Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The abstract gives a good overview, it would be stronger if it clearly highlighted the research gap (limited study of actuator combinations and fragility in path tracking) and summarized the main quantitative findings. This will make the novelty stand out immediately.
2. The introduction is well written, but it could better emphasize what is new here compared to recent robust control and actuator configuration studies. A clearer articulation of the specific challenges addressed would sharpen the focus.
3. The listed contributions are important, but they should be stated more boldly. The explicit integration of the non-fragile property into LQR and the structured comparison of RS, 4ID, and 4IB actuators are significant and deserve more emphasis.
4. The coverage of prior work is quite comprehensive, but including a few very recent papers or surveys on robust path tracking would help position this study more clearly in the current research landscape.
5. The mathematical development is rigorous but dense. Adding a simplified block diagram or schematic of the proposed control architecture would greatly improve accessibility for readers less familiar with LMI-based methods.
6. The introduction of new performance measures (ΔX, ΔY, OS%, ΔDX, ΔSX) is a strong point. It would be helpful to briefly compare them with more conventional metrics, so readers can appreciate why these were chosen.
7. The double lane-change scenario is an appropriate benchmark, but adding a few more challenging cases (e.g., different road frictions, actuator faults, or external disturbances) would better demonstrate robustness and generality.
8. The paper shows robustness against parameter variations, but it remains unclear how well the approach would scale to different vehicle classes, higher speeds, or real-world conditions. Acknowledging these limitations would strengthen the contribution.
9. The actuator comparisons are useful, but the discussion could go a bit deeper into practical trade-offs, for example, cost, response limitations, or integration challenges in real vehicles.
10. The results are simulation-based; experimental validation will eventually be needed to confirm real-world feasibility. Also, factors such as sensor noise or actuator delays were not considered and should be mentioned as limitations.
11. Beyond sliding mode or adaptive control, it would be valuable to consider:

• Integration with Model Predictive Control (MPC) for predictive handling.
• Experimental validation on real vehicles or benchmark datasets.
• Incorporation of environmental uncertainties (e.g., friction changes, wind disturbances).
• Evaluation of computational requirements for real-time use.

12. It may also be worth suggesting model-free or data-driven controllers (e.g., reinforcement learning, adaptive dynamic programming). These approaches can complement model-based control when dynamics are difficult to model or when uncertainty is very high. Cite this paper:

https://link.springer.com/article/10.1007/s44430-025-00004-2

 

13. The conclusion could more strongly connect the findings to practical implications, for instance, when a simple LQR might suffice versus when robust/non-fragile design is necessary. Highlighting the trade-offs between complexity and robustness would add impact.

14. The paper is well written, but polishing some sentences and improving transitions between sections would enhance readability.

Author Response

We would like to express our sincere appreciation to the reviewer for the detailed and thoughtful feedback. The comments were very helpful in refining the manuscript and improving its clarity and overall quality.

  1. The abstract gives a good overview, it would be stronger if it clearly highlighted the research gap (limited study of actuator combinations and fragility in path tracking) and summarized the main quantitative findings. This will make the novelty stand out immediately.

Response : We appreciate the reviewer’s comment. We added a sentence on the abstract :

The robust and non-fragile LQR maintains lateral offset within 0.02 m and overshoot below 1% under ±20% parameter variation, offering improved stability margins compared with the baseline LQR. The results highlight context-dependent actuator effects and clarify the trade-off between control complexity, robustness, and real-world applicability.

 

  2. The introduction is well written, but it could better emphasize what is new here compared to recent robust control and actuator configuration studies. A clearer articulation of the specific challenges addressed would sharpen the focus.

Response :  We clarified the novelty of the study compared with recent robust control and actuator configuration works by emphasizing the explicit modeling of controller fragility and the structured comparison of actuator combinations. These sentences are added on the third page, above the summarized contributions :

Unlike conventional robust control frameworks that primarily address model uncertainty or rely on extensive gain scheduling, the present study emphasizes controller fragility as an equally critical factor. By integrating robustness and non-fragility within a unified LMI-based LQR design, this work offers a distinct contribution that bridges theoretical stability analysis and practical implementation reliability.

