Reddit reviews Optimal Control and Estimation (Dover Books on Mathematics)

Just find a cheap book on the subject(s), ideally an older edition or something like that and work your way through the material. I've been taking a simular approach to Optimal Control and Estimation.

Don't just read the text like a novel though; do at least some of the problems, and ideally find a project you can tinker with and apply what you've learned. Standard test problems like double pendulums and such are an okay place to start, but anything else that interests you is fair game.

These are extremely rudimentary forms of process control theory--and yet they are still taught in almost every undergraduate stats course for non-mathematicians everywhere I have seen.

For more modern approaches, you need to look first towards control theory

https://en.wikipedia.org/wiki/Control_theory

Then toward the theory of optimal control

https://en.wikipedia.org/wiki/Optimal_control
https://math.berkeley.edu/~evans/control.course.pdf

Then finally to the marriage of this with statistics under the theory of Intelligent Control

https://en.wikipedia.org/wiki/Intelligent_control

I highly recommend Stengel's text (even if the formulation is a bit dated) http://www.amazon.com/Optimal-Control-Estimation-Dover-Mathematics/dp/0486682005

This gives a gentle introduction to all of these topics and culminates in some Bayesian control examples.

Corresponding seminar from Princeton by Stengel himself:
http://www.princeton.edu/~stengel/MAE546Seminars.html



So... in short, the SPC that you learned about with control charts etc is not a bad rudimentary alarming system if you can make normality assumptions about your error, and you assume your process is itself should be stationary; however, to have more rigor you can to turn to these other control / statistical decision theory methods

I'd recommend this book to anyone serious about controls. It's a fairly dense though, so you might look for another more readable one as well.

There is an edition out there with an appendix on "Optimal control and the meaning of life". Ignore that part.

edit: I was thinking of this book (Appendix C). There is a PDF of it online somewhere.

You'll find a long list on Amazon. I'm no expert on the subject, but I picked up Optimal Control and Estimation and got through a bit in my spare time. Seems decent enough.