Automatically Generate New WordPress Instances

I want to give users a way to signup for my site and be given access to a WordPress panel that controls theirusername.mydomain.com. I’m running Ubuntu Server and I’ve been looking around quite a bit but I don’t know where to start. Basically, I want to give my users a hosting solution for their profile. They can use the WordPress system to manage their entire profile as if it was their domain. Does that make sense?