Put a person in a "cave", hook them up to sensors, and have the artificial light (with spectrum simulating natural light) be adjusted according to how sleepy they are, as measured with sensors. What kind of circadian rhythm will they develop?
Normally, we would expect that the body will adapt to a given light cycle (so long as it is reasonably close to 24 hours). However, a system in which the light cycle is simultaneously trying to adapt to the body may cause strange effects.
It might be pretty tricky to develop sensors that can detect that a person is getting sleepy, but not actually asleep, (then gradually decrease light). Tangentially, such technology would be the holy grail for cars which detect and warn if the driver is tired.
Inspired by the similar experiment in which the subject was in a cave with constant uniform light, though that experimental setup was technologically much simpler.