Has anyone ever tried to control what is going on in a dream, like to change its outcome? Or more simply, can you be aware that you are dreaming?

So, is it still dreaming when you are aware of it? I found that I become very tired the next day when I have such dreams at night. It is as if I did not sleep.

Here is my theory. We usually wake up with some kind of dreams that we soon forget. So, rem sleep may be our waking up mechanism, sort of an indication that we have had enough sleep. If we are aware, we may not be dreaming anymore. And so, if we refuse to wake up, it starts costing us energy..?