Is there a hormone or group of hormones that regulates when we feel sleepy late at night, or in the morning? Or is sleepiness caused by some other non-hormonal mechanism? (e.g. pure psychological, or neuronal.)
The release of the hormone melatonin is responsible for the feeling of sleepiness. It is released by the pineal gland and production starts when the light fades, as it's production is inhibited by light stimulation of the retina, the onset of the production is called dim-light melatonin onset. Artificial supplementation can increase sleep quality and regularity related to some sleep disorders and is often administered as pills or patches.
Adenosine is an inhibitory neuromodulator, ie it inhibits neural activity. Neural activity can be either excitatory or inhibitory and adenosine more strongly inhibits the excitatory neural activity. Thus, increased adenosine levels should decrease excitatory effect of nervous stimuli and make you feel more relaxed & sleepy.
Other hormones & neural pathways may be involved (serotonin and the serotonergic neural pathways for example) as well as other stimuli like other people's behaviours (yawning, stretching etc.).