A Novel Parameter-dependent Input Normalization-based Direct MRAC with Unknown Control Direction

In this paper, we endow the model reference adaptive control (MRAC) with a novel parameter-dependent input normalization (PIN) to completely eliminate the conventional assumption of the high-frequency gain. Specifically, neither the sign nor the prior knowledge of the upper or lower bounds is required. To this end, we resort to an error augmentation together with a smart design of an adaptive law with a dead zone operation. Global stability in the mean square sense is established with the conventional proof concepts of the augmented error approach. In this way, no persistent excitation requirement is required. Although the system in question is assumed to be unity-relative-degree, the proposed technique can be easily extended to systems of arbitrary relative degrees. Finally, compared with the Nussbaum function-based methods in a numerical experiment, we show that transient behavior in our method is significantly improved.