Robust adaptive control of a class of nonlinear systems with unknown Prandtl-Ishilinskii-Like hysteresis

Control of nonlinear systems preceded by unknown hysteresis nonlinearities is usually difficult and challenging due to the non-smooth nonlinearities of hysteresis. It has received increasing attention recently owing to growing industrial demands involving varied applications. Although many mathematical models have been proposed to describe the hysteresis phenomena, very few models are suitable to be fused with robust control techniques to have the basic requirement of stability of the overall hysteretic system. We first construct a hysteresis model using play-like operators and name it Prandtl-Ishilinskii-Like hysteresis model, and then develop two robust adaptive control algorithms to mitigate the hysteresis without constructing a complicated hysteresis inverse. The new schemes not only perform global stabilization and tracking tasks of the adaptive nonlinear systems, but also guarantee transient performance explicitly. Simulation results are given to illustrate and further validate the effectiveness of the proposed methods of this paper.