Adaptive control for linear time-varying systems using direct least squares estimation

An adaptive controller based on a least squares non-recursive identification algorithm is proposed. The adaptive scheme is capable of dealing with slowly time-varying parameters. The minimized criterion of the estimation algorithm is an L₂ norm of the identification error with forgetting factor. The proposed estimation algorithm does not require explicit knowledge of the noise bound or the region where the true parameters lie. The control stategy involves a pole placement hybrid control law. We study the case when there is no persistent excitation and show how we can modify the estimates in order to avoid singularities in the control law. Finally we show how the control objectives can be achieved