Backstepping Control of a Class of Nonlinear Systems Preceded by Hysteresis with Prandtl-Ishlinskii Presentations

Control of nonlinear systems preceded by unknown hysteresisnonlinearities is a challenging task. In the literature, manymathematical models have been proposed to describe the hysteresis.The challenge addressed here is how to fuse those hysteresismodels with available robust control techniques to have the basicrequirement of stability of the system. The purpose of the paperis to show such a possibility by using the Prandtl-Ishlinskii (PI)hysteresis model. A backstepping based robust control approach,serving as an illustration, is fused with the PI model withoutnecessarily constructing a hysteresis inverse. The globalstability of the system and tracking a desired trajectory to acertain precision are achieved. Simulations performed on anonlinear system illustrate and further validate the effectivenessof the proposed approach.