RGB diodes, the kind you find in an LED computer monitor or television, don't actually produce any wavelength of light you want. As you probably know, the diodes come in triplets, one each of red, green, and blue. Each of those individual diodes only emits one specific wavelength of light.
However, by varying the relative intensities of the three colors, it's possible to simulate the effect of any other wavelength of light on the human eye. Since there are only three types of cones on the retina, for any given wavelength which the eye detects, you can induce the same chemical reaction in the cones as that wavelength naturally would, using only three colors.
The point is, in RGB LEDs there are only three wavelengths ever being produced, and it's only by "fooling" our eye that they create the illusion of the full spectrum. Since human eyes aren't sensitive to UV radiation, the trick wouldn't work for ultraviolet wavelengths. You can't actually create a diode that will produce any wavelength you want dynamically.
Of course, there are a wide range of materials that you can put in a diode in order to affect the wavelength of radiation it does produce. From a physics perspective, UV radiation is no different from light except that it has a higher frequency (shorter wavelength), so by choosing the right material, you can in principle create a diode that will get you any pre-chosen UV wavelength you want. The Wikipedia article on LEDs gives a table of various materials grouped by the wavelengths they can produce, and there are several options for UV radiation. (There may be a lower limit on the wavelength obtainable from an LED due to energy considerations, but I'm not familiar with the details of how LEDs work so I couldn't tell you whether that's the case or what wavelength it might be.)