When Act of Authority enters the battlefield, you may exile target artifact or enchantment. At the beginning of your upkeep, you may exile target artifact or enchantment. If you do, its controller gains control of Act of Authority.
For either ability, if you are the only player who controls an artifact or enchantment, you must choose one of them as the target. However, you may choose to not exile it when the ability resolves.
If you choose to not exile a permanent with the second ability, you'll retain control of Act of Authority.