Adaptive control of systems with unknown non‐smooth non‐linearities

In this paper we unify our recent results in adaptive control of systems with unknown non-smooth non-linearities such as dead-zone, backlash and hysteresis characteristics at the input or output of a linear dynamics. Our adaptive inverse approach employs an adaptive controller structure consisting of an adaptive inverse for cancelling the effect of an unknown non-linearity and a fixed (or adaptive) linear control law for a known (or unknown) linear dynamics. Despite the bilinear dependence on the unknown parameters, a linearly parametrized error system is constructed which enables us to design robust adaptive laws for updating the controller parameters to ensure closed loop signal boundedness and improve system tracking performance. © 1997 by John Wiley & Sons, Ltd.