Edge-Event-Triggered Synchronization for Multi-Agent Systems with Nonlinear Controller Outputs
Round 1
Reviewer 1 Report
In my opinion, the manuscript can be published in the present form.
Author Response
Title: Edge-Event-Triggered Synchronization for Multi-Agent Systems With Nonlinear Controller Outputs.
Manuscript Number: applsci-855138
Reviewer 1
Comments: The manuscript can be published in the present form.
Response: Thank you very much for your comments, which make this paper better.
Reviewer 2 Report
The authors present the control method for a nonlinear system. The reviewer concerns the relationship between the listed novelties of the paper and the experimental results. The authors should clarify the following points with some empirical results:
- It is understandable that the proposed method newly considers the inherent nonlinearity of the output sequence of the system differed from the nonlinear model of the sensing target. However, it is still unclear what is improved. The authors should declare improvement, e.g., accuracy, efficiency, and so on. It may need some additional experiments.
- The consequence of Statement 2 of the novelty list is unclear. What is the implication of the last sentence? Did the authors find the new trade-off? How does it relate to the newly considered nonlinearity?
- The authors appealed the trade-off described as in the last sentence of Section 5. However, it can exist without the proposal, which is additionality considered nonlinearity. If the authors want to assert the result, they should discuss comparing with the difference from the previous research. For example, the trade-off cannot appear with the assumptions of the earlier studies.
The reviewer thinks that the theoretical validation of effectiveness is not easy for the introduced nonlinearity. Thus, with the current version of the manuscript, the authors may not conclude their research appropriately, and consequently, the reviewer does not think the paper should not publish at this time.
Author Response
Title: Edge-Event-Triggered Synchronization for Multi-Agent Systems With Nonlinear Controller Outputs.
Manuscript Number: applsci-855138
Thanks to the Associate Editor and the reviewers for their comments. We list the replies to the reviewers’ comments.
Reviewer 1
Comments: The manuscript can be published in the present form.
Response: Thank you very much for your comments, which make this paper better.
Reviewer 2
Comments: The authors present the control method for a nonlinear system. The reviewer concerns the relationship between the listed novelties of the paper and the experimental results. The authors should clarify the following points with some empirical results:
- It is understandable that the proposed method newly considers the inherent nonlinearity of the output sequence of the system differed from the nonlinear model of the sensing target. However, it is still unclear what is improved. The authors should declare improvement, e.g., accuracy, efficiency, and so on. It may need some additional experiments.
Response: Thank you very much for your comments and suggestions. Actually, we considered how to improve the application scope of the edge event-triggered mechanism. We provided sufficient conditions for the system convergence of the edge event-triggered mechanism under the influences of network transmission data quantization and the controllers’ inherent nonlinearities. This is a supplement to the previously distributed event-triggered sampling theories. The provided numerical simulations are sufficient to verify the effectiveness of the investigated algorithms.
Comments: The consequence of Statement 2 of the novelty list is unclear. What is the implication of the last sentence? Did the authors find the new trade-off? How does it relate to the newly considered nonlinearity?
Response: Thank you for the comments. We did not propose a new trade-off but extended the trade-off between event-triggered and self-triggered control to the scenarios with controllers’ inherent nonlinearities and data quantization nonlinearities. Furthermore, in our self-triggered scheme, data quantization is considered in the control information interaction, which saves communication resources more than the existing results. In this version, we further clarified the innovations of this paper and provided Remark 2 and Remark 3 to further explain the problem. The corresponding revision in this manuscript is shown in Blue.
Comments: The authors appealed the trade-off described as in the last sentence of Section 5. However, it can exist without the proposal, which is additionality considered nonlinearity. If the authors want to assert the result, they should discuss comparing with the difference from the previous research. For example, the trade-off cannot appear with the assumptions of the earlier studies.
Response: Thank you for the comments. In this version, we clarified the effectiveness of the trade-off between different system resources. It is true that this trade-off already exists in the results of previous studies, but its effectiveness has not been verified in the scenarios with the controller output nonlinearities. Our research not only gives the effectiveness of the proposed algorithms in this scenario but also shows that the trade-offs between different algorithms are still effective. We provide TABLE 2 to show this trade-off. Our numerical simulations sufficiently demonstrate this effectiveness. The corresponding revision in this manuscript is shown in Blue.
