Immersion and invariance model reference adaptive control: New parameterizations for the problem

In a series of recent papers the authors have introduced a novel approach to adaptive control exploiting the geometric ideas of system immersion, and manifold invariance. A unique feature of this framework is that it allows to treat in a unified manner the problems of state and parameter estimation. In this brief paper we revisit the classical model reference adaptive control from the immersion and invariance perspective and provide new parameterizations (in terms of the unknown state) to the problem. This radically new viewpoint yields very simple schemes with a clear stabilization mechanism that, in contrast with the classical solutions, does not rely on slow parameter adaptation-induced by the introduction of signal normalization.