“Stabilization of Stable Manifold of Upright Position of the Spherical Pendulum”

Authors: Hallgeir Ludvigsen, Anton Shiriaev and Olav Egeland,
Affiliation: Cybernetica and NTNU, Department of Engineering Cybernetics
Reference: 2001, Vol 22, No 1, pp. 3-14.

Keywords: Passivity, stabilization of the upright position of the spherical pendulum

Abstract: The stabilization problem of the upright position of the sherical pendulum is treated in detail. This problem is reduced to the stabilization of the stable manifold Omega_st 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 Omega_st the closed loop system has a limit cycle Gamma, which does not belong to the desired attractor Omega_st. It is shown that Gamma is hyperbolic.

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BibTeX:
@article{MIC-2001-1-1,
  title={{Stabilization of Stable Manifold of Upright Position of the Spherical Pendulum}},
  author={Ludvigsen, Hallgeir and Shiriaev, Anton and Egeland, Olav},
  journal={Modeling, Identification and Control},
  volume={22},
  number={1},
  pages={3--14},
  year={2001},
  doi={10.4173/mic.2001.1.1},
  publisher={Norwegian Society of Automatic Control}
};