Global adaptive output feedback tracking for a class of non‐linear systems with unknown backlash‐like hysteresis

The authors consider a class of non‐linear systems preceded by unknown backlash‐like hysteresis. Unlike other schemes dealing with hysteresis, the non‐linear systems of this study not only involve unknown parameters but also take non‐linear terms linear in the unmeasured states into account. An adaptive output feedback controller by utilising a modified high‐gain observer and backstepping approach is proposed, which is able to mitigate the effects of the hysteresis, and guarantee the global stability of the closed‐loop system and the arbitrarily small steady‐state tracking error. Moreover, it is proved that by introducing an initialisation technique, the ℒ ∞ tracking performance can be achieved.