A Prescribed Performance Adaptive Control for Hysteresis Hammerstein System

A prescribed performance adaptive control (PPAC) is proposed for Hammerstein system where nonlinearity is described by backlash-like hysteresis. In order to simplify the controller design as well as guarantee the precision of the controlled system, the tracking error is transformed into performance error by two steps. The first step is to transform the tracking error into scalar error, but it magnifies the tracking error decreasing the accuracy of the controlled system. Therefore, a new S(z) is proposed for prescribed performance function (PPF) and the second step is transforming the scalar error into performance error by the proposed PPF, which guarantees the scalar error converges to a prescribed bound to improve the control accuracy. Finally, Lambert W function is introduced for the Lyapunov function candidate to guarantee the closed-loop system bounded and the tracking error converged. Simulations demonstrate the effectiveness of the proposed approaches.