This may be an unusual request but hope this would not be too difficult to build.
My father is in an electric wheelchair and has been for 20 years. He often goes out into town to the shops and to get about his flat where he has regular care in assisted accommodation. However his mental condition is getting worse and he is now posing a danger to other road users and often gets lost. His doctor is suggesting taking away his chair, would stop him going out but also mean he cannot get about his flat.
I wonder if an alternative would be to fit his wheelchair with a GPS and Arduino which would prevent him going too far. How it would enact the restriction is another discussion, but perhaps it could put the chair into super slow mode, so going into town would take too long for him to bother with, but would enable him to turn around and go back home.
As described, no. Directly controlling the wheelchair motor seems fraught with too many exceptions: What if he needs to get out, during an emergency? Should the speed be restricted if he does get into the roadway? If there is any kind of accident, you can bet the insurance company and/or wheelchair manufacturer would not look kindly on your "uncertified" modifications.
If he really should be allowed to roam free, you could implement a GPS tracker (perhaps with a geofence) that sends his location via cell phone to you or the staff. But...
This isn't just a fun Lojack project to protect your property... you're trying to protect a person. You say he "has regular care in assisted accommodation", so the real question is "Why is he free to roam the streets?" It sounds like the facility is not properly caring for him, or has not marked his condition as "memory impaired".
With regard to the care staff, legally no one can be prevented from going outside if they want to, the staff can't stop him leaving even if he wanted to. So it's not the fault of the staff. If he has the means to go outside, then he will, because he believes he is fine.
On the subject of the GPS tracker, is there one in particular you would recommend looking at? I think that's worth a try.
This is a very difficult situation, and since I'm dealing with a similar one, I sympathize.
An option that many can't afford is to have someone accompany him on outings -- that is the solution that my brothers and I have chosen for the time being, but it is expensive. My dad would reject it if he could, but he can't get out of the house without help.
The problem with all trackers is power. You could consider SPOT, but battery lifetime is limited and he has to remember to turn it on and off. And someone has to monitor the location report web page, during his outings.