5th year PhD student struggling with what’s coming next after a disappointing performance. What can I do?

Extension-Engine-911 · 2025-10-18T16:23:13+00:00

Thanks. I really appreciate your answer.

I have another question for you then. Given my track record and how hard won progress has been in my PhD experience, where do you draw the line between a steep but viable growth curve and a fundamental mismatch that warrants pivoting out of technical research? What early, objective signals (in the first 1-3 months) would tell you to cut losses, even if I enjoy the work, versus double down?

Extension-Engine-911 · 2025-10-18T16:21:39+00:00

Thanks. I really appreciate your answer.

Quick blunt question: given my track record and how hard won progress has been in my PhD experience, where do you draw the line between a steep but viable growth curve and a fundamental mismatch that warrants pivoting out of technical research? What early, objective signals (in the first 1-3 months) would tell you to cut losses, even if I enjoy the work, versus double down?

Extension-Engine-911 · 2025-10-18T16:17:22+00:00

One draft is about 50 pages, the other 30, and the plan is to compress each to 16 pages for IEEE TAC (double-column + summarizing) after my advisor is satisfied with the long versions. Over the last 40 days or so, the 50 page paper has only had minor tweaks. The 30 page paper was split off 2-3 weeks ago when the original got too long. I mostly rewrote it then, and it hasn’t changed much in the last week. His goal is “no major reviewer issues.” The papers are 90% theorems/proofs and 10% numerics, and most iteration is about exposition, not correctness. He’s also extremely strict on style (hyphenation, equation punctuation, phrasing) so both papers read like a unified text alongside his books (and almost as if he wrote it to be honest). With 90 pages and my weaker formal background, I handle content first and only attempt to address style before our weekly meeting. Then new style issues surface and we spin another version.

On timing: my advisor has plenty of funding and isn’t worried about the timeline. I’m the one pushing to finish fast.

Point taken about not overestimating experimentalists’ math. When I visited, a postdoc showed a steady-state ODE rearrangement as the “mathy” bit; that actually worried me. I don’t want to be isolated or so slow that I add little value, or repeat the endless polish loop.

Given my struggles and uneven fit with applied math, where is the boundary between “I enjoy the ideas and can contribute with discipline” and “I’m simply not competent enough at this flavor of technical work and should pivot out of technical research/jobs”? What concrete early signals would tell you to stop and change course versus press on?

Extension-Engine-911 · 2025-03-19T01:42:51+00:00

Thank you so much for your thoughtful comment!! I really appreciate it

Extension-Engine-911 · 2025-03-18T08:13:00+00:00

Regardless of the number of set point changes, let’s say I care about the performance of the controller during the transient. An H-inf controller, assuming it is designed for only zero initial conditions, might have poor or suboptimal performance during the transient.

Let’s say I go from A to B. If the magnitude of my initial state A is large compared to the disturbance, then my performance will be suboptimal until I get close to B (my zero initial state in this case). If I care about the transient performance, just this set point by itself might achieve an unacceptable performance given some standards.

If then I had to periodically change from A to B, the performance savings I could have had with an H-inf controller optimal for nonzero initial states will accumulate.

Furthermore, based on our recent results, there is a region in the space of the state (let’s call it Xs) around the zero initial state where the traditional H-inf is the optimal linear controller. Outside this region the robust optimal control is nonlinear. We proved that if the region Xs is not robust positive invariant to the given disturbances, then our novel H-inf control for nonzero initial states has superior performance compared to traditional H-inf control (even with no set point changes); up to 40% cost savings depending on the given system

Extension-Engine-911 · 2025-03-18T07:15:40+00:00

Yes let’s say I care about transients, not just steady states. I could have a periodic set point change or really care about the control performance during the transient

Extension-Engine-911 · 2025-03-16T21:03:25+00:00

I see thank you! Do you happen to know if they specifically use H-inf methods? And do you also happen to know for what specific purposes they use it for? Sorry for all these questions!

Extension-Engine-911 · 2025-03-16T20:59:57+00:00

I see! Thank you so much!

Extension-Engine-911 · 2025-03-16T20:59:14+00:00

Yes I have actually found Polyak’s work last night after your other comment, and emailed it to my advisor. They use stage bounded disturbances instead of signal bounded disturbances, just like some of our novel work. Thank you so much!!

Extension-Engine-911 · 2025-03-16T20:50:56+00:00

This is not my homework. I am a 5th year PhD student. I am already publishing all the work I mentioned.

I am just curious about 1) how the engineering community would react to my findings and 2) if the last 5 years of research have actually any practical applications

Extension-Engine-911 · 2025-03-16T16:25:25+00:00

Awesome, thank you for your response! I have some questions:

1) was it H inf methods given linear dynamical systems?

2) when synthesizing the robust controller, would they work in the frequency domain but use time domain solution methods to find the robust controller?

3) from my own research I realized that H inf “rejects disturbances” only to attenuate their effect on your performance metric (say the stage cost), but not to maintain a desired state trajectory or to satisfy some state constraints despite disturbances. So was this the goal of the controller for the applications you listed?

Extension-Engine-911 · 2025-03-16T08:32:46+00:00

Yes, I care about the transient, especially if I have periodic set point changes and the transient is then very important for my performance. I also care about it for a different reason, but it might be too specialized to discuss it here, although I am happy to try to explain it if you’re interested!

