Adaptively controlling non‐linear systems, using trajectory approximations

Abstract

The structure underlying most adaptive algorithms is a linear parametrized set. This set either represents the universe of controllers the adaptive algorithm can choose from in order to achieve the control task or it may represent a class of models the adaptive algorithm may exploit to approximate the open‐loop plant behaviour. In the latter approach the controller used to close the loop is selected via some non‐linear map of the identified model parameters. The emphasis is on approximating the vector field that generates the trajectories of the system. Alternatively we propose to predict the trajectories over a short period of time directly, not indirectly involving a representation of the ..