Adaptive tracking with one-step-guess estimator and its variants

Following our previous paper on an extremely simple yet long-term ignored one-step-guess (OSG) estimator, which focuses on the adaptive regulation problem of a class of the scalar discrete-time adaptive control system, this contribution aims at examining the counterpart tracking problem with the OSG estimator and its two variants, all of which are shown to be efficient yet rather nontrivial although the form of the OSG estimator is very simple. The OSG estimator is based on the most intuitive idea of guessing the unknown parameter with only the information available from one step, and applying it to the tracking problem with the certainty-equivalence principle results in a complex closed-loop system, which is indeed governed by a time-varying nonlinear difference equation whose stability is not resolved in previous studies of difference equations. Preliminary closed-loop stability analysis is given under wild conditions, and two variants of the OSG-based adaptive controller, called parameter regularized OSG and control regularized OSG, are also proposed to make up weakness of the primordial OSG controller. Extensive numerical simulations also illustrate the effectiveness and differences of the proposed methods.