PONE-D-23-39618Control of complex systems with generalized embedding and empirical dynamic modelingPLOS ONE

Dear Dr. Joseph Park,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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We look forward to receiving your revised manuscript.

Kind regards,

Yasuko Kawahata

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: N/A

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: No

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: My main comments are as follows:

1) The main contribution of this paper should be highlighted. Also, compare with the existing results to reveal the superior performance.

2) An important class of complex systems is Multi-Agent Systems, which can be reviewed in Introduction part by some papers such as "https://doi.org/10.1177/095965182211056", "https://doi.org/10.1016/j.jfranklin.2021.05.033", and "10.1109/TCSII.2021.3128561".

3) The grammatical errors should be considered. Also, the overall of paper should be justified.

Reviewer #2: M/s: Control of complex systems with generalized embedding and empirical dynamic modeling

s. Generalized embedding naturally encompasses multivariate dynamics enabling state space variable cross mapping for direct assessment of multivariate contributions to the dynamics. Further, state space kernel regression allows inspection of intervariable dependencies. To illustrate this an agent based model is used to generate nonlinear dynamics which are then modeled by generalized state space embedding providing state predictions to a controller regulating the system dynamics. The method is generally applicable to any dynamic system representable in a state space.

My comments are as follows:

(1) The novelty of the work can be expressed in detail in the Abstract, Highlights, and Conclusion. The main content should concern your research idea and its experimental effect verification.

(2) The expression of the abstract should be improved. A more detailed presentation of innovation should be conducted as well as the experimental verification.

(3) Recent related work survey is currently missing. More recent literature should be cited and analyzed, such as (a) Double internal loop higher-order recurrent neural network-based adaptive control of the nonlinear dynamical system, (b) Memory Recurrent Elman Neural Network-Based Identification of Time-Delayed Nonlinear Dynamical System, (c) Modeling and adaptive control of nonlinear dynamical systems using radial basis function network, (d) A novel feed-through Elman neural network for predicting the compressive and flexural strengths of eco-friendly jarosite mixed concrete: design, simulation and a comparative study, (e) Self‐recurrent wavelet neural network–based identification and adaptive predictive control of nonlinear dynamical systems, (f) Externally Recurrent Neural Network-based identification of dynamic systems using Lyapunov stability analysis and so on.

(4) The expression logic can be improved for your proposed method so that the innovation can be clearly understood. More expression of the mathematical analysis should be conducted to show your ideas clearly. Also, please try to highlight your proposed method and focus on it.

(5) Grammar should be checked and improved for the entire content. Please try to make every sentence to be correct and easy to be understood.

(6) More experimental result comparisons with references should be conducted for advantage discussion.

(7) What about the stability of the proposed method? It is not discussed. You can refer to the following papers for your reference in the introduction and discuss the stability issue: (a)Lyapunov stability-based control and identification of nonlinear dynamical systems using adaptive dynamic programming, (b) Temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems, (c) Diagonal recurrent neural network-based adaptive control of nonlinear dynamical systems using Lyapunov stability criterion, (d) A Lyapunov-stability-based context-layered recurrent pi-sigma neural network for the identification of nonlinear systems.

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Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

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[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PONE-D-23-39618R1Control of complex systems with generalized embedding and empirical dynamic modelingPLOS ONE

Dear Dr. Park,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Jun 28 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Yasuko Kawahata

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: (No Response)

Reviewer #3: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: (No Response)

Reviewer #3: No

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: (No Response)

Reviewer #3: No

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: (No Response)

Reviewer #3: No

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: (No Response)

Reviewer #3: No

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: (No Response)

Reviewer #3: The article announces the treatment of the modelling and control problem for complex nonlinear dynamical systems. However, apart from a narrative description of the significance of the targeted research topic there are no specific findings and no contribution to the nonlinear control and to nonlinear estimation area. The modeling and system identification part is missing while the control part of the article is absent too. Considering the absence of specific results the article has to be substantially rewritten after taking into account major findings and established nonlinear control and nonlinear estimation methods in the subject area.

Regarding the modelling part one would expect results on nonlinear least squares approaches or on nonlinear Kalman Filtering techniques. The modelling part is a prerequisite for the control part. In the case of model-based control precise estimation of the parameters of the dynamic model of the controlled system can be performed with the use of nonlinear Kalman Filtering or nonlinear least squares algorithms. In the case of mode-free control, identification of the dynamic model can be performed with the training of nonlinear regressors such as neural or neurofuzzy networks.

Regarding the nonlinear control of the targeted complex systems on would expect results on global linearization-based control methods or on approximate linearization-based control schemes Global linearization-based control uses transformations of the system's state variables and of the system's state-space model into equivalent linear forms where the control and estimation problem can be treated with solutions initially designed for linear systems. Approximate linearization-based control techniques considers Taylor series expansion of the system's dynamics around specific operating points through the computation of Jacobian matrices. The control and estimation problems are solved sequentially around the linearization points

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

Reviewer #3: No

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[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Control of complex systems with generalized embedding and empirical dynamic modeling

PONE-D-23-39618R2

Dear Dr. Joseph Park,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Yasuko Kawahata

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments: