Abstract
The method for controlling chaotic transition system was investigated using sampled-data. The output of chaotic transition system was sampled at a given sampling rate, then the sampled output was used by a feedbacks subsystem to construct a control signal for controlling chaotic transition system to the origin. Numerical simulations are presented to show the effectiveness and feasibility of the developed controller.
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References
Chen G, Dong X.From Chaos to Order: Perspectives, Methodologies and Applications[M]. Singapore: World Scientific Press, 1998.
LÜ Jin-hu, LU Jun-an, CHEN Shi-hua,Chaotic Time Series Analysis and Its Application[M]. Wuhan: Wuhan University Press, 2002. (in Chinese)
CHEN Shi-hua, LU Jun-an.The Introduction to Chaotic Dynamics[M]. Wuhan: Wuhan University of Hydraulic and Electric Engineering Press, 1998. (in Chinese)
Ott E, Grebogi C, Yorke J A. Controlling chaos[J].Phys Rev Lett, 1990,64(11): 1196–1199.
Fuh C C, Tung P C. Controlling chaos using differential geometric method[J].Phys Rev Lett, 1995,75(16):2952–2955.
Sanchez E N, Perez J P, Martinez M,et al. Chaos stabilization: an inverse optimal control approach [J].Latin Amer Appl Res, 2002,32(1):111–114.
LÜ Jin-hu, ZHANG Suo-chun. Controlling Chen's chaotic attractor using backstepping design based on parameters identification[J].Phys Lett A, 2001,286(2/3):148–152.
LÜ Jin-hu, ZHOU Tian-shou, ZHANG Suo-chun. Controlling Chen's chaotic attractor using feed-back function based on parameters identification[J].Chinese Physics, 2002,11(1):12–16.
Yang T, Chua L O. Control of chaos using sampled-data feedback control[J].Int J Bifurcation and Chaos, 1998,8(12):2433–2238.
Guo S M, Shieh L S, Chen G,et al. Ordering chaos in Chua's circuit: a sampled data feedback and digital redesign approach[J].Int J Bifurcation and Chaos, 2000,10(9):2221–2231.
YANG Ling, LIU Zeng-rong, MAO Jian-min. Controlling hyperchaos[J].Phys Rev Lett, 2000,84(1):67–70.
MAO Jian-min, LIU Zeng-rong, YANG Ling. Straight-line stabilization[J].Phys Rev E, 2000,62(4):4846–4849.
YANG Ling, LIU Zeng-rong. An improvement and proof of OGY method[J].Applied Mathematics and Mechanics (English Edition), 1998,19(1):1–8.
Lorenz E N. Deterministic non-periodic flows[J].J Atmos Sci, 1963,20(1):130–141.
Stewart I. The Lorenz attractor exists[J].Nature, 2000,406(6799):948–949.
Chen G, Ueta T. Yet another chaotic attractor[J].Int J Bifurcation and Chaos, 1999,9(7): 1465–1466.
Vaněcek A, Celikovský S.Control Systems: From Linear Analysis to Synthesis of Chaos[M]. London: Prentice-Hall, 1996.
LÜ Jin-hu, CHEN Guan-rong. A new chaotic attractor coined[J].Int J Bifurcation and Chaos, 2002,12(3):659–661.
LÜ Jin-hu, CHEN Guan-rong, ZHANG Suo-chun. Dynamical analysis of a new chaotic attractor [J].Int J Bifurcation and Chaos, 2002,12(5):1001–1015.
ZHOU Zhi-ming. A new chaotic auti-control model—Lü system[J]. J of Xianning Techers Colllege, 2002,22(3):19–21. (in Chinese)
LÜ Jin-hu, CHEN Guan-rong, CHENG Dai-zhan,et al. Bridge the gap between the Lorenz system and the Chen system[J].Int J Bifurcation and Chaos, 2002,12(12):2917–2926.
Wilkinson J.The Algebraic Eigenvalue Problem[M]. Oxford: Clarendon Press, 1965.
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Communicated by LIU Zeng-rong
Foundation items: the National Natural Science Foundation of China (50209012); Chinese Postdoctoral Science Foundation; K. C. Wong Education Foundation, Hong Kong
Biography: LU Jun-an (1945≈)
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Jun-an, L., Jin, X., Jin-hu, L. et al. Control chaos in transition system using sampled-data feedback. Appl Math Mech 24, 1309–1315 (2003). https://doi.org/10.1007/BF02439654
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DOI: https://doi.org/10.1007/BF02439654