Fixed-Time Adaptive Control With Predefined Tracking Accuracy for Piezoactuators Subject to Stochastic Disturbances

The work aims to solve the high-speed high-precision tracking control problem of piezoactuators in the presence of stochastic disturbances. First, a cascade model composed of the Preisach operator and a class of stochastic nonlinear systems is proposed to describe the sophisticated actuator dynamics during high-speed operation, and then a hysteresis decomposition strategy is developed to transform the Preisach model into an appropriate form tractable to control design so that a robust adaptive fuzzy control framework can be constructed successfully to suppress the hysteresis nonlinearities, and to robustify bounded stochastic disturbances. More importantly, based on such a framework, the fixed-time stability (instead of practical fixed-time stability), and the prescribed steady-state tracking performance can be established simultaneously. Besides theoretical analysis, some experimental tests are also conducted to illustrate the effectiveness of the proposed scheme.