Robust adaptive control law for a class of nonlinear systems with differential equation-based hysteresis-Duhem representation

When the systems are preceded by the unknown hysteresis, the system performance will be degraded due to the existence of the unknown hysteresis. The unmeasurable output and the strong non-smooth properties of the hysteresis cause the difficulties to utilize the available control approaches to ensure the system performance. Therefore, for the systems with unknown hysteresis input, the main task for the controller design is to find effective control methods mitigating the effects caused by unknown hysteresis. In this paper, a differential equation-based hysteresis model, Duhem model, is employed to represent the hysteresis nonlinearities. By exploring the characteristics of the Duhem model, a robust adaptive control is proposed for a class of nonlinear systems with Duhem-type hysteresis input without constructing the inverse of hysteresis. The developed method ensures the global stability of the system and a desired tracking precision. The effectiveness of the proposed control approach is validated through a simulation example.