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Control systems overlap with other AI topics in that there's usually an option of a "brute force" method that reframes the problem as a constraint optimization, and then applies a mix of lookahead, filtering and backtracking - classical CS ideas - to rank the possible answers to control at any moment in time, pruning incorrect answers. All you need to start is a ranking function that expresses the amount of error, and a way to generate the tree of "all answers over time" - since with a problem like acceleration and overshoot, an answer that looks wrong when looking one step ahead will become correct one hundred steps later.

And this in turn overlaps with machine learning techniques since a problem generalized in this way can subsequently be adapted into a trained system that approximates the same result as the brute force answer.

Ideally, you can use an analytic solution, of course, and that's what you really want to use to get a result that is both fast and precise, but to do that, the "advanced mathematics" are necessary to define the problem appropriately.