Bias issues in closed loop identification with application to adaptive control

Abstract

It is well known in system identification that, under output feedback control without persistent excitation, the resultant estimate of the process will be biased. In non-parametric identification the estimate is biased towards the negative inverse of the controller. A similar relationship is shown to exist for parametric identification. Indeed, we show the existence of a fundamental sensitivity to the noise model in the parametric case. However, in the parametric case, constraints are generally required, depending on the relative degree of the controller, to ensure a causal estimate. The implications of this bias to a simple adaptive control algorithm are also examined.