Robust adaptive control for a class of nonlinear systems with complex uncertainties

This paper considers a robust adaptive stabilization problem for a class of uncertain nonlinear systems which include an unknown virtual control coefficient, an unknown constant parameter, and a time-varying disturbance whose bound is unknown. We propose a new estimator for an unknown virtual control coefficient and present a robust adaptive backstepping design procedure which results in a smooth state feedback control law, a new two-dimensional parameter update law, and a C1 Lyapunov function which is positive definite and proper.