Comments: The reviewer thinks that the theoretical validation of effectiveness is not easy for the introduced nonlinearity. Thus, with the current version of the manuscript, the authors may not conclude their research appropriately, and consequently, the reviewer does not think the paper should not publish at this time.
Response: Thank you for the comments. In this version, we carefully revised this paper and re-described the innovations and conclusions. Our theorems provide several sufficient conditions, and the strict mathematical proofs ensure the effectiveness of the algorithms. Numerical simulations show the effectiveness of the proposed policies, and there is also a system resource trade-off between different policies. We expect this revision to satisfy this reviewer.
Thank you very much for your comments, which make this paper better.
Round 2
Reviewer 2 Report
Thank you for kindly revising the manuscript. My concerns are improved.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
The authors are proposing a control methodology for a nonlinear multiagent system. However, it is seriously unclear which the paper has solved. The most serious reason is the presentation of Section 1. Although many papers have been published around the topic with the combined research words of "event triggered" and "nonlinear multiagent systems," the authors do not discuss them through the paper, and there is no citation for the keyword "nonlinear." If the authors want to propose another, new methodology to control synchronization in nonlinear multiagent systems, they should compare with the researches having a common goal.
In addition, the authors did not sufficiently describe the reasons why they applying particular mathematical models, e.g., Lipschitz systems. It needs an explanation of why did the models be chosen.
As a result, the authors conclude with the existence of a trade-off between event-triggered and even-self-triggered policies. However, the reviewer cannot understand why the trade-off is the non-trivial, meaningful conclusion because the triggering with external events needs continuous measurement, and self-triggering can control the sampling rate but generates more communication if the true event occurrence frequency is lower than self-triggering rate. So, what is the novelty of this paper?
Consequently, because of the reasons above, the reviewer cannot recommend the paper to publish in this opportunity. The research seems to be uncompleted yet and is expected to explore additional results including comparison with others.
References used for this review:
Li, Z. et al, "Event-Triggered Control for a Class of Nonlinear Multiagent Systems With Directed Graph," IEEE Transactions on Systems, Man, and Cybernetics, Early Access, pp. 1-8, 2020.
Li, Z. et al., "Adaptive Event-Triggered Control for Unkown Second-Order Nonlinear Multiagent Systems," IEEE Transactions on Cybernetics, Early Access, pp. 1-10, 2020.
Li, H. et al., "Event-triggered consensus in nonlinear multi-agent systems with nonlinear dynamics and directed network topology," Neurocomputing, Vol. 185, pp. 105-112, 2016.
Hu, W. et al., "An Event-Triggered Control Approach to Cooperative Output Regulation of Heterogeneous Multi-Agent Systems," IFAC-PapersOnLine, Vol. 49, No. 18, pp. 564-569, 2016.
Zhang, X. et al., "Distributed event-triggered control of multiagent systems with general linear dynamics," Journal of Control Science and Engineering, Article No.: 7, 2014.
Theodosis, D. et al., "Event-Triggered Control of Nonlinear Systems With Updating Threshold," IEEE Control Systems Letters, Vol. 3, No. 3, 2019.
Wang, Y.W. et al., "Distributed Control of NOnlinear Multiagent Systems With Unknown and Nonidentical Control Directions via Event-Triggered Communication," IEEE Transactions on Cybernetics, Vol. 50, No. 5, pp. 1820-1832, 2020.
Reviewer 2 Report
The paper discusses the synchronization problem of multi-agent systems with nonlinear controller outputs by event-triggered control.
The paper is well written, contains some original contribution, and I recommend its publication in the journal.
I have comments on missing important references on event-triggered and self-triggered control.
The model of self-triggering was introduced in:
- Velasco, P. Marti, J. M. Fuertes, „The self-triggered task model for real-time control systems”, Proceedings of 24th IEEE Real-Time Systems Symposium RTSS 2003, pp. 1-4, 2003.
