Controlling Newton-Leipnik system via weak control Lyapunov function

Yunzhong Song; Huimin Xiao

doi:10.1117/12.807493

13 October 2008 Controlling Newton-Leipnik system via weak control Lyapunov function

Yunzhong Song, Huimin Xiao

Proceedings Volume 7129, Seventh International Symposium on Instrumentation and Control Technology: Optoelectronic Technology and Instruments, Control Theory and Automation, and Space Exploration; 71291I (2008) https://doi.org/10.1117/12.807493
Event: Seventh International Symposium on Instrumentation and Control Technology, 2008, Beijing, China

Abstract

Controller via Weak Control Lyapunov Function (WCLF) was presented for Newton-Leipnik equation, which has two strange attractors: the upper attractor (UA) and the lower attractor (LA). The final structure of this controller for original stabilization has a variable-structure nonlinear feedback form. Through WCLF principle, three different kinds of chaotic control were investigated, separately: the original control forcing the chaotic motion to settle down to the origin from any arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.

Citation Download Citation

Yunzhong Song and Huimin Xiao "Controlling Newton-Leipnik system via weak control Lyapunov function", Proc. SPIE 7129, Seventh International Symposium on Instrumentation and Control Technology: Optoelectronic Technology and Instruments, Control Theory and Automation, and Space Exploration, 71291I (13 October 2008); https://doi.org/10.1117/12.807493

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