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针对连续时间混沌(超混沌)系统的控制问题, 提出了一种基于扩张状态观测器的快速全线性广义预测控制算法. 利用线性扩张状态观测器估计和补偿混沌(超混沌)系统的非线性动力学和存在的不确定性, 将原始对象近似转化为积分器形式, 随后针对单积分器设计广义预测控制, 解决了预测控制计算量大的问题. 阶跃系数矩阵可以直接得到解析解, 而对于未来输出的预测则可以根据最近两个时刻的输出采样值直接计算得到, 避免了使用自校正算法和在线求解丢番图方程. 该线性算法可以直接应用于非线性对象的控制系统设计. 将该算法应用于典型Lorenz混沌系统的控制中, 数学仿真结果验证了有效性.A kind of fast linear generalized predictive control (GPC) algorithm is proposed based on the extended state observer for chaotic (hyperchaotic) systems. The linear extended state observer is employed to estimate and compensate the nonlinear dynamics and the existing uncertainties of the chaotic (hyperchaotic) systems so that an integrator can be obtained to serve as the model for GPC design. Using this scheme, the computational complexity can be substantially reduced. A step coefficient matrix can be derived analytically and a future output prediction can be explicitly calculated by only using the last two samples of the output. Therefore, the self-tuning algorithms and the Diophantine equation can be completely avoided. The proposed method can be used to control nonlinear targets in a straightforward manner. Simulation results show the effectiveness of this linear algorithm.
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Keywords:
- chaos /
- generalized predictive control /
- extended state observer /
- synchronization control
[1] Ott E, Gregobi C, Yorke A J 1990 Phys. Rev. Lett. 64 1196
[2] Tan W, Wang Y N, Liu Z R 2004 Control Theory and Appl. 20 951 (in Chinese) [谭文, 王耀南, 刘祖润 2004 控制理论与应用 20 951]
[3] Wang Z Y, Cai Y L, Jia D, Liu W J 2000 Control and Decision 15 55 (in Chinese) [王忠勇, 蔡远利, 贾冬, 刘文江 2000 控制与决策 15 55]
[4] Zhang Q S, Ding W C, Sun C 2008 Journal of Vibration and Shock 27 155 (in Chinese) [张庆爽, 丁旺才, 孙闯 2008 振动与冲击 27 155]
[5] Das S, Pan I, Das S, Gupta A 2012 Nonlinear Dyn. 69 2193
[6] Yao J, Guan Z H, Hill D J 2005 Int. J. Bifurcat. Chaos 15 3381
[7] Sun K H, Chen Z S, Zhang T S 2005 Control and Decision 20 207 (in Chinese) [孙克辉, 陈志盛, 张泰山 2005 控制与决策 20 207]
[8] Chang K M 2008 Chaos Soliton. Fract. 36 460
[9] Chang J F, Hung M L, Yang Y S, Liao T L, Yan J J 2008 Chaos Soliton. Fract. 37 609
[10] Yassen M T 2005 Chaos Soliton. Fract. 26 913
[11] Wen S H 2009 Acta Phys. Sin. 58 5209 (in Chinese) [温淑焕 2009 58 5209]
[12] Wen S H, Wang Z, Liu F C 2009 Acta Phys. Sin. 58 3753 (in Chinese) [温淑焕, 王哲, 刘福才 2009 58 3753]
[13] Chen Z W, Liu W L 2011 Acta Phys. Sin. 60 050506 (in Chinese) [陈志旺, 刘文龙 2011 60 050506]
[14] Clarke D W, Mohtadi C, Tuffs P S 1987 Automatica 23 137
[15] Clarke D W, Mohtadi C, Tuffs P S 1987 Automatica 23 149
[16] Xi Y G, Li J Y 1991 Control Theory and Appl. 8 419 (in Chinese) [席裕庚, 厉隽怿 1991 控制理论与应用 8 419]
