A Geometric Framework for Stabilization by Energy Shaping: Sufficient Conditions for Existence of Solutions

Abstract

We present a geometric formulation for the energy shaping problem. The central objective is the initiation of a more systematic exploration of energy shaping with the aim of de- termining whether a given system can be stabilized using energy shaping feedback. We investigate the partial differential equations for the kinetic energy shaping problem using the formal theory of partial differential equations. The main contribution is sufficient conditions for integrability of these partial differential equations. We couple these results with the integrability results for potential energy shaping. This gives some new avenues for answering key questions in energy shaping that have not been addressed to this point.