The event-based control has originated in the 50s. Please, see and refer to the book which comprehensively addresses the research on event-based systems and early works on event-based control:
„Event-Based Control and Signal Processing” edited by M. Miskowicz, CRC Press 2016
I suggest to refer to the early paper by
Karl Johan Astrom, Bo Bernhardsson, „Comparison of periodic and event based sampling for first-order stochastic systems”, IFAC Proceedings Volumes, vol. 32, pp. 5006-5011, 1999
that initiated a modern research interest on event-based control, and also to the paper
M. Miskowicz, „Send-On-Delta Concept: An Event-Based Data Reporting Strategy”, Sensors, vol. 6(1), pp. 49-63, 2006
that initiated the debate on event-based control and communication in MDPI journals.
Furthermore, many studies on event-based control and communication have been published in Applied Sciences, Sensors, Energies, Robotics and Entropy journals in the past. I recommend to refer to them to highlight that MDPI journals are an very active forum for a debate on event-based systems.
For example, recent contributions are:
Event-Triggered Adaptive Fault Tolerant Control for a Class of Uncertain Nonlinear Systems by Chenglong Zhu , Chenxi Li , Xinyi Chen , Kanjian Zhang , Xin Xin and Haikun Wei, Entropy 2020, 22(6), 598
Dynamic Event-Triggered Time-Varying Formation Control of Second-Order Dynamic Agents: Application to Multiple Quadcopters Systems by Anh Tung Nguyen , Thanh Binh Nguyen and Sung Kyung Hong, Appl. Sci. 2020, 10(8), 2814
Distributed Event-Based Control of Hierarchical Leader-Follower Networks with Time-Varying Layer-To-Layer Delays by Guang-Hui Xu , Meng Xu , Ming-Feng Ge , Teng-Fei Ding , Feng Qi and Meng Li, Energies 2020, 13(7), 1808;
Pull-Based Distributed Event-Triggered Circle Formation Control for Multi-Agent Systems with Directed Topologies by Peng Xu , Hongfa Zhao , Guangming Xie , Jin Tao and Minyi Xu, Appl. Sci. 2019, 9(23), 4995;
Signal Source Localization of Multiple Robots Using an Event-Triggered Communication Scheme by Ligang Pan, Qiang Lu, Ke Yin and Botao Zhang, Appl. Sci. 2018, 8(6), 977
A Cognitive-Inspired Event-Based Control for Power-Aware Human Mobility Analysis in IoT Devices by Rafael Pérez-Torres, César Torres-Huitzil and Hiram Galeana-Zapién, Sensors 2019, 19(4), 832
Flocking of Multi-Agent System with Nonlinear Dynamics via Distributed Event-Triggered Control by Yanhua Shen , Zhengmin Kong and Li Ding, Appl. Sci. 2019, 9(7), 1336
Artificial-Intelligence-Based Prediction of Clinical Events among Hemodialysis Patients Using Non-Contact Sensor Data by Saurabh Singh Thakur, Shabbir Syed Abdul, Hsiao-Yean (Shannon) Chiu, Ram Babu Roy, Po-Yu Huang, Shwetambara Malwade, Aldilas Achmad Nursetyo and Yu-Chuan (Jack) Li, Sensors 2018, 18(9), 2833
Event-Based Communication and Finite-Time Consensus Control of Mobile Sensor Networks for Environmental Monitoring by Yu Hu, Qiang Lu and Yanzhu Hu, Sensors 2018, 18(8), 2547
New Control Paradigms for Resources Saving: An Approach for Mobile Robots Navigation by Rafael Socas, Raquel Dormido and Sebastián Dormido, Sensors 2018, 18(1), 281
Yu Hu, Qiang Lu and Yanzhu Hu, Event-Based Communication and Finite-Time Consensus Control of Mobile Sensor Networks for Environmental Monitoring, Sensors 2018, 18(8), 2547
Sparse in the Time Stabilization of a Bicycle Robot Model: Strategies for Event- and Self-Triggered Control Approaches by Joanna Zietkiewicz , Dariusz Horla and Adam Owczarkowski, Robotics 2018, 7(4), 77
