使受控Lorenz系统实现近似有限时间稳定的控制方法.改进并设计一种扩张状态观测器,解决了受控Lorenz系统中不确定非线性未知问题.通过引入奇异扰动性理论,分析了闭环系统的近似有限时间稳定性.仿真实验结果验证了该控制方法及扩张状态观测器的有效性.

关键词:

In the paper, the finite-time stability control problem for the Lorenz chaos system is studied. Considering the existence of uncertainty and nonlinearity in the Lorenz chaos system, a control method is proposed, which makes the controlled Lorenz system achieve approximate finite-time stability. And one kind of extended state observer is improved and designed to solve the unknown problem of uncertainty and nonlinearity for the controlled Lorenz system. The approximate finite-time stability of the closed-loop system is analysed by introducing the singular perturbation theary. Simulation results show the effectiveness of the control method and observer.

Keywords:

作者及机构信息

1.
北京科技大学,高效轧制国家工程研究中心,北京 100083

基金项目: 国家高技术研究发展计划(批准号:2009AA04Z163)资助的课题.

Authors and contacts

1.
National Engineer Research Center of Advanced Rolling, University of Science and Technology Beijing, Beijing 100083, China

参考文献

[1]	Chen G R, L J H 2003 Dynamics Analysis,Control and Synchronization for Lorenz system families (1st ed)(Beijing: Science press) P1,P4(in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步(第一版)(北京:科学出版社) 第1页、第4页]
[2]	Yu J Z,Su N, Vincent T L 1998 Acta Phys.Sin. 47 P0397(in Chinese)[余建祖、苏楠 1998 47 P0397]
[3]
[4]	Tang G N,Luo X S,Kong L J 2000 Acta Phys.Sin. 49 0030(in Chinese)[唐国宁、罗晓曙、孔令江 2000 49 0030]
[5]
[6]	Chen M Y,Zhou D H,Shang Y 2004 Chaos,Solitions and Fractals 21 P295
[7]
[8]
[9]	Chen G P,Hao J B 2009 Acta Phys.Sin. 58 2914(in Chinese)[陈光平、郝加波 2009 58 2914]
[10]
[11]	Cai G L,Zheng S, Tian L X 2008 Chin.Phys. B 17 2412
[12]
[13]	Li S H, Tian Y P 2003 Chin.Phys. 12 P590
[14]
[15]	Wang Y N,Tan W,Duan F 2006 Chin.Phys. 15 P89
[16]	Qi D L,Wang Q,Gu H 2008 Chin.Phys. B 17 P847
[17]
[18]
[19]	Wang C, Ge S S 2001 International Journal of Bifurcation and Chaos 11 1115
[20]	Pishkenari H N, Meghdari A 2008 Proceeding of the 5th International Symposium on Mechatronics and its Applications (ISMA08) 8 4244
[21]
[22]	Bai E W,Karl E L 2000 Chaos,Solitons and Fractals 11 1041
[23]
[24]
[25]	Guo H J,Liu J H 2004 Acta Phys.Sin. 53 4080(in Chinese)[郭会军、刘君华 2004 53 4080]
[26]
[27]	Yang S K,Chen C L,Yau H T 2002 Chaos, Solitons and Fractals 13 767
[28]
[29]	Yau H T,Yan J J 2004 Chao,Solition and Fractals 19 891
[30]
[31]	Zhang H,Ma X K, Liu W Z 2004 Chaos,Solitons and Fractals 21 1249
[32]	Sanjay P B, Dennis S B 2005 Math.Control Signals Systems 17 101
[33]
[34]	Ahmad N A, Hassan K K.A 1999 IEEE Transactions on Automatic Control 44 1672
[35]
[36]
[37]	Zheng Q,Gao L Q, Gao Z Q 2007 Proceedings of the 46th IEEE Conference on Decision and Control ThB07.6 3501
[38]	Hassan K K 2007 Nonlinear Systems(3st ed)(Beijing:Publishing House of Electronics Industry) P613
[39]
[40]
[41]	Hassan K K 2008 International Conference on Control,Automation and Systems xlvii lvii
[42]
[43]	Kokotovic P,Hassan K 1986 Singular Perturbation Methods in control Analysis and Design(London:Academic Press, SIAM) P136
[44]
[45]	Zheng D Z 2002 Linear System Theory(2st ed)(Beijing: Tsinghua University Press) P238 (in Chinese) [郑大钟 2002 线性系统理论(第二版)(北京:清华大学出版社) 第238页]
[46]
[47]	Zhang K Y,Xu Z,Lu Q 2001 MATRIX THEARY(1st ed)(Xi an:Northwestern Polytechnical University Press) P83 (in Chinese)[张凯院、徐仲、陆全 2001 矩阵论(第一版)(西安:西北工业大学出版社) 第83页]
[48]	Andrea B,Lionel R 2005 Liapunov Functions and Stability in Control Theary(2st ed)(Springer-Verlag Berlin Heidelberg) P175
[49]

