Containment Control of First-Order Multi-Agent Systems under PI Coordination Protocol^†

Round 1

Reviewer 1 Report

All good.

Author Response

Thanks very much.

Reviewer 2 Report

The paper entitled “Containment control of first-order multi-agent systems under PI coordination protocol” addresses the containment control problem of discrete-time first-order multiagent system. Simulation results are provided to validate the proposed method.

However, I have some concerns as follows:

Technical aspect:

• The literature review section at the beginning is superficial, and does not represent the state-of-the-art.

Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on automatic control, 49(9), 1520-1533.

Olfati-Saber, R. (2005, December). Distributed Kalman filter with embedded consensus filters. In Proceedings of the 44th IEEE Conference on Decision and Control (pp. 8179-8184). IEEE.

Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1), 215-233.

Rezaei, M. H., & Menhaj, M. B. (2018). Stationary average consensus protocol for a class of heterogeneous high-order multi-agent systems with application for aircraft. International Journal of Systems Science, 49(2), 284-298.

Rezaei, M. H., Kabiri, M., & Menhaj, M. B. (2018). Adaptive consensus for high-order unknown nonlinear multi-agent systems with unknown control directions and switching topologies. Information Sciences, 459, 224-237.

Rezaei, M. H., & Menhaj, M. B. (2018). Adaptive output stationary average consensus for heterogeneous unknown linear multi-agent systems. IET Control Theory & Applications, 12(7), 847-856.

Jiang, W. (2018). Fully Distributed Time-varying Formation and Containment Control for Multi-agent/Multi-robot Systems (Doctoral dissertation, Ecole Centrale de Lille).

Jiang, W., Peng, Z., Rahmani, A., Hu, W., & Wen, G. (2018). Distributed consensus of linear MASs with an unknown leader via a predictive extended state observer considering input delay and disturbances. Neurocomputing, 315, 465-475.

Jiang, W., Wen, G., Meng, Y., & Rahmani, A. (2017, July). Distributed adaptive time-varying formation tracking for linear multi-agent systems: A dynamic output approach. In 2017 36th Chinese Control Conference (CCC) (pp. 8571-8576). IEEE.

Ren, W., Beard, R. W., & Atkins, E. M. (2005, June). A survey of consensus problems in multi-agent coordination. In Proceedings of the 2005, American Control Conference, 2005. (pp. 1859-1864). IEEE.

Ren, W., & Beard, R. W. (2008). Distributed consensus in multi-vehicle cooperative control (Vol. 27, No. 2, pp. 71-82). London: Springer London.

Ren, W., & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on automatic control, 50(5), 655-661.

• We know that there exist obstacles in the real environment and many articles addressed the obstacle avoidance in the multiagent systems, does the proposed method work in such an environment?

Nguyen, T., La, H. M., Le, T. D., & Jafari, M. (2016). Formation control and obstacle avoidance of multiple rectangular agents with limited communication ranges. IEEE Transactions on Control of Network Systems, 4(4), 680-691.

Olfati-Saber, R. (2006). Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on automatic control, 51(3), 401-420.

Tran, V. P., Garratt, M., & Petersen, I. R. (2020). Switching time-invariant formation control of a collaborative multi-agent system using negative imaginary systems theory. Control Engineering Practice, 95, 104245.

• From practical point of view, what would happen if the leader is removed (for example, crashes) from the network? Does the proposed method still hold?

• From practical point of view, what would happen if some of the agents are removed from (or added to) the network? Does the proposed method still hold?

• From practical point of view, how would the proposed method perform for large-scale multi-agent systems? Would it scale well for such systems?

• From practical point of view, does the proposed method hold for MAS system with dynamic graph?

• I would recommend the respected authors to investigate the applicability of the proposed control approach in practical systems.

• Comparison with other existing methodologies is required.

Presentation aspect:

• The paper needs improvement in presentation. For example, many sentences in the introduction begin with reference numbers. I recommend the respected authors to not start their sentences with just a reference number, they could simply start with something like: “the authors in [x]”, “last-name and his/her colleagues”.

• Please verify that all axes are appropriately defined in all figures.

• Revise the English used in the paper. There exist some typos and grammatical errors in this paper.

• Please improve the quality of the figures.

• The bibliography of the work is generally arranged by the order in which the citations appear in the text. However, I see random ordering in the current version of the manuscript. If it is the policy of the editor to have the bibliography placed like this, please do not consider this comment.

Author Response

Technical aspect:

Comment 1: The literature review section at the beginning is superficial, and does not represent the state-of-the-art.

Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on automatic control, 49(9), 1520-1533.

Olfati-Saber, R. (2005, December). Distributed Kalman filter with embedded consensus filters. In Proceedings of the 44th IEEE Conference on Decision and Control (pp. 8179-8184). IEEE.

Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1), 215-233.

Rezaei, M. H., & Menhaj, M. B. (2018). Stationary average consensus protocol for a class of heterogeneous high-order multi-agent systems with application for aircraft. International Journal of Systems Science, 49(2), 284-298.

Rezaei, M. H., Kabiri, M., & Menhaj, M. B. (2018). Adaptive consensus for high-order unknown nonlinear multi-agent systems with unknown control directions and switching topologies. Information Sciences, 459, 224-237.

Rezaei, M. H., & Menhaj, M. B. (2018). Adaptive output stationary average consensus for heterogeneous unknown linear multi-agent systems. IET Control Theory & Applications, 12(7), 847-856.

