New approach to control and filtering of mechanical systems by using the estimates of their Lagrangians

When a mechanical system is defined by its Lagrangian, some control problems can be solved by using directly the latter, instead of the dynamical equations themselves; this is based upon the property that the dynamics is continuous with respect to the Lagrangian. After stating the main lemma which supports the approach, we consider applications to active mechanical systems, that is to say, with time-varying structural parameters, to tracking control via external applied forces, and to state estimation problems for which we propose a new variational principle.This research was supported by the National Research Council of Canada.