 

3. The listed contributions are important, but they should be stated more boldly. The explicit integration of the non-fragile property into LQR and the structured comparison of RS, 4ID, and 4IB actuators are significant and deserve more emphasis.

Response :  We strengthened the phrasing of the contributions to highlight the novelty and importance of the proposed integration.

1. A robust and non-fragile path tracking controller is newly formulated using an LMI-based LQR framework. The proposed approach explicitly integrates the non-fragile property—an aspect rarely addressed in previous path tracking studies—into the controller design, thereby improving both robustness and implementation reliability under parameter perturbations.
2. A systematic comparative analysis of multiple actuators (RS, 4ID, and 4IB) for yaw-moment generation is conducted. While most existing robust PTC studies have relied solely on FS or 4S, this work provides the first structured evaluation of how different actuator combinations affect path tracking robustness and overall vehicle stability.
3. Comprehensive simulation results identify optimal controller–actuator configurations for practical implementation. The study demonstrates that when performance differences are minor, a simpler LQR design remains the most effective choice—offering clear design guidance for real-world autonomous vehicle control.

 

 

4. The coverage of prior work is quite comprehensive, but including a few very recent papers or surveys on robust path tracking would help position this study more clearly in the current research landscape.

Response :  We have additionally cited three papers published within the past three years in our introduction. Each paper is cited separately in the first, second, and third paragraphs.

40. Nam, N. N.; Han, K. Path-tracking robust model predictive control of an autonomous steering system using LMI optimization with independent constraints enforcement. International Journal of Control, Automation and Systems, 2024, 22(11), 3352-3363.
41. Festl, K.; Solmaz, S.; Watzenig, D. Smooth and Robust Path-Tracking Control for Automated Vehicles: From Theory to Re-al-World Applications. Electronics, 2025, 14(18), 3588.
42. Khosravian, A.; Masih-Tehrani, M.; Amirkhani, A.; Ebrahimi-Nejad, S. Robust autonomous vehicle control by leveraging multi-stage MPC and quantized CNN in HIL Framework. Applied Soft Computing, 2024, 162, 111802.

 

5. The mathematical development is rigorous but dense. Adding a simplified block diagram or schematic of the proposed control architecture would greatly improve accessibility for readers less familiar with LMI-based methods.

Response :  We have added a new Figure 1 to the main text of the paper. Fig.1 shows the Overall structure of the proposed robust and non-fragile path tracking controller.

 

6. The introduction of new performance measures (ΔX, ΔY, OS%, ΔDX, ΔSX) is a strong point. It would be helpful to briefly compare them with more conventional metrics, so readers can appreciate why these were chosen.

Response :  We have added a short comparison explaining how the proposed metrics extend conventional measures such as steady-state error, rise time, and settling time, above the figure 4 :

Conventional metrics such as steady-state error and settling time mainly assess steady-state tracking accuracy, whereas the proposed measures (ΔX, ΔY, OS%, ΔDX, ΔSX) capture both lateral and longitudinal agility. In particular, ΔDX and ΔSX quantify transient delay more directly, offering clearer physical interpretation for double lane-change maneuvers.

 

7. The double lane-change scenario is an appropriate benchmark, but adding a few more challenging cases (e.g., different road frictions, actuator faults, or external disturbances) would better demonstrate robustness and generality.

Response :  Thank you for the suggestion. Due to the scope of this study, only the double lane-change scenario was considered, but we have added discussion on how the method could be extended to other conditions (e.g., low μ, actuator faults, crosswind disturbances). We have added two sentences on the end of the Section 4 :

Although this study focuses on the double lane-change maneuver, the proposed framework can be extended to other conditions such as varying road friction, actuator degradation, or external disturbances. These cases are expected to be handled effectively by the LMI-based robust formulation and will be investigated in future work.

 

Note.

