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Chin. Phys. B, 2008, Vol. 17(2): 507-519    DOI: 10.1088/1674-1056/17/2/028
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Controlling chaos based on an adaptive nonlinear compensator mechanism

Tian Ling-Ling(田玲玲)a), Li Dong-Hai(李东海)b), and Sun Xian-Fang(孙先仿)a)
a School of Automation Science and Electrical Engineering, Beijing University of Aeronautics & Astronautics, Beijing 100083, China; b Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
Abstract  The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.
Keywords:  chaotic system      nonlinear compensator mechanism      Lorenz chaotic system  
Received:  26 April 2007      Revised:  04 September 2007      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  
  07.05.Dz (Control systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 50376029).

Cite this article: 

Tian Ling-Ling(田玲玲), Li Dong-Hai(李东海), and Sun Xian-Fang(孙先仿) Controlling chaos based on an adaptive nonlinear compensator mechanism 2008 Chin. Phys. B 17 507

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