If you have a multimeter, check your battery voltage with the Jeep off, should be 12ish. Start the Jeep and it should hang out around 14ish. When you see it spike to 19, verify that as well. Your alternator does not have a built in regulator, its in the computer I believe but it is one of those things that rarely fails. That is what seems to be failing. Typically, your battery is going to get destroyed from this so set aside a little for that as well. Good luck and hopefully someone else will have a better idea!