Adaptive tracking in pure-feedback nonlinear systems

A method of adaptive tracking for pure-feedback nonlinear systems is presented for the case where linear parameterization conditions are met. The resulting adaptive controllers can be viewed as a state-space model reference adaptive controller with updating of both the state diffeomorphism and the control variables. The tracking problem is considered with respect to parametric and dynamic uncertainties, while prior results have been limited to the parametric uncertainty. Restrictive assumptions on the unknown parameters are removed, overparameterization is avoided, computation time is considerably reduced, and an error model is derived for formulation of the adaptive tracking problem. The robustness of the adaptive controller with respect to unmodeled dynamics is analyzed, and simulation results are presented