Robust adaptive dynamic surface control for a class of nonlinear dynamical systems with unknown hysteresis

The output tracking problem for a class of uncertain strict-feedback nonlinear systems with unknown Duhem hysteresis input is investigated. In order to handle the undesirable effects caused by unknown hysteresis, the properties in respect to Duhem model are used to decompose it as a nonlinear smooth term and a nonlinear bounded "disturbance-like" term, which makes it possible to deal with the unknown hysteresis without constructing inverse in the controller design. By combining robust control and dynamic surface control technique, an adaptive controller is proposed in this paper to avoid "the explosion complexity" in the standard backstepping design procedure. The negative effects caused by the unknown hysteresis can be mitigated effectively, and the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is obtained. The effectiveness of the proposed scheme is validated through a simulation example.