cat follows dogs out the dog door--HELP!

We have 3 dogs and a dog door. Works great.

We acquired a kitten and I can't find any products to let the dogs come/go freely, and restrict the cat from using. I also can't find any posts where someone has encountered this before, and found a solution to overcome this.

Seems like the cat could have a collar that locks the dog door when the collar gets near.

Where can I buy a dog door & cat collar like that?

P.S.
I've seen the dog door that opens when the dogs wear special collars, but that won't work for my application---- the cat will just follow the dogs out.

Any way to just keep the cat out of the room with the dog door, or restrict the dogs' leaving to certain times so you can first get the cat out of the way?

Nope-- that's why I'm posting to this site. I'm ready for brainstorming from veteran cat people, and I'm looking for the dog door product name that I was talking about. I can't find a suitable product at stores or online.

Staywell Magnetic Cat Door only responds to a magnetic collar on your cat. It also says it works for small dogs. I thought that may help, although I don't know how large your dogs are.

Thanks for the tip--- The Staywell cat doors are too small for my dogs, although I did find some items with infrared technology. I havent' found one yet that I can adapt to my existing dog door, but the search is looking more promising.

Another restriction I'm running into is that I don't want to swap out my existing dog door unless I can find the same size. My current dog door is cut thru a masonry wall.