Future NASA exploration missions will increasingly require sampling, in-situ analysis and possibly the return of material to Earth for further tests. One of the challenges to addressing this need is the ability to drill using minimal reaction force and torque while operating from light weight platforms (e.g., lander, rover, etc.) as well as operate at planets with low gravity. For this purpose, the authors developed the Ultrasonic/Sonic Driller/Corer (USDC) jointly with Cybersonics Inc. Studies of the operation of the USDC at high power have shown there is a critical need to self-tune to maintain the operation of the piezoelectric actuator at resonance. Performing such tuning is encountered with difficulties and to address them an extremum-seeking control algorithm is being investigated. This algorithm is designed to tune the driving frequency of a time-varying resonating actuator subjected to both random and high-power impulsive noise disturbances. Using this algorithm, the performance of the actuator is monitored on a time-scale that is compatible with its slowly time-varying physical characteristics. The algorithm includes a parameter estimator, which estimates the coefficients of a function that characterizes the quality factor of the USDC. Since the parameter estimator converges sufficiently faster than the time-varying drift of the USDC's actuator physical parameters, this extremum-seeking estimation and control algorithm potentially allows for use in closed-loop monitoring of the operation of the USDC. Specifically, this system may be programmed to automatically adjust the duty-cycle of the sinusoidal driver signal to monitor the quality factor of the USDC not to fall below a user-defined set-point. Such fault-tolerant functionality is especially important in automated drilling applications where it is essential not to inadvertently drive the piezoelectric ceramic elements of the USDC beyond their operation capability. The details of the algorithm and experimental results are described and discussed in this paper.