Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error
Round 1
Reviewer 1 Report
The paper might be interesting, but needs to be improved. Many items need clarification.
First of all, You consider very classic problem with linear SISO system. From the ILC point of view, You use the basic lifting method. You should mention that there are ILC methods related to so- called reptitive processes, i.e. to multidimensional framework.
In this classic problem, You assume the only novelty, so signals quantization, which is in fact always present in practice. But applying it to the purely theoretical ideal model is strange. You might add uncertainties, noises and possibly some nonlinearities, This would make stronger your results.
Also, sometimes, it is hard to understand You.
Part 3, which is crucial , is on Parameter-optimal Iterative Learning Control, in what the sense. I do not see any criteria. This is also a bit strange, as it can be understood that you do not want to consider a given system but some better one, which seems to be a nonsense. Probably it is related wit that you are not describing what do you want do, do not give basicsd but start with some equation with no discussion of them.
Many essential things are omitted. EG, You write on convergence, but I do not see anything about is that monotonical?
Finally, your model in the example is typical math game. Why not to take any real, physical system model (from the literature, eg) and apply your methods.
Might be improved, but not so bad.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
The article is interesting and the topic is definitely worthy of scientific investigation.
There are two problems with the contribution:
1) there are way too many errors and language-related problems. Those should really be corrected by a native English speaker before the final version is submitted.
2) There are a number of notation problems outlined below. Those should be corrected before publication. I would like Authors to answer the ones I marked with "[*]".
[*] page 3, eq. 1 - why do we need to constrain only to SISO systems?
page 4, line 172 - what is \Delta e_k(n)? This has not been previously defined.
[*] page 4, line 182. You've proven the "if" part. What about the "only if"?
[*] page 6, line 255. Theorem 1 (page 5) says about a system converging to a "bound error". This makes perfect sense, as for sure for some (large) quantization establishing a zero error may not be possible. Yet, the Theorem 2 shows that for a similar situation (note eq. (11)) a monotonic converge is possible. If we assume ||e_{k+1}||<\rho ||e_k|| then the error norm will tend to zero as k approaches infinity (i.e. in theory we can go "as low as we want" if we run the ILC algorithm "long enough"). If a quantization is large, does the monotonic convergence still hold?
page 7, line 269. What does non-negativeness (having all non-negative elements) have to do with positive definiteness of a matrix?
3) The article would really benefit from showing why a particular matrix really is positive definite. You often use X*Y^TY*X\succ 0 and it is cumbersome to go back to previous formulas to verify this fact. I do not think a formal proof is needed, just a very rudimentary, rough sketch of it (e.g. "due to the structure of H of ("above (3)"). Of course if there is no space, it's not required, but I think Authors should add this when possible. Note you do NOT need to comment on this point as this is merely a suggesiton.
My general question is: since the journal title is "applied sciences", what is a practical rationale behind assumption that (only) the output is quantized in the particular way? What about the quantization of the input? More importantly, could you elaborate a bit on how you can obtain perfect tracking in the presence of quantization (assuming it is "sufficiently large")?
In general, the article is worthy of publication but the problems outlined above should be corrected first.
I managed to find the following language-related problems. Note that there are for sure many more I missed so this list is not exhaustive.
page 2, line 79 - useless line break
page 4, lines 151-155 - those sentences should be re-written for clarity as currently they are difficult to understand.
page 6, line 219-220. The sentence "If the convergence rate is slower when the iterative learning control219
law converges gradually along the iterative direction, it needs a good adjustment mechanism to improve the speed of converge" needs to be re-written for clarity
page 6, line 229. Lemma 2 is written in a very confusing way. Maybe split it into two different lemmas to make it more clear?
page 6, line 233. Replace "For two matricesF and S with identical dimension and they are invertible matrices, then the identical equality (*) is true" with something similar to "Let F and S be invertible matrices of identical dimensions. Under this assumption, the identity (*) holds".
page 6, line 240. Where is the "data quantization" in Y_k? I was under the impression that Q played the role of the quantizer.
page 7, line 275. What is a "single" matrix? Did you mean "singular"?
page 11, line 422 - \lambda_{max}, "x" in "max" touches a "(".
page 12, line 442 - "cocrete" -> "concrete"
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
It seems that the technique of this paper is well-known. The authors must clearly show the difference and improvements in comparison with the existing results in the view of technique analysis,
1- The contributions should be highlighted in the Abstract. Does the proposed algorithm used show good performance?
2- The novelty of this paper should be highlighted in the main contributions through comparing it with the existing works. Comparison with previous works with nearly four years (2020 to 2023) should be included more.
3- Insert table to summarize the previous work with current work.
4- In Introduction, page 2, line 64 the paper said "In recent years, … control [23-25]. ", whereas these reference belong to years 2004, 2001. So, the word “recent” doesn't match the old years.
5- Most of the references in this paper are too old.
6- Cite some latest publications in introduction section and report novelty of the proposed study.
7- Some remark words on computation complexity of the results should be given,
8- This paper needs more simulations )add more examples(.
9- The conclusion should be brief and indicate the main results.
Other mistakes and typos have been taken into account in the manuscript such as in page 8, line 324 “…matrices [42]. we have”
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Figs 1 and 4 should be reedited in order to be on one page not on two.
Some small English editing would be positive, eg change who to which. denotations should be rather notations.
formulae (29), (40) and (41) rather formulas ...
In specific, rather specifically or particularly
So, English should be improved.
Author Response
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Author Response File: Author Response.pdf
Reviewer 2 Report
The changes made to the article are satisfactory, except rather unclear wording of Lemma 1. There are two more issues I found:
Line 175 - what exactly is a "concrete" number? Maybe you could define it in the Introduction by adding a very short "notation" section?
Lines 259-261.
a) What are "f" and "g"?
b) Can you show any example where the vector \ksi does NOT exist (you wrote "IF there exists a vector")? Note. There is no need to add this example to the paper - it is enough to show it in the Author's comments.
Except those rather minor problems, the article is ready for publication.
There are still numerous problems with English, but this version managed to fix at least some of them. I managed to find the following:
Line 275. "diag" should to be defined beforehand - it may not be obvious to everyone what you mean.
Line 168 - add a space before "by"
Line 193, 194 - This sentence is rather unclear. It should be rewritten for clarity.
line 249 - no space between "Remark" and "4"
Line 259. Replace "who" with "which"
Lines 509-510, 540-542. The plot is outside of the page.
As those are of trivial nature, I see no need of a full re-review process.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
The manuscript seems to have improved based on the reviewer's comments.
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Author Response
Thank you for your hard work. All suggestions are very important and helpful, and it will be great guiding significance to our paper writing and scientific research work.
I sincerely appreciate your kindness and devotion.
Best regaeds.
