Incorporating the true plant dynamics in a non-linear adaptation design for model reference adaptive control

In this paper, a non-linear approach to the design of model reference adaptive control is presented. The essence of the idea is to generate a full non-linear model of the plant dynamics and the parameter adaptation dynamics as a gradient descent algorithm with respect to a Riemannian metric. It is shown how a Riemannian metric can be chosen so that the modelled plant dynamics do in fact match the true plant dynamics. The approach is demonstrated by a case study of a simple single-pole and no zero, discrete-time plant.