A UGES Switched MRAC Architecture Using Initial Excitation

Abstract

This work proposes a novel switched model reference adaptive control (MRAC) architecture, ensuring parameter convergence without requiring the assumption of persistence of excitation (PE). Previous results which ensure parameter convergence with PE suffer from the disadvantage that the condition cannot be verified online as it relies on the future behaviour of the signal. Further, the PE requirement is often imposed by adding perturbation in the reference/input signal, which may deteriorate tracking performance, and thus renders the objectives of control and identification conflicting to each other. Unlike PE, this work ensures parameter convergence by imposing a newly defined, significantly milder, and online verifiable initial excitation (IE) assumption. A switched composite parameter estimator is designed with the help of two layers of low pass filters, where the first layer obviates the need for state derivative knowledge and the second layer along with the switching term in the estimator relaxes the PE condition. Provided the IE condition is satisfied, the proposed design guarantees uniform global exponential stability (UGES) of the error dynamics, where the convergence rate is user-assignable.