Piezoelectric actuators (PEA) are the fundamental elements for high-precision high-speed positioning/tracking task in many nanotechnology applications. However, the intrinsic hysteresis observed in PEAs has impaired their potential, specially, the motion accuracy. In this paper, the complicated nonlinear dynamics of PEA including hysteresis, creep, drift and time-delay etc. are treated as a black-box system exhibited as rate-dependent hysteresis. The multi-valued hysteresis is analyzed as a single-valued function so that a neural network (NN) can be built to model the hysteresis and its inversion. A sliding mode controller (SMC) augmented with inverse hysteresis model is then developed to compensate the hysteretic behavior, modeling error and disturbance to improve the positioning/tracking stability and accuracy. The effectiveness of this algorithm experimentally verified through the actual tracking control of a PEA.