I would highly recommend
https://www.youtube.com/watch?v=PYylPRX6z4Q as a way of framing the problem.
It seems like our options for ML are currently: self-play, dataset fitting, or human feedback. It's possible to solve any problem that can fit into one of those molds.
(Unfortunately the opposite is true: if a problem doesn't fit into those categories, it seems very hard to solve with any form of ML.)
But, now that I think about it a bit more, the sentence "use a trained net as a tool for building a controller with known continuity properties" seems neither obvious nor straightforward to do. I'm decently well-versed in AI techniques at this point, and I can't really think how I'd sit down and write a program that would generate such a system. Anyone have any leads?
Basically, the goal is to make a neural net that helps you design a system that can be predictable. One way would be to write a loss function that penalizes unpredictability, and then let it run until it converges on a predictable control system. But that's a bit like saying "Just draw an owl." Not so easy to think of the actual code to do that.