Online Tuning of Koopman Operator for Fault-Tolerant Control: A Case Study of Mobile Robot Localising on Minimal Sensor Information

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Both the paper's title and its Abstract state sufficiently clearly the main aims of the paper. However, the use of acronyms should be avoided in the paper's Abstract, as they reduce its readability.

2. Abstract of the paper should state the importance, gaps, method and the key results of the paper. Introduction is too long and raw. It should analyse the recent and related works with their advantages and disadvantages. The gaps should be clear and the claimed contributions should be well justified.

3. It is difficult to appreciate the method that the authors propose in the manner in which the paper is currently written or to perceive whether there is a major novelty/if this method solves the problem being presented in an important way. In addition, the main contributions should be listed in the introduction. For clarity of the contribution summarized at the end of the Introduction, the references should be given for comparison.

4. In the section of the introduction, a structural summary of the full text is suggested presented in the revision.

5. Some model-free control or Fault tolerant control methods studied in this paper should be analyzed and compared with other similar studies, which is helpful. For example: “Model-free output feedback optimal tracking control for two-dimensional batch processes”; “Adaptive optimal tracking control of networked linear systems under two-channel stochastic dropouts”; “Model-free output feedback optimal tracking control for two-dimensional batch processes”.

6. In the simulation comparison, model and controller parameters should be included and explain how to get these parameters of model and controller.

7. The reference format is not consistent in many places, such as capitalizing the first letter, incomplete punctuation, etc., and it needs to be checked and revised.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1) The paper uses inconsistent notation, such as mixing small and capital letters for the same variable. This inconsistency creates confusion and undermines the technical rigor of the presentation.

2) What's the advantage of the proposed method compared to model-based fault tolerant control? Moreover, in the last few years, there have been a growing number of studies on fault tolerant control. The paper fails to capture that aspect in their literature survey.

3) The algorithms used for comparison are not described in sufficient detail. Readers cannot evaluate the fairness or validity of these comparisons without knowing how these methods were implemented or configured.

4) Figure 1 is not adequately described in the manuscript. A proper explanation of all visual elements is necessary.

5) Please give more details about FDI.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper proposes an analytical redundancy technique to handle sensor faults in a wheeled mobile robot. The topic is interesting. However, this paper suffers from several critical issues that significantly undermine its scientific rigor, clarity, and contribution. My comments are given as follows

1. The manuscript claims to propose a "novel analytical redundancy technique," but the methodology relies on well-established techniques such as the Koopman operator and Dynamic Mode Decomposition (DMD). The online tuning of the Koopman operator, while practical, is not sufficiently novel to warrant publication without deeper theoretical or experimental advancements.
2. The comparison with MATLAB's System Identification toolbox is not novel, as data-driven modeling for FTC is already a well-explored area. The authors should clearly articulate how their work advances the state-of-the-art beyond existing literature. Besides, the manuscript lacks rigorous validation of the Koopman-based models.
3. How to obtain the matrix C in Eq. (10)?
4. In Eq. (13), the matrix B is constant, while in Eq. (14), it is time-varying, and in Eq. (17), it is constant again, the authors should clarify this change. Besides, the authors should state why in Part 5.2.2, the matrix A is constant but B is not.
5. What’s the relationship between W(k) in Eq. (17) and the state X?
6. Why the sensor fault is represented as f={0,1}? The authors should state this issue clearly according to a practical system.
7. The function of the command “iddata” in Eq. (9) should also be stated.
8. The words in figure 2 is too small to read. Also, in Figure 4, the lines are nearly the same, the authors should provide the enlarged image.
9. Please compare the proposed method with those in such studies as Mixed-Gain Adaption-Based Fault-Tolerant Funnel Control of Robotic Manipulators With Unknown Dynamics and Sensor Faults; High-Accuracy Adaptive Robust Fault-Tolerant Control for Quadrotor With Actuator Uncertainties and Aerodynamic Drag Compensation; Adaptive Sensor-Fault Tolerant Control of Unmanned Underwater Vehicles With Input Saturation; and Zonotoptic Fault Estimation for Discrete-Time LPV Systems With Bounded Parametric Uncertainty.
10. There are some typos in the paper, such as:
11. Initial capitalization of proper nouns and technical terms should be standardized throughout the manuscript. The paper’s title should use title format.
12. On page 4, “as shown in (3)” should be ““As shown in (3)”.
13. The manuscript contains several grammatical errors (e.g., on page10, "Leunberger observer" should be "Luenberger,"). A thorough proofreading is required.
14. Some abbreviations (e.g., DMD, VDMD) are defined multiple times, while others (e.g., RMSE) are not defined at all.

Comments on the Quality of English Language

See above.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The language needs further polishing. The innovation points are not prominent enough and require more refined summarization, which should be clarified in the introduction, the section on contributions, and throughout the paper. Additionally, the references need to be further improved, addressing the issues previously raised.

Comments on the Quality of English Language

The language needs further polishing. 

Author Response

Comments 1: The language needs further polishing. The innovation points are not prominent enough and require more refined summarisation, which should be clarified in the introduction, the section on contributions, and throughout the paper. Additionally, the references need to be further improved, addressing the issues previously raised.

Response 1: Thank you for your valuable time and constructive feedback. We have revised the introduction and the contributions section, and refined the summary to make the innovation points more prominent and enhance overall readability. Additionally, we have improved the relevant references. However, given the vast body of literature on sensor fusion, we have included only the most significant works we reviewed to avoid redundancy.

Reviewer 2 Report

Comments and Suggestions for Authors

The revision is good. All of my concerns have been addressed effectively.

Author Response

Comments 1: The revision is good. All of my concerns have been addressed effectively.

Response 1: Thank you for your valuable time and providing constructive comments.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

I have no further comments.