Nonlinear adaptive control of systems in feedback form: An alternative to adaptive backstepping

An algorithm for the regulation via state feedback of a class of linearly parameterised systems in feedback form is presented. The algorithm resembles the well-known adaptive backstepping/tuning functions approach, but differs in the way the parameter estimator is constructed and in the way the nonlinear damping factors are assigned. 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 and practically recovers the performance of the known-parameter controller. For systems with matched uncertainties 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. A comparative example is presented, highlighting the advantages of the proposed methodology.