I understand that on ex dividend day, the price will fall by the dividend amount from the previous day. Since the company has no control over share price, what is actually controlling the price?

Bhhg

There are designated market makers (I think these are the major banks and various financial entities).

When these market makers make the trades for the day, they will corresponding adjust the opening bids for the day - notice the opening price per day is not exactly the same as the ending price the previous day.