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In this paper, intelligent sensorless control of a smart-material actuator is presented. The smart material that we used to develop a novel type of linear actuator is Terfenol-D. The peristaltic motion in the actuator is generated by inducing a traveling magnetic field inside the Terfenol-D element. The sensorless control of the actuator is based on an observation illustrating a direct relationship between the active element's position and the coils' inductances. To detect the inductance change, the coil's current response to a pulse voltage input is monitored. Then a fundamental relationship between the coils' current response pulse widths and active element's position is developed using a combination of a Sugeno fuzzy model and neural networks. Eventually, the closed-loop sensorless control of the magnetostrictive actuator was successfully performed. The neuro-fuzzy-based sensorless control demonstrated the position-estimation capability with a ±0.5-mm maximum error. The sensorless control scheme combined with the unique features of this actuator is promising in the applications where conventional actuation and sensing methods are proved inapplicable due to technical or reliability issues.