Discrete-time adaptive control of systems with unknown output hystereses

We develop an inverse for a parametrized hysteresis model and present its discrete-time version. We then design two adaptive hysteresis inverse controllers for discrete time systems with an unknown hysteresis at the output: one for systems with a known linear part-followed by an unknown hysteresis and the other for both the linear part and the hysteresis unknown. Our control schemes consist of a linear feedforward part and a linear-like feedback part combined with an adaptive hysteresis inverse. Despite the bilinear appearance of the parameters of the linear part and the hysteresis, a linear parametrization of the closed-loop error system is achieved, based on which we apply the linear adaptive control theory to develop adaptive laws to update the controller parameters.