Can voltage be controlled in a fixed DC circuit?
Usually power supplies are designed to try to output a constant voltage (to approximate an ideal voltage source). If the resistance is also constant then you can predict the current from Ohm's law. Usually if a wattage is specified, that's a maximum input or output wattage. 

It's also possible to design a power supply that attempts to output a constant current or even a constant power, but that's not the norm. 

If the load resistance is too low for the constant voltage supply, or too high for a constant current it won't be able to deliver the set voltage or current. Constant power is a bit more tricky because if the load is too low resistance or too high resistance it won't be able to deliver the desired power (it will run into a current limitation at the low resistance end and a voltage limitation at the high resistance end).