Jiang, W. (2018). Fully Distributed Time-varying Formation and Containment Control for Multi-agent/Multi-robot Systems (Doctoral dissertation, Ecole Centrale de Lille).

Jiang, W., Peng, Z., Rahmani, A., Hu, W., & Wen, G. (2018). Distributed consensus of linear MASs with an unknown leader via a predictive extended state observer considering input delay and disturbances. Neurocomputing, 315, 465-475.

Jiang, W., Wen, G., Meng, Y., & Rahmani, A. (2017, July). Distributed adaptive time-varying formation tracking for linear multi-agent systems: A dynamic output approach. In 2017 36th Chinese Control Conference (CCC) (pp. 8571-8576). IEEE.

Ren, W., Beard, R. W., & Atkins, E. M. (2005, June). A survey of consensus problems in multi-agent coordination. In Proceedings of the 2005, American Control Conference, 2005. (pp. 1859-1864). IEEE.

Ren, W., & Beard, R. W. (2008). Distributed consensus in multi-vehicle cooperative control (Vol. 27, No. 2, pp. 71-82). London: Springer London.

Ren, W., & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on automatic control, 50(5), 655-661.

Response: We have cited the above references and renewed the reference list.

Comment 2. We know that there exist obstacles in the real environment and many articles addressed the obstacle avoidance in the multiagent systems, does the proposed method work in such an environment?

Nguyen, T., La, H. M., Le, T. D., & Jafari, M. (2016). Formation control and obstacle avoidance of multiple rectangular agents with limited communication ranges. IEEE Transactions on Control of Network Systems, 4(4), 680-691.

Olfati-Saber, R. (2006). Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on automatic control, 51(3), 401-420.

Tran, V. P., Garratt, M., & Petersen, I. R. (2020). Switching time-invariant formation control of a collaborative multi-agent system using negative imaginary systems theory. Control Engineering Practice, 95, 104245.

Response: Thanks for the question. We have not concerned about the trajectory of the systems in this work, since the agents’ movement is quite different form the situation in normal consensus or formation problem. The current proposed method in our paper is not able to handle the obstacle avoidance problem.

Comment 3: From practical point of view, what would happen if the leader is removed (for example, crashes) from the network? Does the proposed method still hold?

Response: Thank you for the problem. Since the method is proposed in our early research, it does not consider the topology change in the system. Then, back to your question, in our opinion, whether our method could work depends on how to deal with the leader. When the leader is removed, if its information connection to other agents is cut simultaneously, the proposed method can still work since the change will not influence other agents.

Comment 4: From practical point of view, what would happen if some of the agents are removed from (or added to) the network? Does the proposed method still hold?

Response: Thanks for the question. The question still considers about the topology change. Different from removing a leader, adding or removing followers may influence the stability of the closed-looped system. Hence, it is hard to give a clear conclusion about whether our proposed method can still hold when this topology changes.

Comment 5: From practical point of view, how would the proposed method perform for large-scale multi-agent systems? Would it scale well for such systems?

Response: Thanks for the question. The proposed method is distributed, so it can be used for large-scale multi-agent systems, and it can scale well for such systems.

Comment 6: From practical point of view, does the proposed method hold for MAS system with dynamic graph?

Response: Thanks for the question. As we have mentioned, the topology may influence the stability of the close-looped system. Hence, the method with dynamic topology still needs to be further researched.

Comment 7: I would recommend the respected authors to investigate the applicability of the proposed control approach in practical systems.

Response: Thanks for the advice. The proposed method is only analyzed theoretically in our research, so the practical application needs more research and discussion.

Comment 8: Comparison with other existing methodologies is required.

Response: Thanks for the advice. While in fact, the question that discussed in our paper is hardly considered in other works, so there are few works to compare.

Presentation aspect:

Comment 1: The paper needs improvement in presentation. For example, many sentences in the introduction begin with reference numbers. I recommend the respected authors to not start their sentences with just a reference number, they could simply start with something like: “the authors in [x]”, “last-name and his/her colleagues”.

Response: We have rewritten the sentences about the reference introduce.

Comment 2: Please verify that all axes are appropriately defined in all figures.

Response: We have checked all axes in the figures are defined appropriately.

Comment 3: Revise the English used in the paper. There exist some typos and grammatical errors in this paper.

Response: We have checked the paper and revise the typos and grammatical errors.

Comment 4: Please improve the quality of the figures.

Response: The quality of figures has been improved.

Comment 5: The bibliography of the work is generally arranged by the order in which the citations appear in the text. However, I see random ordering in the current version of the manuscript. If it is the policy of the editor to have the bibliography placed like this, please do not consider this comment.

Response: We have rearranged the order of the bibliography.

Round 2

Reviewer 2 Report

First, I would like to thank the respected authors for the time and effort put into improving their manuscript. 

I have carefully read the response letter and the updated manuscript. Since the respected authors mentioned that their focus is only on the theoretical side of the problem so I do not have any further comments on the practical aspects of the proposed method.

Here are some minor comments:

• Regarding the improvement of the quality of the figures, please use thicker lines both for trajectories and axis.

• Regarding the appearance of the citations in the text, I can see the last reference appeared is [24], and references [25-44] never mentioned anywhere in the revised manuscript. They just appeared in the reference section.