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For chaos control problem, in accordance with the constraints of control system energy, a quadratic objective function is first determined, and then a simple method for obtaining the optimal control law is proposed. This method gives the optimal control law by solving linear quadratic optimal control problem and avoids the difficulty of solving Hamilton-Jacobi-Bellman equation. Using Lyapnuov method, we prove the stability of the closed-loop system. For the unified chaotic system and Liu chaotic system the simulation results show the effectiveness of the control method.
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Keywords:
- chaos control /
- linear state feedback /
- unified chaotic system /
- Liu chaotic system
[1] ［1］Colet P, Roy R 1994 Opt. Lett. 19 2056
[2] ［2］Sugawara T, Tachikawa M, Tsukamoto T, Shimizu T 1994 Phys. Rev. Lett. 72 3502
[3] ［3］Lu J A, Wu X Q, Lü J H 2002 Phys. Lett. A 305 365
[4] ［4］Ott E, Grebogi C, Yorke A J 1990 Phys. Rev. Lett. 64 1196
[5] ［5］Pyragas K 1992 Phys. Lett. A 170 421
[6] ［6］Pyragas K 1993 Phys. Lett. A 180 99
[7] ［7］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 物理学报 49 0030］
[8] ［8］Guan X P, Fan Z P, Peng H P, Wang Y Q 2001 Acta Phys. Sin. 50 2108 (in Chinese) ［关新平、范正平、彭海朋、王益群 2001 物理学报 50 2108］
[9] ［9］Song Y Z, Zhao G Z, Qi D L 2007 Control Theory and Applications 24 795 (in Chinese) ［宋运忠、赵光宙、齐冬莲 2007 控制理论与应用 24 795］
[10] ］Gao X，Liu X W 2007 Acta Phys. Sin. 56 0084 (in Chinese) ［高心、刘兴文 2007 物理学报 56 0084］
[11] ］Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) ［王发强、刘崇新 2006 物理学报 55 5055］
[12] ］Chen X P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) ［陈光平、郝加波 2009 物理学报 58 2914］
[13] ］Wang X F, Xue H J, Si S K,Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) ［王晓锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3729］
[14] ］Lü J H，Chen G, Cheng D, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[15] ］Liu C X, Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[16] ］Zheng D Z 2002 Linear System Theory (2nd Ed.) p324 (Beijing: Tsinghua University Press) (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324页］
[17] ］Lorenz E N 1963 J. Atmos. Sci. 20 130
[18] ］Lü J, Chen G 2002 Int. J. Bifur. Chaos 12 659
[19] ］Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
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[1] ［1］Colet P, Roy R 1994 Opt. Lett. 19 2056
[2] ［2］Sugawara T, Tachikawa M, Tsukamoto T, Shimizu T 1994 Phys. Rev. Lett. 72 3502
[3] ［3］Lu J A, Wu X Q, Lü J H 2002 Phys. Lett. A 305 365
[4] ［4］Ott E, Grebogi C, Yorke A J 1990 Phys. Rev. Lett. 64 1196
[5] ［5］Pyragas K 1992 Phys. Lett. A 170 421
[6] ［6］Pyragas K 1993 Phys. Lett. A 180 99
[7] ［7］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 物理学报 49 0030］
[8] ［8］Guan X P, Fan Z P, Peng H P, Wang Y Q 2001 Acta Phys. Sin. 50 2108 (in Chinese) ［关新平、范正平、彭海朋、王益群 2001 物理学报 50 2108］
[9] ［9］Song Y Z, Zhao G Z, Qi D L 2007 Control Theory and Applications 24 795 (in Chinese) ［宋运忠、赵光宙、齐冬莲 2007 控制理论与应用 24 795］
[10] ］Gao X，Liu X W 2007 Acta Phys. Sin. 56 0084 (in Chinese) ［高心、刘兴文 2007 物理学报 56 0084］
[11] ］Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) ［王发强、刘崇新 2006 物理学报 55 5055］
[12] ］Chen X P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) ［陈光平、郝加波 2009 物理学报 58 2914］
[13] ］Wang X F, Xue H J, Si S K,Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) ［王晓锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3729］
[14] ］Lü J H，Chen G, Cheng D, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[15] ］Liu C X, Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[16] ］Zheng D Z 2002 Linear System Theory (2nd Ed.) p324 (Beijing: Tsinghua University Press) (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324页］
[17] ］Lorenz E N 1963 J. Atmos. Sci. 20 130
[18] ］Lü J, Chen G 2002 Int. J. Bifur. Chaos 12 659
[19] ］Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
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