Composite learning: An efficient way of parameter estimation in adaptive control

Abstract

Parameter convergence is desirable in adaptive control as it brings several attractive features, including accurate online identification, exponential tracking and robust adaptation without parameter drift. However, a strong persistent-excitation (PE) condition has to be satisfied to guarantee parameter convergence in the conventional adaptive control. This paper proposes a novel composite learning technique to guarantee parameter convergence without the PE condition for a class of affine nonlinear systems with parametric uncertainties. In the composite learning, a time-interval integral is utilized to construct a prediction error, a linear filter is applied to estimate the derivative of a tracking error, and both the tracking error and the prediction error are employed to update parametric estimates. It is proven that the closed-loop system achieves semiglobal practical exponential stability by an interval excitation (IE) condition which is much weaker than the PE condition. The effectiveness of this approach has been illustrated by a numerical example of aircraft wing rock control.