Device with independent voltage and current
From what you say it is implicit that this hypothetical device is a two-terminal device, therefore its behavior can be described, as you say, by some V-I relationship, however complicated, so not even a function, but a generic mathematical relation.


Note: in English technical literature voltages are indicated by V, not U. Since the language of this site is English, I'll stick to that convention.


The problem here is that you assume we can test this device by impressing both current and voltage and this is impossible. You have only two terminals in your device, so you either connect an (ideal) voltage source or an (ideal) current source to them. Whatever complicated system you use to create those sources, they have only two accessible terminals to your device. The problem is that to impress the current you have to put the current source in series with your device, whereas to impress the voltage you have to put the voltage source in parallel with it. If you want to impress both quantities, you should be able to put both sources together, but the requirements are incompatible: you either connect both sources in series with your device or in parallel. 







simulate this circuit &ndash; Schematic created using CircuitLab

In the latter case the current source cannot impress the current in the device alone, whereas in the former the voltage source cannot impress the voltage across the device alone.

If you object that you could devise a strange "testing apparatus" that "magically" has only two terminals and puts out a fixed voltage across those terminals and impress a fixed current across them, well that is impossible either, because its V-I relationship would be a single point in V-I plane. 

If you don't get why such a V-I relationship is absurd physically (mathematically is OK) think a moment about it: such a testing device is able to impress both a fixed current and a fixed voltage on whatever load it is connected to, so it is able to turn everything into a resistance of value R=V/I (that's magic!)

Ok. Maybe I misunderstood what your X-device is intended to do (your wording wasn't very clear). Let's get back to square one. You said it should have "power dissipation that simply adjusts on the current and voltage. Ie P(U,I) where U and I are independent variables". And again in your comment: "Both current and voltage are fixed and cannot be used in feedback."

That's another problem: you seem to imply that your X-device is able to draw a fixed amount of power, whatever the values of V and I, but that's impossible from the beginning. The fact that the power absorbed by any two-terminal network is given by P=VI is a physical fact, and that very relation makes it impossible to have V and I independent once you select a power value. Only two out of three can be independent, so if you fix V and I, the power your device absorbs is VI, no matter what.

EDIT (in response to a comment)


  And 
  yes, by my device I mean one that 'magically' adjusts its
  power/resistance in order to obey energy conservation/ohms law. At
  which point does such a device contradict physical law?



You don't need to obey Ohm's law unless you want to create a (linear) resistor. An ideal linear resistor is, by definition, the only device that obeys Ohm's law. So, no need to do "magic".
Obeying conservation of energy implies that P = VI must be satisfied at each instant of time, i.e. P(t) = V(t)I(t) for each t.
This latter "requirement", from a practical point of view, makes no sense: any device you could build will satisfy that requirement because there is no phenomenon in the known universe that don't obey conservation of energy, so your device doesn't need to "adjust" anything to obey P=VI, it just will!