Currently, the FAA is on record - in writing - that they will not permit or certify any flight critical software (DAL A or B) that incorporates AI (or anything resembling AI). The reason is quite simple - AI isn't predictable in it's responses - and unpredictability is the exact opposite of what you want in aircraft avionics.
Personal example - my last BMW 3 series had a simple form of AI - it would 'learn' my driving habits and incorporate that into the engine and transmission response algorithms. I'd taken the car in for service, I mentioned that I'd seen an error message for "BMW Connect" a couple of times (BMW Connect is similar to "On Star", but cell phone based). After I picked up the car, it had turned into a gutless wonder - the engine was literally so slow and unresponsive as to be dangerous to drive. I took it back the next day, let the service manager drive it around the block and he immediately confirmed something was seriously wrong.
Turns out they'd re-flashed the memory to correct the BMW Connect error messages - somehow in doing that, they'd inadvertently set all the AI learning to "little old lady", making the car almost undriveable. They reset all the AI, and the car drove perfectly. When I talked about this with some co-workers later, it turns out one of the others had a similar occurrence - on their Jeep Grand Cherokee...
Programing for 'known' failures is relatively easy - the first step in any fully autonomous aircraft would be to catalog every single known survivable failure, and come up with the best solution to every one. Not to shortchange Sully in any way, but an all engine power loss is pretty straight forward - a proper program could evaluate the possible glide range based on all the relevant parameters (altitude, airspeed, aircraft weight and drag), and determine if it was feasible to land at an airport or a water landing would be better - and do all that in a faction of a second, while simultaneously trying to restart the engines. Where the computer falls short is something that's never happened before - e.g the failures associated with an uncontained engine failure (think Qantas 32) - what works and what doesn't work after such a failure is somewhat random - a programmers nightmare.
As I mentioned previously - I have no doubt fully autonomous aircraft will eventually occur, but it's going to take a long time.