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Stabilization of stable manifold of upright position of the spherical pendulum

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3 Author(s)
H. Ludvigsen ; Dept. of Eng. Cybern., Norwegian Univ. of Sci. & Technol., Trondheim, Norway ; A. Shiriaev ; O. Egeland

The stabilization problem of the upright position of the controlled spherical pendulum is treated in detail. This problem is reduced to the stabilization of the stable manifold Ωst of the upright position of the unforced spherical pendulum. It is shown that for any smooth feedback control derived by the speed-gradient algorithm with the objective to stabilize Ωst the closed loop system has a limit cycle Γ, which does not belong to the desired attractor Ωst. It is shown that Γ is hyperbolic

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American Control Conference, 1999. Proceedings of the 1999  (Volume:6 )

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