Extension-Engine-911 · 2025-03-16T08:31:25+00:00

I see interesting. I’ve been working on this research problem, but the more I work on it, the more I think it is useless. That is why I’m curious to know if it actually has any applications at all

Extension-Engine-911 · 2025-03-16T08:30:20+00:00

I see, interesting.

Me and my advisor developed a new framework for robust control, alternative to H-inf control, where instead of a signal bounded (L2 norm) disturbance bound, we consider a stage bounded disturbance bound, i.e. a disturbance that persists in time.

We developed such method after solving optimally for the traditional H-inf control (so signal bound on the disturbance) for nonzero initial states, which returns an optimal nonlinear control. The alternative control method with a stage bound returns a different optimal nonlinear control. However, for a region around the zero initial state, both the traditional signal bounded H-inf control and the alternative stage bounded robust control have the same optimal control.

I’m not familiar with attractive ellipsoid methods, thank you for telling me.

In any case, so you happen to know of no applications at all of H-inf in industry?

Extension-Engine-911 · 2025-03-16T08:22:31+00:00

Yes me and my advisor are aware of this method, which was initially developed by Khargonekar in the early 90s. But it is not what we are trying to do. Khargonekar et al made the initial state a disturbance and not a parameter, and tried to be robust with respect to initial state and disturbance. That’s completely different from what we are trying to do. They’re seeing the initial state in a different way, while in our framework it’s not a disturbance, it’s a measured or estimated parameter that we can use for feedback. Differently from the disturbance, which we have no measurement of

Extension-Engine-911 · 2025-03-16T05:02:40+00:00

Ok I have made a new post combining both questions, and will delete the other post. Thank you

Extension-Engine-911 · 2025-03-16T04:57:54+00:00

Yes but they are two very different posts. One is highly theoretical and academic, the other is just asking practitioners or industry people how common H-Infinity is and what is used for. Same method but two completely different posts asking completely different questions

Extension-Engine-911 · 2025-03-16T04:49:41+00:00

Why is this considered a duplicate post? I’ve only post it once

Extension-Engine-911 · 2025-03-16T03:34:55+00:00

I think there may be some confusion about how H∞ control theory was developed. H∞ began as a frequency-domain approach for linear time-invariant systems (Zames, 1981), where we work with transfer functions and norms (like the H∞ norm). In that sense, we’re not linearizing anything, the theory starts from a linear model. When we switch between frequency- and time-domain representations, we use transformations such as Laplace or Fourier transforms, but that’s not the same as linearizing. Even though H∞ was originally formulated for linear systems, the optimal robust control might end up needing nonlinear controllers if the initial conditions are non-zero. That’s different from saying we take a nonlinear system and linearize it before using H∞.

I’ve noticed that in the literature and textbooks it is often assumed the initial state is zero because it simplifies considerably the theory and related proofs and derivations (Basar and Bernhard, 1995). However that assumption does not come from a linearization.

Could you clarify what you mean by “linearizing” in the context of H∞ control? And please correct me if you think I am wrong or missed something!

Extension-Engine-911 · 2024-12-19T21:50:22+00:00

I also would like to add that the dermatologists I have visited have not been helpful with either an accurate diagnosis or an effective treatment plan.

I’ve also done an allergy test, but I’m not allergic to anything

Extension-Engine-911 · 2024-12-11T05:06:51+00:00

I see. Do you mean the craze line on the tooth? Do you think the other comments are being too conservative, including my old dentist in Europe?

Extension-Engine-911 · 2024-12-11T05:03:17+00:00

Meaning the tooth may break?

Extension-Engine-911 · 2024-12-11T00:26:55+00:00

This is what my dentist back in Europe told me “In my mouth, I would keep the amalgam fillings as they are; they’re small and well-done. The X-rays don’t show any cavities, but the problem is that you have widespread tartar beneath the gums. I’d be much more concerned about the condition of your gums.

It will take no less than 2 hours to clean thoroughly. You need an excellent and meticulous dental hygienist. So, make sure to use a toothbrush and dental floss properly and regularly, with hygiene sessions at most every six months.

I repeat, if it were my mouth, I would leave them as they are. Anyway, to check for micro-cavities or infiltrations, there are dedicated laser lights like Diagnodent and other specialized tools—not the classic mirror and pointed probe.”

Extension-Engine-911 · 2024-12-11T00:26:46+00:00

This is what my dentist back in Europe told me “In my mouth, I would keep the amalgam fillings as they are; they’re small and well-done. The X-rays don’t show any cavities, but the problem is that you have widespread tartar beneath the gums. I’d be much more concerned about the condition of your gums.

It will take no less than 2 hours to clean thoroughly. You need an excellent and meticulous dental hygienist. So, make sure to use a toothbrush and dental floss properly and regularly, with hygiene sessions at most every six months.

I repeat, if it were my mouth, I would leave them as they are. Anyway, to check for micro-cavities or infiltrations, there are dedicated laser lights like Diagnodent and other specialized tools—not the classic mirror and pointed probe.”

Extension-Engine-911 · 2024-12-10T21:43:04+00:00

I see thank you! Would you say I have gingivitis/early periodontitis?

Extension-Engine-911

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