Composite Learning From Adaptive Dynamic Surface Control

In the conventional adaptive control, a stringent condition named persistent excitation (PE) must be satisfied to guarantee parameter convergence. This technical note focuses on adaptive dynamic surface control for a class of strict-feedback nonlinear systems with parametric uncertainties, where a novel technique coined composite learning is developed to guarantee parameter convergence without the PE condition. In the composite learning, online recorded data together with instantaneous data are applied to generate prediction errors, and both tracking errors and prediction errors are utilized to update parametric estimates. The proposed approach is also extended to an output-feedback case by using a nonlinear separation principle. The distinctive feature of the composite learning is that parameter convergence can be guaranteed by an interval-excitation condition which is much weaker than the PE condition such that the control performance can be improved from practical asymptotic stability to practical exponential stability. An illustrative example is used for verifying effectiveness of the proposed approach.