[17] Wang W, Yang J J 1997 Control Theory and Appl. 14 777 (in Chinese) [王伟, 杨建军 1997 控制理论与应用 14 777]
[18] Henson M A 1998 Comput. Chem. Eng. 23 187
[19] Han J Q 2009 IEEE Trans. Ind. Electron. 56 900
[20] Gao Z Q 2010 Proceedings of the 29th Chinese Control Conference Beijing, China, July 29-31, 2010 p6071 (in Chinese) [高志强 2010 第29届中国控制会议论文集 北京, 中国, 7月29–31日, 2010 第6071页]
[21] Huang Y, Xue W C, Zhao C Z 2012 J. Sys. Sci. & Math. Scis. 31 1111 (in Chinese) [黄一, 薛文超, 赵春哲2012 系统科学与数学 31 1111]
[22] Gao Z Q 2003 Proceedings of the American Control Conference Denver, Colorado, June 4-6, 2003 p4989
[23] Li S, Li Y, Liu B, Murray T 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 12
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[1] Ott E, Gregobi C, Yorke A J 1990 Phys. Rev. Lett. 64 1196
[2] Tan W, Wang Y N, Liu Z R 2004 Control Theory and Appl. 20 951 (in Chinese) [谭文, 王耀南, 刘祖润 2004 控制理论与应用 20 951]
[3] Wang Z Y, Cai Y L, Jia D, Liu W J 2000 Control and Decision 15 55 (in Chinese) [王忠勇, 蔡远利, 贾冬, 刘文江 2000 控制与决策 15 55]
[4] Zhang Q S, Ding W C, Sun C 2008 Journal of Vibration and Shock 27 155 (in Chinese) [张庆爽, 丁旺才, 孙闯 2008 振动与冲击 27 155]
[5] Das S, Pan I, Das S, Gupta A 2012 Nonlinear Dyn. 69 2193
[6] Yao J, Guan Z H, Hill D J 2005 Int. J. Bifurcat. Chaos 15 3381
[7] Sun K H, Chen Z S, Zhang T S 2005 Control and Decision 20 207 (in Chinese) [孙克辉, 陈志盛, 张泰山 2005 控制与决策 20 207]
[8] Chang K M 2008 Chaos Soliton. Fract. 36 460
[9] Chang J F, Hung M L, Yang Y S, Liao T L, Yan J J 2008 Chaos Soliton. Fract. 37 609
[10] Yassen M T 2005 Chaos Soliton. Fract. 26 913
[11] Wen S H 2009 Acta Phys. Sin. 58 5209 (in Chinese) [温淑焕 2009 58 5209]
[12] Wen S H, Wang Z, Liu F C 2009 Acta Phys. Sin. 58 3753 (in Chinese) [温淑焕, 王哲, 刘福才 2009 58 3753]
[13] Chen Z W, Liu W L 2011 Acta Phys. Sin. 60 050506 (in Chinese) [陈志旺, 刘文龙 2011 60 050506]
[14] Clarke D W, Mohtadi C, Tuffs P S 1987 Automatica 23 137
[15] Clarke D W, Mohtadi C, Tuffs P S 1987 Automatica 23 149
[16] Xi Y G, Li J Y 1991 Control Theory and Appl. 8 419 (in Chinese) [席裕庚, 厉隽怿 1991 控制理论与应用 8 419]
[17] Wang W, Yang J J 1997 Control Theory and Appl. 14 777 (in Chinese) [王伟, 杨建军 1997 控制理论与应用 14 777]
[18] Henson M A 1998 Comput. Chem. Eng. 23 187
[19] Han J Q 2009 IEEE Trans. Ind. Electron. 56 900
[20] Gao Z Q 2010 Proceedings of the 29th Chinese Control Conference Beijing, China, July 29-31, 2010 p6071 (in Chinese) [高志强 2010 第29届中国控制会议论文集 北京, 中国, 7月29–31日, 2010 第6071页]
[21] Huang Y, Xue W C, Zhao C Z 2012 J. Sys. Sci. & Math. Scis. 31 1111 (in Chinese) [黄一, 薛文超, 赵春哲2012 系统科学与数学 31 1111]
[22] Gao Z Q 2003 Proceedings of the American Control Conference Denver, Colorado, June 4-6, 2003 p4989
[23] Li S, Li Y, Liu B, Murray T 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 12
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