To improve the swing accuracy of the piezoelectrically driven fast steering mirror ( FSM) in the precise image stabilization system of the space telescope, the hysteresis nonlinear compensation and control technology of the piezoelectric actuator are studied. Aiming at the asymmetry of piezoelectric hysteresis and the complex inversion process of the Duhem model, the differential equation of the Duhem model is transformed, and the asymmetric Duhem inverse hysteresis model is directly formulated as a hysteresis feedforward compensator, and the immune differential evolution algorithm is used to identify model parameters. On the basis of compensating piezoelectric static hysteresis nonlinearity with Duhem inverse model, a linear quadratic Gaussian with optimal reference tracking (LQGORT) control method is introduced to further improve the dynamic performance of piezoelectric actuators. The dynamic hysteresis ratedependent auto-regressive exogenous (ARX) model is used to establish the state space equation, which is used for the Kalman filter to predict the state variable and the controller to calculate the optimal control coefficient matrix of the state variable. Experimental results show that the directly established asymmetric Duhem inverse hysteresis model can effectively describe the asymmetric inverse hysteresis curve of the piezoelectric actuator. The fitting root mean square error is 0. 635 9 V ( 0. 5 Hz), and the relative error is 0. 79% (0. 5 Hz). Real-time tracking of target displacement signals with an amplitude of 24 μm and a frequency range of 1 to 80 Hz. The tracking error of the LQG-ORT algorithm is 0. 065 5 μm, and the relative error is 0. 27% .