Higher Order Tracking Properties of Model Reference Adaptive Control Systems

It is well known that for a linear time-invariant plant whose transfer function has relative degree n* and stable zeros, a model reference adaptive control (MRAC) system ensures that the plant output y(t) asymptotically tracks the output ym(t) of a stable reference model system of the same relative degree n*: limt→∞(y(t) - ym(t)) = 0. In this note, it is shown that under the same MRAC design conditions without the knowledge of the plant parameters, an MRAC system ensures that the tracking error e(t) = y(t) - ym(t) has the stronger higher order convergence die(t) property: limt→∞(die(t))/(dti) = 0, for i = 0,1,..., n*-1. Such a new MRAC system property leads to several new results of adaptive stabilization and tracking control using either state feedback or output feedback, as clarified in this paper.