We respectfully note that Comments 8, 10, 11, 12, and 13 are closely interrelated, all focusing on the interpretation of results, practical implications, and directions for future research. For this reason, instead of responding to each point separately, we have addressed them collectively by comprehensively revising the Conclusion section. The revised version now incorporates all relevant suggestions, and we kindly ask for your understanding that these comments are discussed together in that section rather than in sequential order.

 

8. The paper shows robustness against parameter variations, but it remains unclear how well the approach would scale to different vehicle classes, higher speeds, or real-world conditions. Acknowledging these limitations would strengthen the contribution.
9.  
10. The results are simulation-based; experimental validation will eventually be needed to confirm real-world feasibility. Also, factors such as sensor noise or actuator delays were not considered and should be mentioned as limitations.
11. Beyond sliding mode or adaptive control, it would be valuable to consider:

- Integration with Model Predictive Control (MPC) for predictive handling.

- Experimental validation on real vehicles or benchmark datasets.

- Incorporation of environmental uncertainties (e.g., friction changes, wind disturbances).

- Evaluation of computational requirements for real-time use.

12. It may also be worth suggesting model-free or data-driven controllers (e.g., reinforcement learning, adaptive dynamic programming). These approaches can complement model-based control when dynamics are difficult to model or when uncertainty is very high. Cite this paper:

https://link.springer.com/article/10.1007/s44430-025-00004-2

13. The conclusion could more strongly connect the findings to practical implications, for instance, when a simple LQR might suffice versus when robust/non-fragile design is necessary. Highlighting the trade-offs between complexity and robustness would add impact.

Response (for the comment 8, 10, 11, 12, 13) :  We sincerely appreciate these valuable comments, which all relate to how the results are interpreted, their practical meaning, and possible extensions of this work. Since these points are closely connected, we chose to address them together rather than separately.

The Conclusion section has therefore been fully rewritten to clarify when a simple LQR is sufficient and when the robust or non-fragile version becomes necessary, to discuss actuator effects and integration in practical terms, and to outline future work including MPC extension, reinforcement-learning-based adaptation, and experimental validation. We hope this revised section better conveys the practical relevance and future potential of the proposed framework.

 

 

9. The actuator comparisons are useful, but the discussion could go a bit deeper into practical trade-offs, for example, cost, response limitations, or integration challenges in real vehicles.

Response : We have expanded the discussion on practical trade-offs, including cost, complexity, and integration feasibility. The added sentence is on the middle of page 19 :

Although 4ID and 4IB improve yaw-moment controllability, their implementation increases system cost and hardware complexity. In contrast, RS and 4S require less modification but offer limited yaw control authority. These trade-offs should be considered in practical applications.

 

14. The paper is well written, but polishing some sentences and improving transitions between sections would enhance readability.

Response : We have carefully reviewed the overall flow and sentence structure of the manuscript. To improve readability and ensure smoother transitions between major sections, a linking sentence has been added at the beginning of Section 2.3 to connect it naturally with the preceding section :

In Section 2.2, the fundamental formulation of the LQR problem was presented, focusing on the nominal system without uncertainty. In this section, the LQR framework is extended to explicitly address parameter uncertainty and controller fragility. A system subject to both effects can be represented as in (16), where the state-space matrices and controller gains include uncertain components.

And another transition sentence has been inserted at the start of Section 4 to provide a clear link from the performance measures in Section 3 to the simulation study. These revisions enhance the continuity and readability of the paper.

The performance measures defined in Section 3 are now applied to evaluate the proposed controllers through simulation.

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

this manuscript focuses on one of many systems that underpin autonomous driving. Lane tracking is a crucial system, and this research may be of interest to various communities, not just science and engineering. The presented research results are promising and important. Therefore, I believe the work is worthy of publication in this journal, although it requires some additions and clarifications.

