First things first, you don't own the other person,nor does the other person own you. You are two (or more,not judging) people who on their own free will chose to be together for whatever amount of time,either finite or infinite,it does not matter. Focus on that idea for a while. Nobody can own another person,it's a choice of free will.
Moving on, there is the exclusivity part. What do you define as cheating?Is it so strict as to include saying hi to someone else or flirting with others,or does cheating only include having sex with others,or is it just the aspect of lying and going behind someone's back that makes it cheating? Do you have a clear picture in your head about that? Ok, now that you have clearly established what cheating means to you, just don't do whatever it is you consider cheating. Don't impose your standards on your partner, enforce them on yourself. You are the one who wants to be exclusive, so it only makes sense that you will be the one not cheating.
Have you had the mutual exclusivity conversation yet?If no, don't expect them to adhere to your own standards,they can't read your mind.They might even be exclusively dating you but you would not even know without having this "dreaded" conversation.
After having this conversation,you will propably reach a conclusion together, either you can't be together like that or - congrats- you want the same thing. And here is how it gets complicated. Now that you both are on the same page and want to be in an exclusive relationship with each other, you have to police each other's behavior to keep them from cheating while also not letting them control you,right?Noooope,that's wrong!The only person you can hold accoundable on honoring the agreement you had and not cheat,is yourself and only yourself. Get it? Good! You are only responsible to "prevent" yourself from cheating or hurting the other person in any way,and the other person is only responsible to "prevent" themselves from cheating on you or hurting you in any way.
If you get those points right,you are focused on the only real way to keep an exclusive relationship functional and keep your head clear from thoughts of jealousy,possessiveness and guess what,you will not be able to be controlling and oppressive to the other person because you will not actively try to control their actions,only yours. Good luck,have fun and never forget to be respectful and kind, it makes the world a better place for everyone.