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This paper investigates target tracking control for a high intensity focused ultrasound (HIFU) transducer to follow liver motion induced by respiratory cycles. Motivated by the apparent respiratory cycles repetitive control is first considered. Adaptive control, which employs recursive least squares adaptive filtering to minimize the tracking error, is also proposed. Adaptive feedfoward and feedback actions and their integration are formulated respectively. The target tracking performance of the repetitive control and adaptive control are evaluated by simulating the tracking of a measured data obtained from implanting a beacon in a pig's liver. To relate the target tracking performance to thermal ablation effectiveness thermal dosage is calculated for a volume of interest based on the simulated target tracking error. Performance indices specifically defined for target tracking, but not the beam focusing under moving target, are defined to evaluate the effectiveness of the proposed control algorithms.