Adaptive Proportional-Integral Sliding Mode-Based Fault Tolerant Control for Autonomous Underwater Vehicles with Thrusters Saturation and Potential Failure

Round 1

Reviewer 1 Report

The paper, a novel APISM-FTC method to deal with the dynamic nonlinearity and possible actuator failure in AUV systems was designed.

The results obtained in the paper are noteworthy but several points need to be completed and clarified.

1) Literature review is insufficient for methods containing neural networks and those based on other solutions; not enough newer literature from 2021-2022 (only one from 2021). 

2) Why was RBFNN used to estimate the uncertainty of the dynamics when there are others ? Please comment.

3) The advantages and disadvantages of the proposed approach (control scheme) in comparison with other NN-based as well as non-NN-based methods would need to be presented in more detail (a more detailed literature analysis would suffice in a separate section at the end of the paper and before the conclusions).

4) The simulation study lacks comparison with results obtained by any other method. This would need to be supplemented or, alternatively, another example should be added for a vehicle with different dynamic parameters (such an example would also be relevant because there are at least 3 known papers in which it was shown that some control algorithms failed when the dynamic parameters were changed even though they were effective for the conditions assumed in the original papers). Thus, it is expected to add 1 example from the proposed 2 possibilities. 

Other remarks:

1) Reference [25] does not contain equation (1). This should be changed.

2) It is necessary to explain the difference between equation (10) and the corresponding formula from the paper [27].

3) The formulas (40)-(44) used for the simulations are from the work of [3]. Please cite it correctly.

 

Author Response

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Reviewer 2 Report

Dear Authors,

You have dealt with a very important research topic, which is fault tolerant trajectory tracking. You have described in a very detiled way the theoretical background of Your work. But in overall this research result presentation is weak and needs some corrections.

1. In my  opinion some important publications about fault tolerant control in marine applications are missing. Your Introduction section should contain some examples of real fault tolerant systems.

2. You have written some theory about RBFNN, but I think there is missing description how they have been implemented, where the training data came from and how theses RBFNN simulate faults. There is also a lack of their modelling quality and reliability of the model.

3. I suggest to include desription of the test bed and simulations procedure, type of software used, model of UAV used in simulations. This will supplement You theoretical analysis and increase the quality or research results presentation.

4. In the Results section in Fig.7 oscillations in thrust are presented and in line 275 you write that "AUV can return to a stable state as soon as possible". There are also presented oscillations in Uc, Pc, vc in Fig.6, which is not stable state. There are no oscillations presented in "Healthy" mode and the controller is stable there.

5. I suggest deeper analysis why controller looses control performance after some time. These increasing oscillations suggest that controller is not stable and it is important to discuss it to present full overwiev for the controller. It cannot be written that it is "meaningless to discuss..." (line 291).

6. Conclusions are very limited and need to be rewritten in order to streamline it to highlight the focus of the paper. It is recommended to support them by results.

7. In line 297 "designed a novel APISM-FTC method to deal..." needs some broader comment. Because according to the presented simulation results this method is not good enough to be applied to UAV and controller looses stability after some time after thruster fault, which is proven by the increassing oscillations in the control signal.

Moreover there are some language mistakes. I suggest rewritting sentences in the following lines in order to guarantee better article understanding: line 47, line 53 (to approximate/for approximation), line 77 (F instead f in for), line 91 ("As shown in Figure 1, define..."), line 224 (square at the end of line),line 236 (to big space), line 239 (dots in [ ]).

 

Author Response

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Reviewer 3 Report

Review of the Article

Adaptive proportional-integral sliding mode-based fault tolerant control for autonomous underwater vehicles with thrusters saturation and potential failure

Jian Xu, Xing Wang, Ping Liu and Qiaoyu Duan

 

^{The article describes one method of autonomous underwater vehicles (AUVs) control. The principal approach is to linearize known motion models, and compensate for the error that occurs by evaluating it using the Radial basis function neural network (RBFNN). A useful feature is the accounting of thrusters’ failures. The stability of the obtained linear control is analyzed by the Lyapunov function method. The result is illustrated by a model example.}

^{In general, the article makes a favorable impression. But it is impossible to publish it in this form, because there are too many errors and inaccuracies. Exactly}

 

^{1) Authors without identifiers except for one. There is no information for a single author with an ID. How to understand the reference [14]? Or is this the first article for all authors? The reviewer must also understand the scientific interests and achievements of the authors, how to do this?}

