Yes, asthma can make you tired.

More Info: Fatigue is not a general symptom of asthma, but some patients do experience fatigue as well as an inability to exercise properly as a symptom of asthma.  Other unusual symptoms of asthma include sighing, anxiety, difficulty sleeping, and rapid breathing.

Unusual Asthma Symptoms  WebMD

What Body Systems Control the Need for Sleep?

The Body System that controls the need for sleep is the nervous system. There are two different sets of nerves in our brain: the nerves that are in control when we are awake, and the nerves that are in control when we are asleep. When we feel fatigued and are ready for sleep, neurotransmitters are passed to the wake nerves as a signal to turn off. Control is passed to the sleep nerves, which control automatic bodily functions and the three stages of brain activity involved in sleep: light sleep, deep sleep, and REM activity.

What Is the Circadian Biological Clock?

The circadian biological clock, or circadian rhythm, is a system of physical, mental and behavioral changes that occur approximately once within a 24 hour cycle. Circadian rhythms are endogenous but are also influenced by external time cues, such as daylight or artificial, indoor light. The circadian biological clock is entrained, meaning it can also be adjusted to match the local time. Plants, animals, fungi and cyanobacteria have all been observed to have circadian biological clocks. Within the human brain, a group of nerve cells, the suprachiasmatic nucleus, controls the circadian biological clock.