I believe that NASA and aviation researchers developed fatigue tests some time ago. There's also discrimination-timing tests.

For example, if the object on the screen is a blue circle, press the right side shift; if it's a red square press left side. Reaction time is used as the indicator.

But these are only proxies for what is, after all, a largely subjective experience. You will necessarily need to rely on measuring inputs (hours of sleep, caffeine consumed, exercise length and intensity) and using subjective measures for outputs (a bit slow, tired, very tired, exhausted).