Finite-Time Adaptive Neural Control Scheme for Uncertain High-Order Systems with Input Nonlinearities and Unmodeled Dynamics

Round 1

Reviewer 1 Report

1.      Introduction should be numbered as 1 and the rest sections should follow.

2.      The mathematical formulation is too detailed and such a presentation is mostly suited in a book chapter. However, in a research article (and especially in a journal that is not fully defined as a control journal) such an analysis is unnecessary and needs to be shortened significantly.

3.      The case study should be realistic and presented in more details (perhaps with an actual case or at least present an actual case where it can be applied).

Author Response

We gratefully appreciate for reviewing our papers and giving valuable comments. We have carefully considered the comments and revised the manuscript accordingly. Please find below our responses to the your comments and all the revisions have been addressed in the reply. All changes made in the revised paper based on your comments are highlighted in yellow color. We hope that the revised manuscript may meet the standard of the journal. Thank you very much.

Author Response File: Author Response.docx

Reviewer 2 Report

Dear Editor and Authors

This work considers the problem of adaptive neural network control for a class of nonlinear systems with uncertainties, under deadzone inputs. The problem under study is undoubtedly interesting and state of the art. Moreover, the procedures are correct as far as I can verify. The authors also illustrate their results through numerical simulations, which are especially helpful for the readers.

So overall, I believe this work has merit for its respective community and can be considered for publication.

But there are parts that consider improvement. Mainly, this has to do with the fact that it is a very densly written manuscript, with a lot of notations, so it is hard to follow. So unless a reader is in an expert on the field, browsing though this manuscript would be very hard. So my main suggestion is that parts of the work be revised and extended.

My comments are available below.

--Sections 2.1 controller design and 2.2 stability analysis practically need to be heavily revised, as they are densly written, and at least for me, hard to follow. The authors should expand the discussion here on the design approach. Moreover, due to the many parameters and degrees of freedom, I suggest using a table, or any other prefered way to clarify all parameters.

--An important remark. I believe some discussion is required on the system formulation (3). Where do we expect such systems to appear for example? Why does sigma only depend on x_n and not the rest of the state variables? As this formulation seems very structured, I believe the discussion on these issues must be included.

--line 123, the text after 'instead of' is stated twice.

--line 144, should this be 'bi-u, u<bI' for the 3rd scale?

--line 159, I believe the authors mean pi are known integers.

--line 163, the authors consider as a design assumption the fact that the signs of the functions g_i are known. To me, this seems far too specific as a knowledge. It seems too specialized as an assumption, how can we assurein a physical system that this would be measurable? I believe the authors should further comment on this in their manuscript.

--For (7), to avoid confusion, since this is a vector, specify that this is not positive definiteness, but rather we require every state z_i>=0

--Lemma 3 is include in [3] as the authors mention, but I could not find any reference to it. Can you please specify it?

--line 232, 'later'

--line 233, specify epsilon_i as terms.

--line 244, what is l_i used in the power superscript? Please specify.

--Line 487, use 'Fig.' without bold when refering to figures.

--Figure 2, the zoom refers to a different part, please fix this.

--Figure 3, is it possible to plot in the graph the deadzone regions based on 484-485 and (1)?

I hope I have provided the authors with suggestions that will improve the manuscript.

Author Response

We gratefully appreciate for reviewing our papers and giving valuable comments. We have carefully considered the comments and revised the manuscript accordingly. Please find our responses to the your comments and all the revisions have been addressed in the attachment. All changes made in the revised paper based on your comments are highlighted in yellow color. We hope that the revised manuscript may meet the standard of the journal. Thank you very much. 

Author Response File: Author Response.docx

Reviewer 3 Report

In this study, a nonlinear prescribing control for high-order nonlinear system.

Comments for this submission are as follows:

1. The fact that a nonlinear transformed error surface can compensate the effect of deadzone was studied by S. Han (IEEE Trans. Industrial Electronics, Vol. 64, No. 2, pp. 1269-1278, 2017, Feb). The quotation for this paper should be added.

2. Authors wrote “It should be mentioned that any control design for high-order nonlinear systems should not neglect some crucial aspects, such as finite-time tracking, unmodeled dynamics and input nonlinearities.”

However, there have been much paper to study finite-time convergence, robust problem, and input nonlinearity. Authors insistence does not match the real fact. These problems were dealt with many researchers.

3. The adopted prescribing function follows the traditional method and the presented RBF NN is also very conventional one. What are novel methods?

4. The designed controllers contain the sign functions. This term may cause chattering problem.

How authors treated this problem?

5. Authors insisted that the traditional nonlinear control methods are complex. Then, what point of the proposed controller is simpler than the conventional method?

 

English needs to be polished such as

1. a class of high-order nonlinear systems -> system

2. Based in the Lyapunov theorem, the tracking error is -> the tracking errors are

Author Response

We gratefully appreciate for reviewing our papers and giving valuable comments. We have carefully considered the comments and revised the manuscript accordingly. Please find our responses to the your comments and all the revisions have been addressed in the attachment. All changes made in the revised paper based on your comments are highlighted in yellow color. We hope that the revised manuscript may meet the standard of the journal. Thank you very much. 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have provided a response to the reviewers which is detailed. In my opinion, the presentation of this articles with so many mathematical expressions (lemma, notations, remarks, hundrends of symbols, etc) does not belong to a research article but rather to a book that needs more details. 

 

Reviewer 2 Report

Dear editor and authors.

I believe the authros have addressed my comments in the revised version. I still think there are dense parts, but the authors have made a move to improve them.

The work can now be considered for publication.

Finally, check line 257, I believe there is a typo, 'which will be defined later' does not belong in this line.

Reviewer 3 Report

In the revised submission, sufficient answers for comments from reviewer arrived and thus, this paper can be accepted in current form at this step.