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)
aSchool of Automation Science and Electrical Engineering, Beijing University of Aeronautics & Astronautics, Beijing 100083, China; bDepartment 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.
Received: 26 April 2007
Revised: 04 September 2007
Accepted manuscript online:
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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