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In this brief, a direct adaptive controller (DAC) is proposed to control a shape memory alloy (SMA) actuator. The DAC, with its advantages in parameter tuning and noise robustness, was successfully applied to control an SMA actuator. The control signal in DAC was derived via a feedback linearization method. A radial basis function neural network (RBFNN) was then employed to approximate the control signal due to the system nonlinearity and parameter uncertainties. The weighting factors of the RBFNN are updated on the condition of system stability. Due to the system states requirement of the DAC and measurement noise, a Kalman filter was introduced in this work to eliminate the output measurement noise and estimate the system states. From the simulation and experimental results, it was verified that the DAC controller with the Kalman filter was successfully applied to a SMA actuator and the hysteresis phenomenon was almost compensated. The experimental control results were also compared with those of a conventional proportional-integral-derivative controller.