Stochastic Game-Based Anti-Jamming Control Method for Heavy-Haul Train Group Operation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript proposes a stochastic game-based anti-jamming control strategy to ensure the system stability and operational safety of the VCTS in HHR. It is well organized. However, the novelties of the work are not clearly clarified. And there are sever issues in writing and presentation.

1. The citation and references mismatch. For example, Ref. [2] is not cited in the text. Literature review is not sufficient to support the ideas proposed in the introduction part.
2. Figures, like 1 and 2, are not cited in the text as well. Some explanations and illustrations should be given to describe the figures. There two figures should not be placed in the introduction part.
3. The paragraph at beginning of Section 2 repeatedly mentions the work plan. It is suggested to delete it or reorganize for conciseness.
4. What do the terms, basic resistance and line resistance, mean? These two concepts need to be explained. Also, equations (2) and (3) need to be checked for their correction. What does the variable m in these two equations mean?
5. Sections 2.3 to 2.3 illustrate the proposed method for anti-jamming control. However, it is still not very clear how the method works for the VCTS.
6. It is very hard to distinguish the difference between Figure 3(a) and (d). How to verify the validation of SGAC algorithm under jamming attacks? Similarly, I cannot find the differences between Figure 4 (a), (c) and (e). How are the percentages 50%, 70%, and 90%, illustrated in these figures? Please explain them.
7. Figures 3 to 5 are not enough explained and discussed in detail to get some new findings.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Authors present a stochastic game-based anti-jamming control method for heavy-haul train group operation in this manuscript. There exists 5 major issues. Comments are listed as follows.

 

Major issue 1:Authors should summarize main contributions of the proposed method in the part of introduction.

 

Major issue 2: The part of experiment lacks comparison.Authors should compare the proposed method with at least 3 relevant methods while at least one method is proposed within 5 years. Methods of DP and MPC lack references.

 

Major issue 3: Authors should evaluate experimental results with quantitative criteria.

 

Major issue 4: Authors should present a flowchart of the proposed method.

 

Major issue 5:What are differences between heavy-hual train and not-heavy-hual train in anti-jamming control method?

 

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript presents a stochastic game-based anti-jamming control (SGAC) strategy to enhance the stability and robustness of virtual coupling train systems in heavy-haul railway operations. The topic is relevant, and the paper is generally well-structured. Overall, it is a good paper, but before it can be considered for publication, the following issues should be addressed:

 

1) The mathematical derivations, while detailed, are sometimes difficult to follow. Certain parts (e.g., the transition from the stochastic game formulation to the H∞ controller design) would benefit from additional explanatory text or flow diagrams to improve readability.

 

2) Although the paper highlights limitations in existing approaches, the novelty of the proposed SGAC framework compared with other robust or game-theoretic methods is not sufficiently emphasized. The discussion of how this work advances beyond previous H∞-based control approaches should be expanded.

 

3) The related work section could be better integrated with the motivation of the study. Some recent and relevant works in stochastic control and imitation learning-based approximations of stochastic models are missing, such as:

 

-Pozzi, A., Incremona, A. & Toti, D. Imitation learning-driven approximation of stochastic control models. Appl Intell 55, 838 (2025). https://doi.org/10.1007/s10489-025-06704-x

 

4) While simulation results are convincing, the lack of experimental validation or case studies on real railway data is a limitation that should be acknowledged more explicitly.

 

5) There are occasional inconsistencies in notation (e.g., switching between subscripts and superscripts, unclear variable definitions). A thorough proofreading is required to ensure consistency across equations and explanations.

Author Response

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Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I didn't find any point-by-point response to my comments in the first-round revision.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Authors do not present point-to-point response and revision according to previous peer-review.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for your careful revisions. All of the issues I raised in my previous review have been satisfactorily addressed, and I find the manuscript much improved. I have no further concerns.

Author Response

We wish to express our sincere gratitude for the valuable time and expertise you dedicated to reviewing our manuscript. Your constructive and insightful comments were exceptionally helpful and provided us with invaluable guidance. We believe that reflecting on your feedback has been instrumental in significantly elevating the overall quality, clarity, and scientific rigor of the paper. We appreciate this opportunity to improve our research, and we remain hopeful that our work, thus enhanced, will be found suitable for publication in MDPI Electronics.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all my concerns. I thereby recommend the paper for publication in Machines.

Author Response

We wish to express our sincere gratitude for the valuable time and expertise you dedicated to reviewing our manuscript. Your constructive and insightful comments were exceptionally helpful and provided us with invaluable guidance. We believe that reflecting on your feedback has been instrumental in significantly elevating the overall quality, clarity, and scientific rigor of the paper. We appreciate this opportunity to improve our research, and we remain hopeful that our work, thus enhanced, will be found suitable for publication in MDPI Electronics.

Reviewer 2 Report

Comments and Suggestions for Authors

 Major issue 1: Novelty of the proposed method does not reach the level of framework. It is just a new method.

 

Major issue 2: What are differences between heavy-hual train and not-heavy-hual train in anti-jamming control method?

Author Response

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Author Response File: Author Response.pdf

Round 4

Reviewer 2 Report

Comments and Suggestions for Authors

Authors have answered all questions reviewer concerned.