A Novel Distributed Adaptive Controller for Multi-Agent Systems with Double-Integrator Dynamics: A Hedging-Based Approach

Round 1

Reviewer 1 Report

The paper has some good mathematical development, but important issues must be solved before publication:

- Write the manuscript in the MDPI format.

-Correct some grammar errors (e.g., do not use "reference therein").

-Divide the section 3 (Main results) in the theoretical analysis/development of the proposed controller and the results.

- Justify the use of equations (1), (2), (3) and (4) to represents the dynamics of the agent and the actuator output (e.g., a mathematical analysis or a reference). Why not using a space-state model?

- Besides, the performance and application of the control system may be limited by the plant model. Can the proposed control system can be applied to  systems with different models than the defined in (1) to (4) ?

- Define Ki, Kdi in equation (7).

- Indicate that the projection operator (Proj) is defined in the appendix. I suggest to define this operator  in a sub-section (e.g. preliminaries). Indicate the reference that describes this operation and some of its properties that allows applying this operator into the development of the controller. 

-Indicate the parameters of the plant used in simulations, for the proposed controller and the approach in [29].

- Indicate the reference, and the system output (or the tracking error) in each simulation test. Showing the trajectories of the states (Xi,j) does not necessarily prove the performance of the controller. 

-Add figures that illustrate the structure of the proposed control system.

Few errors should be corrected.

Author Response

Please see the attached and merged response to review document and revised manuscript. We thank this reviewer for their time.

Best,

The authors

Author Response File: Author Response.pdf

Reviewer 2 Report

I believe that the paper is a good quality paper. It is clearly written, and the English is good. In my opinion, the topic afforded is currently of interest to a large community of scholars. The methodological section, though restricted, is clearly written and discussed. The simulation part is also widely debated. I don't have any key criticism or issue to prevent its publication. To improve its quality and readability, figures are small and authors may improve their quality. It is not clear to me why the reference trajectories are diverging in Case 1.

Author Response

Please see the attached and merged response to review document and revised manuscript. We thank this reviewer for their time.

Best,

The authors

Author Response File: Author Response.pdf

Reviewer 3 Report

Please see attached file. 

Comments for author File: Comments.pdf

Author Response

Please see the attached and merged response to review document and revised manuscript. We thank this reviewer for their time.

Best,

The authors

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The corrections were done. I have no more comments.