Detailed comments on the manuscript:

1. Abstract and key word are correct.
2. I would strengthen the introduction section with additional literature on public perception of autonomous vehicles and their impact on transport congestion and safety (the latter has been discussed in detail). I would add relevant references in lines 30 and 32. On line 30, add, for example: https://doi.org/10.3390/en14185778 and on line 32, add, for example: https://doi.org/10.20858/sjsutst.2020.108.1 and https://doi.org/10.14669/AM.VOL90.ART2
3. In line 43, the list of references could be broken up, avoiding multiple citations in a single line. Some of these works, refs 1 to 5, could be cited above. Try to reduce the number of multiple citations in the manuscript.
4. In the excerpt (lines 158-166), this publication may also be helpful, providing knowledge from experimental studies of vehicle behavior in various conditions: https://doi.org/10.1007/s12239-021-0071-x and https://doi.org/10.2478/logi-2022-0005  
5. Could the authors explain where the input data for their simulations came from? Was it preceded by experimental studies, based on literature, etc.?
6. Section 4 presents the results, but lacks a summary of them in relation to other research results; this is a weak part of the manuscript.
7. The conclusions of the paper are correct, but could the authors more clearly indicate directions for further work?

8.  In what software environment was the simulation performed, Matlab, Python?

9.  

   What was the basis for selecting the wheel forces? Based on our own research or other research?

10.  

    In Table 2, separate the values from the units in the lines.

Editorial Notes:

1. In my opinion, the research methodology section is missing, which should have been placed before section 2.
2. Tables 3 to 6 should be placed higher in line 464.
3. Tables 7 to 12 should be placed higher in line 496.
4. There are minor editing errors, such as missing spaces between units or words, e.g., in lines 462 and 483.

Thank you

Author Response

We would like to express our sincere appreciation to the reviewer for the detailed and thoughtful feedback. The comments were very helpful in refining the manuscript and improving its clarity and overall quality.

 

Detailed comments on the manuscript:

1. Abstract and key word are correct.
2. I would strengthen the introduction section with additional literature on public perception of autonomous vehicles and their impact on transport congestion and safety (the latter has been discussed in detail). I would add relevant references in lines 30 and 32. On line 30, add, for example: https://doi.org/10.3390/en14185778 and on line 32, add, for example: https://doi.org/10.20858/sjsutst.2020.108.1 and https://doi.org/10.14669/AM.VOL90.ART2

Response : Two of the suggested references on public acceptance and traffic impact of autonomous vehicles have been incorporated into the first two sentences of the Introduction :

1. Dudziak, A.; Stoma, M.; Kuranc, A.; Caban, J. Assessment of Social Acceptance for Autonomous Vehicles in Southeastern Poland. Energies, 2021, 14(18), 5778.
2. Bartuska, L.; Hanzl, J.; Lizbetin, J. Urban traffic detectors data mining for determination of variations in traffic vol-umes. Archiwum Motoryzacji, 2020, 90(4), 15-31.

 

  3. In line 43, the list of references could be broken up, avoiding multiple citations in a single line. Some of these works, refs 1 to 5, could be cited above. Try to reduce the number of multiple citations in the manuscript.

Response : For Comment 3, the citation style has been improved by reducing multiple consecutive references and reorganizing or removing less relevant ones to achieve a more balanced and readable structure.

 

  4. In the excerpt (lines 158-166), this publication may also be helpful, providing knowledge from experimental studies of vehicle behavior in various conditions: https://doi.org/10.1007/s12239-021-0071-x and https://doi.org/10.2478/logi-2022-0005  

Response : Regarding this comment, the reviewer’s recommended experimental studies have been added to Section 2.1 with a new supporting sentence:

This modeling approach has also been validated through various experimental studies on real vehicles under different operating conditions [47,49].

 

  5. Could the authors explain where the input data for their simulations came from? Was it preceded by experimental studies, based on literature, etc.?

Response : The source of the simulation data is now explicitly stated at the end of the introductory paragraph of Section 4:

All parameters and input signals were derived from the validated CarSim vehicle database and literature-based tire data, ensuring consistency with experimentally verified vehicle dynamics.

 

  6. Section 4 presents the results, but lacks a summary of them in relation to other research results; this is a weak part of the manuscript.

