Adaptation and Nonlinear Parametrization: Nonlinear Dynamics Prospective

We consider adaptive control problems in the presence of nonlinear parametrization of model uncertainties. An approach that foregoes on the need for domination in the control loop during adaptation is proposed. Our approach is based on the notions of attractivity, limit sets, equilibria, and multistability from the theory of nonlinear dynamical systems rather than on the conventional method of Lyapunov functions. As a result of this, our algorithms are applicable to general smooth non-monotonic parametrization and do not require any damping or domination in control inputs. Copyright c © 2005 IFAC