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Math Research (mander.xyz)

submitted 4 days ago by [email protected] to c/[email protected]

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[–] [email protected] 46 points 4 days ago* (last edited 4 days ago) (6 children)

my guess is the comic is about Pontyragin's maximum principle, a theorem in control theory. He was a blind Russian mathemematician and his mother helped him learn maths by reading books to him. He developed control theory for an application on optimizing rocket speeds or maybe logistic trains or something like that.

[–] [email protected] 18 points 4 days ago (5 children)

Can you do what you just did, but for "control theory". Pretty pretty please with a cherry on top?

[–] [email protected] 12 points 3 days ago* (last edited 3 days ago) (2 children)

you want to find "forces" to apply to a dynamical system so that you steer it in behaving the way you want. it can be as simple as asking "what are the forces that I need to apply so that it eventually goes to a place I want it to". In general applications are in the domain of optimal control theory which also requires to minimize a certain cost while you are controlling the system. So then the questions become

1- Can I find external influences such that I can force this system to end up there

2- Among all possible ways of forcing the system to end up there, what is the minimal cost way I can force this system to end up in there

In the example of a rocket it could to reach a certain speed or a certain location (both can be seen as subsets of the coordinate,speed phase space which is where the dynamical system evolves) while minimizing fuel usage. The control mechanism in thise case would be deciding on a set of times in which to apply an amount of force to your rocket (by releasing an amount of exhaust gas).