施引文献

[1]	Chen G R, L J H 2003 Dynamics Analysis,Control and Synchronization for Lorenz system families (1st ed)(Beijing: Science press) P1,P4(in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步(第一版)(北京:科学出版社) 第1页、第4页]
[2]	Yu J Z,Su N, Vincent T L 1998 Acta Phys.Sin. 47 P0397(in Chinese)[余建祖、苏楠 1998 47 P0397]
[3]
[4]	Tang G N,Luo X S,Kong L J 2000 Acta Phys.Sin. 49 0030(in Chinese)[唐国宁、罗晓曙、孔令江 2000 49 0030]
[5]
[6]	Chen M Y,Zhou D H,Shang Y 2004 Chaos,Solitions and Fractals 21 P295
[7]
[8]
[9]	Chen G P,Hao J B 2009 Acta Phys.Sin. 58 2914(in Chinese)[陈光平、郝加波 2009 58 2914]
[10]
[11]	Cai G L,Zheng S, Tian L X 2008 Chin.Phys. B 17 2412
[12]
[13]	Li S H, Tian Y P 2003 Chin.Phys. 12 P590
[14]
[15]	Wang Y N,Tan W,Duan F 2006 Chin.Phys. 15 P89
[16]	Qi D L,Wang Q,Gu H 2008 Chin.Phys. B 17 P847
[17]
[18]
[19]	Wang C, Ge S S 2001 International Journal of Bifurcation and Chaos 11 1115
[20]	Pishkenari H N, Meghdari A 2008 Proceeding of the 5th International Symposium on Mechatronics and its Applications (ISMA08) 8 4244
[21]
[22]	Bai E W,Karl E L 2000 Chaos,Solitons and Fractals 11 1041
[23]
[24]
[25]	Guo H J,Liu J H 2004 Acta Phys.Sin. 53 4080(in Chinese)[郭会军、刘君华 2004 53 4080]
[26]
[27]	Yang S K,Chen C L,Yau H T 2002 Chaos, Solitons and Fractals 13 767
[28]
[29]	Yau H T,Yan J J 2004 Chao,Solition and Fractals 19 891
[30]
[31]	Zhang H,Ma X K, Liu W Z 2004 Chaos,Solitons and Fractals 21 1249
[32]	Sanjay P B, Dennis S B 2005 Math.Control Signals Systems 17 101
[33]
[34]	Ahmad N A, Hassan K K.A 1999 IEEE Transactions on Automatic Control 44 1672
[35]
[36]
[37]	Zheng Q,Gao L Q, Gao Z Q 2007 Proceedings of the 46th IEEE Conference on Decision and Control ThB07.6 3501
[38]	Hassan K K 2007 Nonlinear Systems(3st ed)(Beijing:Publishing House of Electronics Industry) P613
[39]
[40]
[41]	Hassan K K 2008 International Conference on Control,Automation and Systems xlvii lvii
[42]
[43]	Kokotovic P,Hassan K 1986 Singular Perturbation Methods in control Analysis and Design(London:Academic Press, SIAM) P136
[44]
[45]	Zheng D Z 2002 Linear System Theory(2st ed)(Beijing: Tsinghua University Press) P238 (in Chinese) [郑大钟 2002 线性系统理论(第二版)(北京:清华大学出版社) 第238页]
[46]
[47]	Zhang K Y,Xu Z,Lu Q 2001 MATRIX THEARY(1st ed)(Xi an:Northwestern Polytechnical University Press) P83 (in Chinese)[张凯院、徐仲、陆全 2001 矩阵论(第一版)(西安:西北工业大学出版社) 第83页]
[48]	Andrea B,Lionel R 2005 Liapunov Functions and Stability in Control Theary(2st ed)(Springer-Verlag Berlin Heidelberg) P175
[49]

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