# Does there exist mathematical background for ultra-slow process control?

I want to ask a question to respected mathematicians and specialists in control theory: Is there a separate direction in nonlinear control theory that develops control of super slow processes? Are special control algorithms known, etc.? Is there a (at least initial) mathematical background for this?

Example: ball rolling along a predetermined path at a speed of 1 cm per day, taking into account friction.

• What technical challenges would arise in the control of slow processes? I don't see any. Commented Apr 30, 2020 at 7:28
• Direct drive telescope. That drive includes an induction motor, a support platform and other components. If we imagine this system in the state-space, we get a non-stationary dynamic model with slowly changing parameters, taking into account friction, etc. It is necessary to minimize the speed of movement from point A to point B algorithmically. This is not a task from the university or anything like that. Just a small research project and a desire to delve deeper into control theory.
– ayr
Commented Apr 30, 2020 at 9:04
• I think your question is too broad and should be broken into several questions. Since this is Math SE, here you can ask about the control of slowly-changing systems of a specific form. Show the ODEs, please. At Engineering SE, you can ask about sensors and actuators. I assume that the computation part is trivial. Commented Apr 30, 2020 at 10:14
• I need at least some hints in the mathematical field, which is aimed at a slowly changing process. And yet, in a nutshell, I understood from your words that it is necessary to study the differential equations that describe these processes. What methods are used, what is investigated, etc.? In addition to this, I do not know, and I need to have some specific guidance in this area. So let's get started with math
– ayr
Commented Apr 30, 2020 at 10:38
• Have you consulted a book like Khalil's Nonlinear Systems? Is there anything specific you need and that is missing from Khalil's book? Commented Apr 30, 2020 at 10:41