Dynamic extension for adaptive backstepping control of uncertain pure-feedback systems

An adaptive backstepping algorithm is developed for a class of uncertain systems in pure-feedback form. The control is based on a dynamic state feedback that allows to compensate for parametric uncertainties which enter linearly into the system. As possible in the nominal case, a dynamic extension of just order one is required, in addition to the dynamics of the identifiers for the adaptation. The regularity of the control law only requires standard assumptions.