Multivariable Adaptive Super-Twisting Guidance Law Based on Barrier Function

Round 1

Reviewer 1 Report

Please find attached the comments.

Comments for author File: Comments.pdf

Author Response

Dear Professor,

Thank you for your detailed and kind review and comments.

The comments are impressive, and help us a lot in improving our manuscript and expanding our knowledge, especially the comments about the dynamical environment in the Monte Carlo simulation.

Our responses are stated in the attachment. Thanks for your time again.

Best regards,

Y.L., G.L., Y.D., Y.Z., and Z.Q.

Author Response File: Author Response.docx

Reviewer 2 Report

In general, the paper submitted for review entitled "Multivariable Adaptive Super-Twisting Guidance Law Based on Barrier Function" I find interesting. It is not a breakthrough work, but it is an interesting voice in the discussion of issues related to modern methods of guiding missiles at aerial targets. Of particular importance is the fact that the guidance method proposed by the authors generates relatively small accelerations in the terminal phase of missile guidance, which is beneficial both from a technical and tactical point of view.

Nevertheless, a few issues raise my doubts, hence I kindly ask the authors to comment on the following issues:

1. As a rule, a correctly formulated guidance law considered in terms of pure kinematics (missile and aerial target considered as material points) does not introduce any guidance errors, i.e. r = 0 always occurs at the moment of meeting the missile with the target. Of course, in real conditions r = 0 does not hold. My point is that the authors use some kind of mixed approach. Namely, they consider the missile and target as material points and formulate a kinematic model of the missile-target engagement - the reader therefore expects that the system is considered only theoretically (and then r = 0 must occur). Then an assumption of neglecting the dynamics of actuators is introduced, the parameters of the seeker are (marginally) mentioned, some disturbances are introduced, and the simulation results show a miss distance values - which suggests that some phenomena related to the dynamics of the system were taken into account. Hence, it would be good to consider two situations: a) demonstrate the operation of the algorithm on the basis of pure kinematics - showing that the method as such is correctly formulated, i.e. r = 0 (with accuracy to numerical errors); b) demonstrate the correctness of the algorithm operation in the presence of disturbances in the guidance loop, delays introduced by the seeker and actuators (even simplified, as presented in the article, or a simple first-order inertia) - then it is justified to show the miss distances and small spread values, which is a significant advantage of the developed guidance method.

2. The authors assume that the missile velocity is constant. Such an approach does not raise doubts in the case of a short time horizon, when the characteristics of the airframe do not change significantly. In the paper, the considered time period covers a dozen seconds. In real conditions, over such a long period of time, the characteristics of the missile, including its velocity, change dramatically. The authors use numerical simulations in MATLAB in their research. So it is not a problem to introduce velocity as a function of time. Why hasn't this been done? Will the algorithm be effective in such a situation?
3. The Authors use the variable "tau" to denote the seeker time constant (line 154) and the timescale (line 233). It seems reasonable to distinguish between these variables.
4. The reason for placing the Eq. (44) is unclear (in fact it is a repetition without commenting the Eq. (36)). I am asking for a broader comment in the paper or for deletion of Eq. (44).
5. In Fig. 3e the acceleration histories for individual angular coordinates look identical, although the angles and angular rates for "phi" (3b, 3c) and "theta" (3d) different significantly. I am not sure, but was there an editorial mistake? Please check. Alternatively I am asking for a different presentation and an appropriate comment to dispel any doubts.
6. Why in Fig. 3e the acceleration histories are shown only for "phi" = 25 deg, and not for the four values: 20, 25, 30, 35?
7. I think that to ensure a more complete presentation of the results, it would be worth supplementing Fig. 4 with pos. e) and f), similarly to Fig. 3.
8. What was the distribution model of simulation parameters for the Monte Carlo method?
9. How the appearance of "peaks" in Fig. 5a and 5b around 3rd second of missile flight can be justify?
10. In general, the paper is written in clear and concise language. There are, however, some typos in the text, such as "unknow" (line 12), "brrier" (line 206), "prposed" (line 212), etc., as well as unjustified spaces. Please correct the text in terms of editing.

At this time is all for me, in the future, I hope that authors consider all of my suggestions and comments.

Author Response

Dear Professor,

Thank you for your detailed and kind review and comments.

The comments are impressive, and help us a lot in improving our manuscript and expanding our knowledge. The valuable comments about the figure presentation make us reconsider the details of our manuscript, such as the “peaks” in the acceleration curves of the Monte Carlo simulation.

Our responses are stated in the attachment. Thanks for your time again.

Best regards,

Y.L., G.L., Y.D., Y.Z., and Z.Q.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper is written in good English and fits the journal scope. According to the TurnItIn system, it has a 38% similarity index. Still, after investigating the numbers, it can be found that the majority of the text-similarity is due to the nomenclature explanation. Therefore, I do not consider this unacceptable. The research is solid, but I would like the authors to comment on the following issues:

1. Can the authors comment on Mach number and compressibility, i.e. what were the conditions in the simulations? Was Mach number a fixed value or not? If not, how large were the changes, and how strongly nonlinear the model was?

2. Can the authors present the dynamical model of the object?

3. Can the authors comment on the object uncertainty in terms of noise in the inputs (modelling process noise e.g. due to turbulence)? If the authors have results like this, those should be included. If not, this can be commented with respect to the following paper:
Dul F., Lichota P., Rusowicz A.: "Generalized Linear Quadratic Control for a Full Tracking Problem in Aviation", Sensors, Vol. 20(10), 2020, Paper 2955

For now, this is all for me. I hope that the authors will take into consideration all my remarks.

Author Response

Dear Professor,

Thank you for your kind review and comments.

The comments are impressive, and help us a lot in improving our manuscript and expanding our knowledge, especially the comments about object uncertainty in terms of noise.

Our responses are stated in the attachment. Thanks for your time again.

Best regards,

Y.L., G.L., Y.D., Y.Z., and Z.Q.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Dear Authors,

thank you for taking into account my recommendations. I am fully satisfied with the answers.

Reviewer 2 Report

Dear Authors,
thank you for sending the revised version of the article. A lot of work has been done. In my opinion the paper is ready to further proceeding.
Just please correct two little editorial mistakes that caught my eye:
1) line 133: "Error! Reference source not found" (ref. [14])
2) line 218: "Prposed" again :)
Best wishes!

Reviewer 3 Report

Thank you for providing responses.