Response : In addition to summarizing the simulation results, we added sentences that we wanted to emphasize from these results to the end of Section 4 :

The proposed robust and non-fragile LQR consistently maintained lateral offset within about 0.02 m and overshoot below 1% under ±20% parameter variations, outperforming the baseline LQR. More importantly, the results demonstrate stable and uniform control behavior across different actuator configurations and uncertainties, emphasizing that the strength of this approach lies not in a specific algorithm or actuator setup but in its inherent robustness and non-fragility. This consistency highlights a practical balance between controller simplicity and reliability under diverse conditions.

 

  7. The conclusions of the paper are correct, but could the authors more clearly indicate directions for further work?

Response : Based on your comments, I have rewritten the Conclusion, and the direction of further work is specified in the revised conclusion.

 

  8. In what software environment was the simulation performed, Matlab, Python?

Response : The simulation was conducted in a CarSim–MATLAB/Simulink co-simulation environment, with all control algorithms implemented in MATLAB. We have added a sentence on the first paragraph of the Section 4:

The controllers were implemented in MATLAB/Simulink and coupled with the CarSim vehicle simulation platform.

 

  9.  What was the basis for selecting the wheel forces? Based on our own research or other research?

Response : The wheel-force selection and allocation are not based on arbitrary or empirical tuning but follow standard formulations in vehicle dynamics literature, as described in Section 2.5, above the equation (49) :

In this study, the traction and braking torques (T_Bi and T_Di​) at wheel i are derived from the longitudinal forces DF_x1, DF_x2, DF_x3 and DF_x4​, which are obtained via the WLS method using the optimal solution q_opt​ in (46). The sign of DF_xi​ determines whether the value corresponds to T_Bi and T_Di​, and the computation is carried out as given in (49) [44,45,57,59].

 

   10.  In Table 2, separate the values from the units in the lines.

Response : We have revised Table 2 in the main text of the paper according to your comment.

 

 

Editorial Notes:

1. In my opinion, the research methodology section is missing, which should have been placed before section 2.

Response : In this paper, Section 2 (“Design of Robust Non-Fragile Path Tracking Controller”) already presents the research methodology, including the modeling framework and controller design procedures. To make this clearer to readers, we have added the following introductory sentence at the beginning of Section 2:
Section 2 presents the research methodology, including controller design and modeling procedures.
This clarification ensures that the methodological scope of Section 2 is explicitly recognized.

 

  2. Tables 3 to 6 should be placed higher in line 464.

Response : The tables are replaced, as your suggestion.

 

  3. Tables 7 to 12 should be placed higher in line 496.

Response : The tables are replaced, as your suggestion.

 

  4. There are minor editing errors, such as missing spaces between units or words, e.g., in lines 462 and 483.

Response : We appreciate the reviewer’s attention to detail regarding unit formatting. Following the SI convention, all numerical values and their corresponding units have been reviewed and corrected to include a space between the number and unit symbol (e.g., 50 km/h instead of 50km/h)

Reviewer 3 Report

Comments and Suggestions for Authors

The paper needs major revisions. My comments are in below:

• There is no conclusion at the end of abstract section. The paper needs nomenclatures.
• I did not see that the author talked about settling time, rise time, and overshoot of the transient response in figure 3.
• The author in the paper used controller. Is this controller PID or adaptive? Please explain. Where is the gain of proportional, integrator and differentiator? If any can you please provide a mechatronics circuit in the paper?
• I did not see any verification in the paper. The results are not enough to better understand the philosophy of the paper.
• It is not right to put abbreviation in the introduction section. The conclusions section needs to be paraphrased.
• I need to see Fast Fourier Transform of power density spectrum (FFT). I need to see the response against time.
• Please pay attention on the self-citation.

Author Response

We sincerely thank you for the time and effort devoted to evaluating our manuscript. We carefully reviewed all comments and have revised or clarified the manuscript where appropriate. However, several of the reviewer’s points appear to reflect a misunderstanding of the scope and methodology of this paper. Detailed responses are provided below.

 

1. There is no conclusion at the end of the abstract section.

Response : We appreciate the comment. The abstract has been slightly revised to make the concluding statement more explicit, summarizing the main findings and their implications.

