Consider this example
Having switched off the lights, I went to bed.
It implies that I went to bed after I had switched off the lights. The action of switching off the lights happened prior to going to bad, which was in the past. Although I understand Perfect aspect of participles, I don't quite get why they are "Present" if they represent action occurred in the past prior to another action?
Also, is this sentence correct?
Having switched off the lights, I go to bed.