Parameter Convergence in Adaptive Control in Presence of Unmatched Uncertainty

The problem of convergence of uncertainties to their true values is of great interest in adaptive control. It is desirable as it facilitates accurate online modeling of structured uncertainties and robust adaptation to disturbances. The adaptation law based on the classical gradient method requires the restrictive persistent excitation (PE) condition to be satisfied for parameter convergence. This paper deals with the relaxation of this PE condition for a class of nonlinear systems in the presence of unmatched uncertainty. The design of the proposed adaptive backstepping controller involves multiple filtered models that translate the restrictive PE condition to linear independence of the filtered regressor models. The proposed controller guarantees asymptotic convergence of the tracking and parameter estimation errors globally in the presence of unmatched uncertainty. Numerical simulations show the efficacy of the proposed controller.