Adaptive Regulation for Nonlinear Systems with Unknown Virtual Control Coefficient and Nonlinear Parameterization

A global adaptive stabilizer is developed for a class of nonlinear systems which contains an unknown virtual control coefficient and nonlinear parameterization. By using a new parameter estimator and backstepping technique, we design a smooth state feedback control law, a 2-dimensional parameter update law that estimates an unknown virtual control coefficient and parameter uncertainties, and a C1 Lyapunov function which is positive definite and proper.