An adaptive regulator of the minimum-variance type in the presence of disturbance uncertainty is considered in the paper. Supposing a linear ARMAX model of the single input-single output system, a robustified direct adaptive control algorithm is derived using the robust statistical approach named M-estimation. The derived algorithm differs from the conventional linear algorithms by the insertion of a suitably chosen nonlinear transformation of the prediction error, which has to cut off the large noise realizations named outliers. The global stability of the proposed control system and self-optimizing property of the adaptive regulator is established theoretically using the martingale theory. The feasibility of the approach is demonstrated with simulation.