Backstepping based variable structure control of a class of nonlinear systems preceded by hysteresis

Control of nonlinear systems preceded by unknown hysteresis nonlinearities is a challenging task. In the literature, many mathematical models have been proposed to describe the hysteresis. The challenge addressed here is how to fuse those hysteresis models with control techniques to have the basic requirement of stability of the system. The purpose of the paper is to show such a possibility by using the Prandtl-Ishlinskii (PI) hysteresis model. A backstepping based variable structure control approach, serving as an illustration, is fused with the PI model without necessarily constructing a hysteresis inverse. The global stability of the system and tracking a desired trajectory to a certain precision are achieved. Simulations performed on a nonlinear system illustrate and further validate the effectiveness of the proposed approach.