^{2) Line 79. "tr(P) stands for the matrix's rank for matrix P ∈ R^m×n." There are more accepted designations for the rank of the matrix. Moreover, considering what follows, I would like to see the definition of tr(P) here.}

^{3) Line 83. "s·, c·, and t· denote sin(·), cos(·), and tan(·), respectfully." is a very economical designation, but let's read (44), for example, "0.05πt" is 0.05πtan(·).}

^{4) Line 142. "over time Think about" what is it about?}

^{5) Term 143. "reference desired trajectory which changes n^d∈ R^6." The article is about a very practical task, specifics are needed. Perhaps the reader understands where the desired trajectory comes from in position variables, but why might it be needed and what might the desired trajectory look like in angle variables? And in general, it is necessary to pay attention to the issue of the practical purpose of the desired trajectory. Where to get 6 differentiable time functions describing the target trajectory? What examples can be given?}

^{6) Continuing the previous question, see (44). What is the meaning of such a desired trajectory?}

^{7) In (15) the notation R^k×1 appears for the first time, until now the authors have designated vectors by the space R^k. At least it should be uniform.}

^{8) (15) it is not quite clear: the exponent gives a scalar, why is it a vector? What is b^2 if b is a vector?}

^{9) It is not entirely clear for what purpose the authors numbered all the formulas, if there are only some references in the text, and most of the numbered formulas are not mentioned?}

^{10) (27). Are the authors sure that the rank of the matrix appears in the Lyapunov function?}

^{11) Lines 194-195. Here you can see how the designations R^k×1 and R^1×k are used to denote vectors and columns. There are no comments on why there is no usual R^k. There is no mistake here, but it is not customary to write this way.}

^{12) The rank of the matrix does not have the property (31) or (32).}

^{13) There is no explanation why RBFNN is used. The network used in the example is so primitive that it can be assumed that almost any neural network architecture, starting with the perceptron, will work no less successfully in this scheme. Why is there no comparison with at least simple alternatives? Why are there no calculations with other hidden layer sizes?}

^{14) The language of the article requires a very serious revision}

^{Thus, a significant revision of the article is required.}

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

The article is a relevant subject and written at a good level. The authors treat and important and interesting problem in this paper. However, there are some points that need to be corrected, so I recommend a Major revision of the article

1/ My major concern on this paper is its innovation. First of all, there are extensive works being done using the same technique, the introduction on relevant works is not comprehensive and the unique contributions of this work are not explicitly described. A quick literature search yields many articles with the same keywords: autonomous vehicles, adaptive neural network, etc. This weakness, in my mind, is clear and will require a significant improvement.

2/ The motivation and background of wide practical use of the theoretic results presented should be clearly emphasized to facilitate the readers.

3/ In the introduction part, the literature survey is quite good. However, I think that the authors could enrich the reference section by discussing some new works related to sliding mode control and adaptive robust control methods, especially the dynamic sliding mode control methods, robust sliding mode method, multiple sliding mode methods and so on, should be included. To help the authors in this direction, I suggest the following reference: robust position control of an over-actuated underwater vehicle under model uncertainties and ocean current effects using dynamic sliding mode surface and optimal allocation control, station-keeping control of a hovering over-actuated autonomous underwater vehicle under ocean current effects and model uncertainties in horizontal plane, perturbation observer-based robust control using a multiple sliding surfaces for nonlinear systems with influences of matched and unmatched uncertainties, design of a non-singular adaptive integral-type finite time tracking control for nonlinear systems with external disturbances, finite-time convergence of perturbed nonlinear systems using adaptive barrier-function nonsingular sliding mode control with experimental validation, fast terminal sliding control of underactuated robotic systems based on disturbance observer with experimental validation, adaptive nonsingular terminal sliding mode control for performance improvement of perturbed nonlinear systems, robust tracking composite nonlinear feedback controller design for time-delay uncertain systems in the presence of input saturation, and the introduction should be added to do a better job of explaining the existing methods and why they are or are not valuable. What research gap did you find from previous researchers in your field (it is still partially described, but needs to be expanded and made clearer)?  Mention it in the Novelties section. It will improve the strength of the article.

