13 October 2008 Controlling Newton-Leipnik system via weak control Lyapunov function
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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.
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Yunzhong Song, 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); doi: 10.1117/12.807493; https://doi.org/10.1117/12.807493
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