btw, you need a pump - a fan has no real pressure behind it.
Probably. But maybe not. We haven't heard anything about the inflatable object yet. How much pressure? How much volume? What leakage rate?
Though if a fan will be appropriate for the job, there's probably not much of a control loop needed -- you can just select an appropriate fan and power it continuously. If you ever turn a fan off, it will let air rapidly escape unless you seal off the inlet somehow. Fans work for things like those jumpy bouncy houses for kids, for some kinds of holiday lawn ornaments, even for the roofs of some stadiums. They work for low pressure, high volume situations, and will handle reasonably high leakage rates.
If the inflatable thing is a higher pressure device, there are off-the-shelf air pumps with a pressure switch cutoff. Most mains-powered air compressors for powering pneumatic tools and for inflating vehicle tires have this type of mechanism to pump the tank up to a standard pressure, and many have an adjustable pressure regulator on their output.