Data-Driven Adaptive Control With Hopfield Neural Network–Based Estimator for Piezo-Actuated Stage With Unknown Hysteresis Input

In this study, a data-driven adaptive controller (DDAC) is designed for piezo-actuated stages (PASs). The primary objective of the controller design is to achieve high tracking accuracy and ensure system stability in the presence of nonaffine uncertainties and unknown hysteresis in the PAS. The proposed DDAC involves three aspects: 1) description of a PAS as a nonaffine nonlinear discrete-time system with a hysteresis input; 2) design of a DDAC using a full-form dynamic linearization (FFDL) model of the PAS; and 3) development of a Hopfield neural network (HNN)-based estimator to update the unknown parameters of the control system online. The key advantages of this study are that prior knowledge of the system nonaffine uncertainties and an offline model are not required. Moreover, the HNN-based estimator can not only update the parameters of the controller, but it can also estimate the output of a PAS to ensure whether these parameters are valid. The stability of this control system is proved based on the Lyapunov stability analysis theory. Experimental results obtained using the proposed controller on a PAS are compared with those of the existing control methods to verify the effectiveness of the control method.