Since you specified open loop control, these are the issues to consider:
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With open loop-only control there is a small risk that the cycle offset will drift over time. After running the test for some time, you may find that the cylinder starts to hit the stop on one side or the other. You might want to consider Adaptive Amplitude control. This algorithm does not attempt to control the cylinder’s motion profile exactly, it only makes sure the required amplitude is reached. It will also make sure the cylinder stays in approximately the same location as at the beginning of the test.
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High response valve - clearly it must be able to respond at 300 Hz, minimum. Because it is open loop you won’t be concerned about the ability to follow a target profile, but see the discussion on Adaptive Amplitude if you decide to use that method.
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Oil supply - the pump must be able to keep the oil pressure and oil volume steady at the same time.
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Accumulators - it is likely adding an accumulator or accumulators to the design will help keep the oil supply steady, and may allow the use of a smaller pump.
As @ndzied1 mentioned, the accelerations for that test profile are very high. It will be challenging to find a valve that will have acceptable frequency response. We have some test data for various valves in our Third Party Recommendations: Actuators section.
Also, this discussion on Maximum Cylinder Acceleration might be useful as you consider the system design.