“…Especially, hysteresis is an inherent characteristic of piezo-actuated mechanisms that are widespread in the micro/nano stage (Cai et al, 2021b; Chen et al, 2019; Gan et al, 2022b; Gu et al, 2016), amplifier instrument (Bhagat et al, 2013), microgripper (Chen et al, 2021; Gan et al, 2022a), atomic force microscope (Oubellil et al, 2019), piezoelectric energy harvester (Alamin Dow et al, 2011). Piezo-actuated mechanisms have advantages of compact structure, high resolution, large force output, and low heat and noise (Chen et al, 2020b; Gan et al, 2021), widely used in practical engineering. Moreover, piezo-actuated mechanisms are consist of the piezoelectric actuator (PA), whose inherent property is hysteretic nonlinearity.…”