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arXiv · 1602.01673

The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems

M. Farré Puiggalí·T. Mestdag
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Abstract

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 Lagrangian to provide a stability criterion for the equilibrium.

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M. Farré Puiggalí, T. Mestdag. 2016-02-04. The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems. https://doi.org/10.1137/16m1060091

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