The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems
Abstract
We apply methods of the socalled `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of twodimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2016
 arXiv:
 arXiv:1602.01673
 Bibcode:
 2016arXiv160201673F
 Keywords:

 Mathematical Physics;
 Mathematics  Dynamical Systems;
 Mathematics  Optimization and Control;
 70H03;
 70Q05;
 49N45
 EPrint:
 SIAM J. Control Optim. 546 (2016), pp. 32973318