Robust adaptive control of systems with hysteretic nonlinearities: A Duhem hysteresis modelling approach

When the systems are preceded by unknown hysteresis nonlinearities, the system performance will be degraded due to the existence of the unknown hysteresis. In order to mitigate the effects caused by the unknown hysteresis nonlinearities, it is generally required to describe these unknown hysteresis phenomena exactly, and it is one of fundamental tasks to address the hysteresis systems. To avoid the computation complexity, one of differential-based hysteresis models, Duhem model, is utilized to describe hysteresis phenomena in this paper. However, it is not easy to construct the inversion of the differential-based hysteresis models, and this is the motivation of this paper to design a robust adaptive control approach without constructing the inverse of the hysteresis. By exploiting the characteristics of the Duhem model, the developed robust adaptive controller can ensure the global stability of the system and the system performance. The simulation example demonstrates that the proposed control approach can mitigate the effects of hysteresis effectively.