Adaptive stabilization of a class of nonlinear systems with nonparametric uncertainty

We consider adaptive stabilization for a class of nonlinear second-order sy stems. Interpreting the system states as position and velocity, the system is assumed to have unknown, nonparametric position-dependent damping and st iffness coefficients. Lyapunov methods are used to prove global convergence of the adaptive controller. Furthermore, the controller is shown to be abl e reject constant disturbances and to asymptotically track constant command s. For illustration, the controller is used to stabilize the van der Pol li mit cycle, the Duffing oscillator with multiple equilibria, and several oth er example systems.