[ilayn]

Another control theorist here. I strongly disagree with your premise of rigor in control. The whole field is ripe with math snobbery and virtually plotted its own funeral to the point of absurdity.

The field's key contribution is in the ideas and the insights it can provide otherwise extremely laborious to obtain. Definitely not in senseless dry exposition of unnecessarily general theorem proof parroting.

[wenc]

As a control engineer (and former theorist), also agree. Practical control is less algebraic theory and more numerical algorithms.

We don't directly use Pontryagin's maximum principle or solve Euler-Lagrange equations (impractical for large systems) for instance. A lot of the stability proofs are nice in controller design, but rarely used in practice.

We do use Model Predictive Control, which solves a numerical optimization problem at every time step. We also use state estimators like the EKF, which is also numerical. Much of the heavy lifting here is actually in the tuning and understanding of the process, not the control theory itself.

The usefulness of control theory isn't in its actual use, but to provide a foundation for developing newer theories. There's a place for it. It's a set of building blocks.

But I submit you don't need to really know the mathematical theories to truly understand feedback loops, optimization etc. Most of us control things intuitively when we're driving a car (feedback loop with feedforward), running a business (state estimation, feedback and stochastic control), etc.

Very good businessmen -- i.e. those with acumen -- are natural control engineers despite not knowing a whit of differential geometry or state-space models.

[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?

[ilayn]

I have rather unorthodox view on this subject, I would already concede defeat if you object to it. However, to criminally box my view into a few sentences, we should start cleaning up our undergrad curriculum from root loci, routh hurwitz, Laplace transform etc. and put industrially relevant things like PID and all kinds of heuristics. We also need to fire anyone who says yes but "that's trial and error" as if engineering is not 90% that.

This is not an easy task by any means, it would require a lot of expertise. However we have to get back to being related to the field and not hijack control engineering to do applied math. A mech/electrical engineering curriculum, with all their flaws, will leave you around the neighborhood of a working engineer. You will not be ready for the production-grade however you would be a cadet.

With control engineering, you don't learn anything about the field but learn bunch of haphazardly put together half-assed math concepts. When you get out not only you don't know anything, you also have this elite view that "oh they are just doing PID, peasants!". In other words, control design is 5% of the whole process. Understanding the system is the crucial part. Anyone can tune something that barely works. Not everyone understands the system. Strogatz' nonlinear book should be more important then Ogata.

Let me give one example; Laplace transforms or all integral transforms with different kernels are extremely hard topics at undergrad level and confuse the hell out of students. To the point that when you present them the intricacies of analytical continuation and other necessary things to treat the subject you lose them. Hence we should not pretend to teach these things. Hence "oh replace dots with powers of s and then replace s with iw" is not helping anyone.

Apologies for cutting it short but I have to get shit-faced with my guests soon :) Hence I wish all a happy new year!

[pl922]

Great points! Happy New Year to you too!

[calf]

By funeral are you saying the field is currently moribund? Is it going through some kind of crisis? I had a few control/systems professors in the past, what appealed to me about it was it was a kind of "theoretical engineering" approach to engineering.

[ilayn]

By funeral I mean, academia completely killed the applicability of this rich branch of engineering and left it as "exercise to the reader". Take MPC control, it originated from the industry and academia did not care for very long time until it has been realized that you can play around with optimization problems and now being put forth as the one of the jewels that rigorous mathematical gave birth to.

Industry, exceptions notwithstanding, pretty much got used to ignoring the the theoretical advances. Hence control theory became this testeless pages long article sillyness where you get 9 pages of integral inequalities to tune 2 parameters and call it adaptive control success.

[amelius]

I suppose they are referring to black box methods like those based on deep learning.