A robustly stabilising adaptive controller for systems in feedback form

A novel algorithm for the stabilisation via state feedback of a class of linearly parameterised systems in feedback form is presented. The prominent feature of the proposed approach is that it allows for prescribed (uniformly stable) dynamics to be assigned to the estimation error, thus leading to a modular scheme which is easier to tune than the one obtained from Lyapunov redesign. An additional property is that, in contrast with adaptive feedback linearisation, the corresponding non-adaptive controller globally stabilises the system and renders it robust with respect to the estimation error, provided a structural condition on the regressor holds. Some extensions to systems with unknown control coefficients and appended dynamics are also considered. As an application the algorithm is used to design a longitudinal controller for an unmanned air vehicle and its efficacy is tested via simulations