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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 物理学报 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 物理学报 58 3753]
[13] Chen Z W, Liu W L 2011 Acta Phys. Sin. 60 050506 (in Chinese) [陈志旺, 刘文龙 2011 物理学报 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 物理学报 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 物理学报 58 3753]
[13] Chen Z W, Liu W L 2011 Acta Phys. Sin. 60 050506 (in Chinese) [陈志旺, 刘文龙 2011 物理学报 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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