Adaptive Estimated Inverse Control for Uncertain Nonlinear Systems with Hysteresis Effect

An adaptive estimated inverse control methodology for a class of uncertain nonlinear system subjected to unknown Prandtl-Ishlinskii (PI) hysteresis nonlinearity is studied in this paper. The largest difficulty in the inverse hysteresis compensation mechanism lies in that its parameters are hard to determine. To obviate such obstruction, the unknown hysteresis parameters are estimated online by the adaptive techniques together with uncertain system parameters. Thus, hysteresis effects as well as parameter uncertainties can both be suppressed without the time-consuming off-line identification. Meanwhile, the tracking differentiator is utilized to solve ?explosion of complexity? problem in backstepping control by calculating the derivatives of the virtual control laws. Based on the Lyapunov stability analysis, it has been revealed that the boundedness of all the system signals is achieved and the tracking error along with estimation errors can all converge to an compact set around zero. Contrastive simulations are performed to demonstrate the theoretical findings of this control algorithm.