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These lights are from Deals Direct. They have 8 channels; 1 for each ring of LEDs. The controller has no button, hence they just do their own thing. The power supply is 24Vac 200mA. Diameter is approx 800mm. I will probably make a small DMX controller for these.
I pulled the controller apart (you just knew I would!) and it's pretty much the same as the 2 and 4 channel 24Vac controllers you see, apart from having 8 SCRs and no selection button.
The good news is that it uses a common positive wire, so will be compatible with standard DC controllers. I've yet to work out the best DC voltage to run it from and what series resistors it requires in each channel line.
Each ring contains 20 LEDs and appears to be split into two parallel strings of 10 LEDs, so maybe 40mA per channel will be the target current limit.