A survey on hysteresis modeling, identification and control

•The various mathematical models of hysteresis are surveyed.•The applications of hysteresis models are investigated in different areas.•Different methods of system identification are considered.

The various mathematical models for hysteresis such as Preisach, Krasnosel’skii–Pokrovskii (KP), Prandtl–Ishlinskii (PI), Maxwell-Slip, Bouc–Wen and Duhem are surveyed in terms of their applications in modeling, control and identification of dynamical systems. In the first step, the classical formalisms of the models are presented to the reader, and more broadly, the utilization of the classical models is considered for development of more comprehensive models and appropriate controllers for corresponding systems. In addition, the authors attempt to encourage the reader to follow the existing mathematical models of hysteresis to resolve the open problems.