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).
wikipedia article on optimal control theory might have a nice intro
Can you do what you just did, but for “control theory”. Pretty pretty please with a cherry on top?
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).
wikipedia article on optimal control theory might have a nice intro
This is why I fucking love this community.
Reddit comments would be filled with meme jokes instead of insightful and patient people here elaborating this meme into lamen.
Thank you!
You are awesome. I hope you know that
I think control theory, after reading the Wikipedia first paragraph, is using doing math to calculate how to consistently do a thing.
Fucking nailed it. My favorite application of it is to brew espresso at exactly the right temperature.