Lyapunov design for convergence rate improvement in adaptive control

Abstract

This note deals with the improvement of the convergence rate and robust properties in an adaptive error model. A new adaptive control algorithm is presented which includes both the estimate of the prediction error to drive the parameter adaptation and the proportional-integral or integral-relay adjustment law. To prevent unbounded growth of feedback gains, a least-squares gain update is used. The adaptive controller is constructed using measurements of state variables only. The design is based on the Lyapunov function method and a new general form of the Lyapunov function was found. As a result, exponential convergence of the Lyapunov function in the presence of persistent excitation, is obtained.