Why do you think PID is an improvement here? IMHO the bang bang approach is preferable because it behaves extremely predictably. Operationally, knowing how the system will react to extreme conditions might be more valuable than being a little more optimal.

With today's systems, we typically have neither.

But there's a lot of theory around PID control to show how PID control systems behave under all sorts of circumstances. Hell, there's even things that are mathematically provable, like for example stability, which I strongly suspect you may often not even be able to reason about in case of many an ad-hoc systems like the ones GP is talking about.

Its not very clear from your comment but are you claiming that PIDs are not predictable ?

Yes, PID upset is a real problem when things start going sideways, as they tend to occasionally in the real world.

Not that PID is better, not that bang-bang is better, just that.. learning from control theory is likely a fruitful direction to go in.

Most autos along algorithms have heuristically hacked hysteresis built in to stop them oscillating between provisioning a node, dropping a node, provisioning, dropping. That kind of threshold tuning stuff is ripe for replacement with something more rigorous. PID control is an example of a rigorous way to solve that in continuous control. It likely doesn’t directly work for capacity, but control theory in general does have better answers for this kind of thing than just PID.

You clearly failed to read (and quote) what OP said, and therefore understand his point.

Please pay attention to OP's point that PID is more sophisticated with the current state of affairs, which don't even qualify as bang bang controllers.

The OP quite clearly and unambiguously stated that "Even rudimentary control theory is an improvement."

Just because you feel the need to one-up other people's work that does not mean it is ok you distort and strawman the points they made.

The ones that did were usually from an academic background and might have had some side-track with robotics, industrial control software development or just plain theoretical studies.

I suppose it's not as much that nobody wants it, or nobody wants to know about it, but there is so much else to be known that it might not 'fit' when assembling study materials or in-house learning systems.

Maybe the best way to integrate control theory into the datacenter (or cloud) from an ops perspective would be starting out by getting some traction with control systems in general fist, just like a general software engineer might have had some software architecture and patterns for one or two semesters.