Bloch, A. M., J. E. Marsden and G. Sánchez
The basic idea is to modify the kinetic energy of the free Lagrangian using a generalization of the Kaluza-Klein construction in such a way that the extra terms obtained in the Euler-Lagrange equations can be identified with control forces. The fact that the controlled system is Lagrangian by construction enables one to make use of energy techniques for a stability analysis. Once stabilization is achieved in a mechanical context, one can establish asymptotic stabilization by the further addition of dissipative controls. The methods here can be combined with symmetry breaking controls obtained by modifying the potential energy and also can be used for tracking.