 

2. The paper needs nomenclatures.

Response : To improve readability, a short Nomenclature table summarizing key symbols (e.g., β, γ, δf, ΔMz) has been added in the Appendix.

 

3. I did not see settling time, rise time, and overshoot of the transient response in Fig. 3.

Response : The performance of the proposed controller is evaluated using five quantitative indices (ΔX, ΔY, OS%, ΔDX, and ΔSX) introduced in Section 3. These correspond conceptually to rise time, settling time, and overshoot, but are defined in a trajectory-based framework suitable for path tracking rather than a single-input single-output (SISO) time-response system. This has been clarified in Section 3.

 

4. The author in the paper used controller. Is this controller PID or adaptive? Please explain. Where is the gain of proportional, integrator and differentiator? If any can you please provide a mechatronics circuit in the paper?

Response : We would like to clarify that the controller used in this study is not a PID-type controller but a Linear Quadratic Regulator (LQR) designed via Linear Matrix Inequality (LMI) optimization. It is a state-feedback optimal controller, not a circuit-based implementation. The manuscript now explicitly states this distinction at the beginning of Section 2.2.

 

5. I did not see any verification in the paper. The results are not enough to better understand the philosophy of the paper.

Response : Verification was conducted through co-simulation using CarSim and MATLAB/Simulink, as detailed in Section 4. These results serve as numerical validation of the proposed controller under parameter uncertainties and actuator variations. The term “verification” has been explicitly mentioned in Section 4 for clarity.

 

6. It is not right to put abbreviation in the introduction section.

Response : We respectfully disagree. Abbreviations are introduced once and defined in the introduction for clarity, which is a common and acceptable practice in MDPI journals. Nevertheless, we have ensured that each abbreviation is defined upon first appearance.

 

7. The conclusions section needs to be paraphrased.

Response : The conclusion section has been rewritten for improved flow and conciseness, emphasizing practical implications and future research directions.

 

8. I need to see FFT or power density spectrum (FFT). I need to see the response against time.

Response : This study focuses on path tracking control, which is fundamentally a trajectory-following problem rather than a frequency-domain vibration analysis. Therefore, FFT or power spectral density is not applicable. The responses of interest are the lateral and yaw trajectories, which are already presented in Section 4. A clarification sentence has been added to avoid misunderstanding.

 

9. Please pay attention on the self-citation.

Response : We confirm that self-citations are minimal and limited only to essential prior works directly relevant to the proposed method. No excessive self-citations remain.

Reviewer 4 Report

Comments and Suggestions for Authors

The paper presents a robust and non-fragile path tracking controller for autonomous vehicles, which can handle variations in vehicle speed and tire cornering stiffness. The proposed controller is based on an LQR framework with explicit modeling of controller fragility and incorporation of non-fragile properties. The study compares the performance of different actuator configurations (FS, RS, 4IB, and 4ID) in robust path tracking and provides insights into the trade-off between controller complexity, robustness, and practical performance.

The topic is timely and relevant to autonomous vehicle control. Modeling and suppressing controller fragility is practically important. The integration of fragility metrics into an LMI-LQR design is a useful methodological contribution. The experimental evidence supports the main claims. However, the following points should be improved:
- While "fragility" is briefly described in the introduction, it should be defined formally in the paper to clearly distinguish the contribution from "robust only" approaches. This is important, as robust approaches have been widely explored in automated driving.
- The work was evaluated only in simulation. Strengthen the manuscript by either adding hardware-in-the-loop or scaled-vehicle experiments, or by clearly stating limitations and outlining a concrete experimental plan for future work. Evaluating more scenarios would also be helpful. 
- Discuss how the controller would handle actuator saturation, sensor faults, and delays.
- Robust approaches tend to be hard to tune and to have a poor performance over all relevant scenarios in practice. Please provide a brief guideline how this could be mitigated.
- Expand the related-work summary to include recent developments in sliding-mode control, adaptive control, and robust MPC applied to vehicle yaw control. Clearly state how this paper differs from and improves upon those methods.

