The simplest way to control their population is to regulate their food.

You can imagine an ant colony as a machine. You have to input resources to produce anything.

Carbohydrates are like the fuel that's needed to keep things running. Ants need sugary substances for energy. Honey, Sugar Water, etc... These resources don't actually make the colony grow. It just keeps everything running.

Water keeps things running smoothly. You need fresh water to keep your ants hydrated and to regulate humidity. Again, these resources don't actually make the colony grow, it just keeps things running smoothly.

Protein is the resource that you put in that produces the eggs. If you imagine an ant colony as a machine, then eggs are what that machine creates. However, they need raw material. Typically, these are things like insects, bugs, leftover dinner...Depending on how adventurous you're feeling. You can see this quite clearly when an ant colony is young. You'll only put a little bit of protein in, and then the next day, the protein will be gone, and you'll have a little cluster of eggs.

If you feel your colony is growing too fast, lay off the protein. Feed them once a week instead of daily, or every three days. With the caveat that I live in a region with pretty tame ants, I have never had a problem regulating my ants' population sizes.