4/ All assumptions and physical constraints should be provided. A sub-section “Assumptions” should be added to make the problem clearer

5/ Equation (5), the matrices M, C, D, g should be described more about their forms? Please refer the paper, study on dynamic behavior of unmanned surface vehicle-linked unmanned underwater vehicle system for underwater exploration.

6/ in line 238, what is Qiaolei double-loop….?

7/ How to define the input, hidden, output layers as 6,20,6 respectively?

8/ In simulations, lot of parameters are set to certain values, please add more details of how the parameters of the controller are obtained. What are theK1 and K2? How the full-state constraints are chosen? It is better to explain how the values of the control parameters in the proposed method are adjusted? Whether these parameters are optimal for simulation results? More explanation and evidence should be given in detail.

9/ The authors have to show the manner of implementation in professional details which will be beneficial to the readers. In-depth studies of neural network identification method to exploit the data is not given. It is not clear how the neural network training, testing and validation are carried out.  You are advised to make available the programs, datasets and schemes in the reviewing phase. You could better highlight the architecture and training algorithm. A figure shows the relationship of layers and architecture of the proposed method? What novelties you have introduced in the structure of the neural network.

10/ Considering there are a lot of adaptive control methods like Extremum Seeking Control, what are the major advantages by adaptive neural network?

11/ It  is  not  clear  how  the  sliding  mode  controller  is  combined  with  the  neural network. Which is the motivation for this neural network architecture? Which is the sliding mode existence domain?

12/ You  should  better  specify  the  control  law  and  the  computation  of  its parameters using sliding mode and neural network control.

13/ Which are the advantages and benefits compared with the general adaptive and non-adaptive control and non-neural network-based control approaches for these systems? Discussions and explanations should be provided on this issue.

14/ The example used to demonstrate the main results needs to be improved. More discussions should be given to clearly demonstrate the effectiveness of the obtained results. The example is simple and introduced directly and the nonlinearities do not result from it, and the uncertainties as well.

15/ In this study, the over-actuated ROV is used. The reviewer recommends that the author should apply the allocation control to distributes suitable thruster forces to 8 thrusters of the ROV. The author can refer to the following paper, robust position control of an over-actuated underwater vehicle under model uncertainties and ocean current effects using dynamic sliding mode surface and optimal allocation control.

16/ Obviously, the performance of underwater vehicle is affected by environmental disturbances such as wind, wave, and current. There is no result robustness under the disturbance. To examine the validity of the proposed approach, disturbance and load effects should be included to examine the effectiveness and validity of the approach.

17/ The reviewer would like to suggest the authors to compare, if possible, their results  with  some  recent  published  work  and  clearly  show  the  new  design features in the current work.

18/ The authors only simulate the controller, and no implementation in the actual vehicle is done. Consequently, it is tough to assess if such excellent properties of the controller are needed. From the simulations with satisfactory results, the system performance is expected in actual experiments with your proposed method. The analysis in this paper should be supported by experimental results. The authors should use practical systems to validate the proposed methods with experiment results. This paper now is difficult to prove the advantages of the proposed algorithm.

19/ The conclusion of the article is brief. It lacks a critical view of the results of the study and a detailed description of plans for further research. Please complete it.

 

20/ There exist some gramma errors and typos in this paper. Therefore, the English presentation should be improved carefully.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The simulation study still lacks a comparison with results obtained by any other method. I understand that in such a short correction time it may be impossible to prepare another model and test it. However, perhaps the authors have some previous experience of testing on another model. If so, a comment on this would be welcome possibly comments on studies such as the one presented so that the reader does not get the impression that perhaps the studies are only valuable in the case studied (for the model studied). 

Author Response

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Reviewer 2 Report

Dear authors,

In my opinion, now corrected paper is acceptable.

 

Author Response

Dear authors,

In my opinion, now corrected paper is acceptable.

Response: Finally, I would like to express my sincere thanks to you for your review of our work.

Reviewer 3 Report

Attached.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Thank you for the revised manuscript. The authors have made substantial revisions that have covered all my concerns. Most of the recommendations I made were addressed by the authors. The Paper is publishable in its current form.

Author Response

Thank you for the revised manuscript. The authors have made substantial revisions that have covered all my concerns. Most of the recommendations I made were addressed by the authors. The Paper is publishable in its current form.

Response: Finally, I would like to express my sincere thanks to you for your review of our work.

Round 3

Reviewer 3 Report

In my opinion, there is only one question about the appropriateness of numbering all formulas. Let the editorial team decide this issue.