Persistency of excitation and overparameterization in model reference adaptive control

It is shown that if a model-reference adaptive controller is designed for an overparameterized plant, the persistence of excitation of the measured vector signal in the adaptive loop will be lost independently of the number of frequencies in the reference input. The model-plant transfer-function-matching parameters lie in a linear variety in the parameter space. The estimated parameters will converge to this variety if the reference input has enough frequencies. Parameter perturbations and unmodeled dynamics in the plan may cause near-overparameterization which can result in a low level of persistent excitation (PE). The loss of PE or the low level of PE can lead to loss of stability and robustness in the presence of modeling errors