Adaptive passivation of a class of uncertain nonlinear systems

We propose in this work an adaptive passivation procedure for affine nonlinear systems with constant but unknown parameters, which is achievable through an adaptive state-dependent input coordinate transformation. The unknown parameters are assumed to enter linearly into the drift vector fields of the dynamic equations defining the nonlinear system. It is shown that the update law designed for the unknown parameters qualifies as a "force which does not work" in the context of a general passivity canonical form for nonlinear systems. The design of passivity-based controllers, via energy shaping and damping injection, is addressed and an application of this approach for the adaptive stabilization of a gravity-tank/pipe system is also considered.