[pl922]

Definitely agree! When reviewing papers I've come across bad (incorrect) mathematics and unnecessary posturing. I guess I'm seeing controls for what it is at it's best. Any thoughts on geometric control theory (in the vein of Jurdjevic, Sachkov)? I like the differential-geometry viewpoint. How about sum-of-squares/algebraic geometric results?

[ilayn]

I have worked heavily on SOS and LMI based methods in general, IQCs to be precise. Sum-of-squares are so stupidly explosive in the size of required conditions, (pretty much impossible to do anything more than 5-6 parameters), you can play around with it theoretically. You might feel good about it.

If you call yourself an applied mathematician and keep working on these things, I will be the last person to object. But if you say Sigma* algebra or Sobolev spaces, or infinite dimensional systems, or this or that is required to understand dynamical systems that means you are not really getting the central ideas in control and confusing the methods with the problems we are trying to solve. That is my premise.

[pl922]

Thank you for this much needed perspective. I do agree that tools shouldn't take precedence over the problems they're used to solve (like you say, unless you're a mathematician). If you're willing to spare more time, which central ideas do you think researchers should orient towards?