Hysteresis exhibited by smart materials hinders their wider applicability in actuators and sensors. In this paper methods are studied for recursive identification and adaptive inverse control of smart material actuators, where a Preisach operator with a piecewise uniform density function is used to model the hysteresis. Persistent excitation conditions for parameter convergence are discussed in terms of the input to the Preisach operator. Two classes of recursive identification schemes are explored, one based on the hysteresis output, the other based on the time difference of the output. Asymptotic tracking for the adaptive inverse control method is proved, and the condition for parameter convergence is given in terms of the reference trajectory. Practical implementation issues are also investigated. Simulation and experimental results based on a magnetostrictive actuator are used to illustrate the approach.