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

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.

References in corpus (2)

• On the generalized Helmholtz conditions for Lagrangian systems with dissipative forces
• The inverse problem for Lagrangian systems with certain non-conservative forces

Cited by in corpus (1)

• An extension to the theory of controlled Lagrangians using the Helmholtz conditions