Like, the title says, is there ANY way I can get the computer to upgrade? I've seen them upgrade a few times in my RPG maps when they're running AI scripts, but is there absolutely no other way?

http://www.staredit.net/topic/5332/ Is the only thread that I saw that related to this. No other easy way yet that we've found. You can use several different players with the same colour with different upgrades to imitate "upgrading", but that takes player slots. You can also use new units, but that takes up units too. I usually go with the different players method.