The Inverse Problem of the Calculus of Variations and the Stabilization of Controlled Lagrangian Systems

@article{Puiggal2016TheIP,
  title={The Inverse Problem of the Calculus of Variations and the Stabilization of Controlled Lagrangian Systems},
  author={Marta Farr{\'e} Puiggal{\'i} and Tom Mestdag},
  journal={SIAM J. Control. Optim.},
  year={2016},
  volume={54},
  pages={3297-3318}
}
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the inverted pendulum on a cart and the inertia wheel pendulum. By making use of a condition that follows from Douglas' classification, we derive feedback controls for which the control system is variational. We then use the energy of a suitable controlled… 

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