Persistency of excitation and overparametrization in model reference adaptive control

Abstract

In an overparametrized model reference adaptive control system, the measured signal (t) cannot be persistently exciting (PE) for any bounded reference input r(t). The controller parameter vector for model-plant transfer function matching lies in a linear variety in the parameter space and its estimate converges to this variety asymptotically if r(t) has enough frequencies. In the presence of disturbances or unmodeled dynamics, the PE property can no longer be used to achieve robustness unless no near-overparametrization exists. © 1990 IEEE