Minor:
- Discuss why RS without additional yaw actuators increases side-slip. Further, why is actuator effectiveness context-dependent, and what do you specifically mean by "integration should be carefully designed"?
- Move some of the lengthy LMI derivations to an appendix and focus on the most important steps.

Author Response

We sincerely thank you for the constructive and thoughtful comments. We appreciate the overall positive evaluation of the paper’s topic, relevance, and methodology, and have carefully addressed each point below. Some of the reviewer’s suggestions have been incorporated into the revision, while others have been clarified to maintain the manuscript’s focus and conciseness.

 

1. While ‘fragility’ is briefly described in the introduction, it should be defined formally in the paper to clearly distinguish the contribution from ‘robust only’ approaches.

Response:

Thank you for pointing this out. We agree that the distinction between robust and non-fragile designs is important. Accordingly, we have expanded the description of “controller fragility” in Section 2.3 to provide a more formal definition and clarify its difference from conventional robust control formulations.

 

2. The work was evaluated only in simulation. Strengthen the manuscript by either adding hardware-in-the-loop or scaled-vehicle experiments, or by clearly stating limitations and outlining a concrete experimental plan for future work.

Response:

We appreciate this valuable suggestion. At present, only simulation results are available; however, we have added a clear statement in the Conclusion acknowledging this limitation and describing plans for future work, including hardware-in-the-loop and real-vehicle validation. Expanding the study to additional driving scenarios has also been noted as a next step.

 

3. Discuss how the controller would handle actuator saturation, sensor faults, and delays.

Response:

Thank you for the insightful comment. A short paragraph has been added to the Discussion section explaining how actuator saturation can be addressed by incorporating limit constraints into the LMI framework, and how sensor faults or delays can be managed through estimation schemes or predictive compensation in future implementations.

 

4. Robust approaches tend to be hard to tune and to have a poor performance over all relevant scenarios in practice. Please provide a brief guideline how this could be mitigated.”

 

Response:

We agree that robust control design often involves tuning complexity. To address this, we have included a brief discussion in the Conclusion outlining how parameter weighting (via Bryson’s rule) and iterative simulation-based tuning can be used to balance robustness and responsiveness in practice.

 

5. Expand the related-work summary to include recent developments in sliding-mode control, adaptive control, and robust MPC applied to vehicle yaw control. Clearly state how this paper differs from and improves upon those methods.”

 

Response:

We appreciate this suggestion. To maintain focus and manuscript length, we have selectively added two recent papers on robust MPC and adaptive control (2023–2024) in the Introduction, and included one clarifying sentence highlighting how the present work differs—specifically by integrating fragility modeling into an LMI-based LQR framework and conducting a structured actuator comparison.

 

Minor Comments

 a. “Discuss why RS without additional yaw actuators increases side-slip.”

Response : A short explanation has been added in Section 4 noting that rear steering alone can amplify side-slip due to phase lag between front and rear tire lateral forces at high speed.

 

   b. “Why is actuator effectiveness context-dependent, and what do you specifically mean by ‘integration should be carefully designed’?”

Response : The text has been refined to clarify that actuator effectiveness depends on road friction, steering geometry, and control allocation priority; integration refers to coordinating yaw-moment and steering actuators without conflict.

 

  c. “Move some of the lengthy LMI derivations to an appendix.”

Response : We appreciate the suggestion. While we have retained the essential derivation steps in the main text for completeness, explanatory comments and intermediate details have been simplified to improve readability.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The revisions have been addressed with care, and the manuscript shows clear improvements in both clarity and quality. Thank you for your thorough responses to the feedback. Based on the revisions, the paper can be accepted for publication.

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

thank you for your satisfactory responses to the review comments and for the corrections and additions to the manuscript. The manuscript is substantially improved, so I recommend the work for publication in its current form.

Regards!

Reviewer 3 Report

Comments and Suggestions for Authors

The paper needs minor revision. If possible, the author put all the results in in table form. I need to see these numbers in plot like in figure 4 to more understand the philosophy of the research. Thanks

Reviewer 4 Report

Comments and Suggestions for Authors

The manuscript has been improved and my major concerns have been addressed.