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Robotic models have been used as one of the approaches to study fish locomotion. Therefore, this paper proposes an effective control scheme that enables robotic models to mimic fin-ray undulation kinematics of live fish. We found in the experiments of robotic fin undulation that the difference between the desired and actual trajectories can be significant. It is believed that the difference might be caused by the phase lagging effect. To tackle the phase tracking problem, a modified iterative learning control (ILC) scheme is proposed and implemented on the robotic fish model. Furthermore, a memory clearing operator is proposed to satisfy the Lipschitz condition. This is necessary for the convergence and feasibility of the ILC scheme. Finally, experimental results illustrate the effectiveness of the proposed learning control approach, including the memory clearing operator.