Undulatory fin propulsion, inspired by the locomotion of aquatic species such as electric eels and cuttlefish, holds considerable potential for endowing underwater vehicles with enhanced propulsion and maneuvering abilities, to address the needs of a growing number of applications. However, there are still gaps in our understanding of the effect of the fin undulations' characteristics on the generated thrust, particularly within the context of developing propulsion control strategies for such robotic systems. Towards this end, we present the design and experimental evaluation of a robotic fin prototype, comprised of eight individually-actuated fin rays. An artificial central pattern generator (CPG) is used to produce the rays' undulatory motion pattern. Experiments are performed inside a water tank, with the robotic fin suspended from a carriage, whose motion is constrained via a linear guide. The results from a series of detailed parametric investigations reveal several important findings regarding the effect of the undulatory wave kinematics on the propulsion speed and efficiency. Based on these findings, two alternative strategies for propulsion control of the robotic fin are proposed. In the first one, the speed is varied through changes in the undulation amplitude, while the second one involves simultaneous adjustment of the undulation frequency and number of waves. These two strategies are evaluated via experiments demonstrating open-loop velocity control, as well as closed-loop position control of the prototype. [ABSTRACT FROM PUBLISHER]