On Forwarding Mod{lg V} Method Applied to Mechanical Systems

In this paper a nonlinear control methodology for mechanical systems based on the forwarding technique is considered. Forwarding takes advantage of the cascade structure of some nonlinear systems in order to design stabilizing control laws. A key step in this design technique is the obtention of the explicit solution to a partial differential equation (PDE), which may be hard to solve, and in some cases even not be solvable at all. In order to simplify the PDE we propose the combination between an energy shaping controller and a variant of the conventional forwarding, namely forwarding mod{L
_g
V}. This new method is illustrated with the design of a control law for an inverted pendulum