I have a fairly severe form of delayed sleep-phase syndrome: left to my own devices, as when I was on summer vacation back in school, I would gladly stay awake for 24 hours and sleep for 12. I've long noticed anecdotally this pattern is associated with geeks. Ask yourself: if a 6:00 AM Twitter update says your geekiest friend is waiting for his code to compile, is it because he woke up early or because he hasn't been to bed yet?
It turns out there's a reason for this. There's a gene called the ASMT gene, which codes for enzymes responsible (in part) for the synthesis of melatonin from serotonin in the pineal gland. This gene is often deleted in individuals with autism or Aspergers syndrome, which results in extremely low levels of serum melatonin. The effect is so strong that even family members of autistic children, even those not themselves diagnosed with autism or Aspergers, have been shown to have abnormally depressed melatonin levels. More information: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2199264/
Melatonin is one of the biggest chemical regulators of the sleep cycle in humans, and increased melatonin at night has been shown experimentally to reduce the time of sleep onset. I'm not aware of any studies comparing the effect size between autistic/Aspergers patients and healthy controls, but it stands to reason that the former group might stand more to gain.
I've personally experienced tremendous benefit in my sleep patterns from taking melatonin. I spent my entire teenage life showing up to classes in a sleep-deprived haze because I wasn't aware of this. Hopefully I can save someone else from that.
Now, for the catch: We have no idea why Aspergers symptoms are associated with reduced melatonin synthesis. Melatonin is a regulator of neural plasticity during fetal and early childhood brain development. Melatonin is synthesized from serotonin, and serotonin levels at various stages of development are drastically different in autistics/Aspergers compared to healthy children. We don't know to what extent these are causes or effects of autistic symptoms, and what effect there might be on development from long-term melatonin supplementation during early childhood. However, in healthy adults, the safety of long-term melatonin use, even at doses many dozens of times higher than the maximum clinically effective dose, has been shown to be completely safe. How you generalize from that is up to you.