Real-Time Weight Optimization of a Nonlinear Model Predictive Controller Using a Genetic Algorithm for Ship Trajectory Tracking

Round 1

Reviewer 1 Report

The manuscript entitled "Real-time weight optimization of nonlinear model predictive controller using genetic algorithm for ship trajectory tracking" by Dunjing Yu et al, presents an optimization method regarding the coefficients Q and R of the objective function in a nonlinear model predictive controller (NMPC). The method is then applied to ship trajectories tracking.

The problem of tracking the trajectory of ships has gained significant attention nowadays and is very important for applications of autonomous navigated ships.

The proposed method is general and can be applied in many systems. One question is, what is the difference between the proposed method and the one presented by X. Du, K. K. K. Htet, and K. K. Tan, "Development of a Genetic-Algorithm-Based Nonlinear Model Predictive Control Scheme on Velocity and Steering of Autonomous Vehicles," in IEEE Transactions on Industrial Electronics, vol. 63, no. 11, pp. 6970-6977, Nov. 2016, DOI: 10.1109/TIE.2016.2585079.

Could the authors comment on any advantages of their method that differentiates it from the published one? Could it be that this manuscript presents an application of the published methodology? 

Regarding the results of this work, I would suggest the authors add a table presenting the error per unit length of the position of the ship for each one of the methods under investigation. It could be the root mean squared error per unit length for each method. Such a table could give a better understanding to the reader of the performance of the proposed method.

Could this method be applied to real-world data? What if the authors add some noise to the simulated trajectories? Could they present the trajectories and in the table of errors, the error of each one of the methods under consideration for 1%, 5%, and 10% Gaussian noise (of a given standard deviation) on the trajectories? 

The presented method looks solid, and well explained but the authors should comment on the advantages of this method regarding the published one as commented above and on the robustness of their method under noisy environments.

General comments:

In the title "...  of a nonlinear model predictive controller using a genetic algorithm..." instead of " ... of nonlinear model predictive controller using genetic algorithm ..."

Line 27:  "maneuverability" instead of "manoeuvrability"

Line 106. I would suggest the notation \tau_{u}^{min} putting the words "min" and "max" as a superscript.

Figure 1. Are all the vectors notated in bold font?

Figure 2. I would suggest the authors present the units of each plot in parenthesis, i.e., t (s), x (m), and not with a division. This also applies to Figures 3, 4, and 5.

Figure 2. Variables q1, q2, q3, r1, r2, and r3 should be presented as q_{1}, the numbers as subscripts. This also applies to Figure 4.

Figure 2. Caption "(b)Ship velocities" needs a space between the parenthesis and "S". This also applies to Figures 4(b) and 4(d)

Figure 2 (c) and (d). The legend is not needed. It would be nice if the authors could find a way to increase the font size for the legend of Figures (a) and (b). This also applies to Figure 4.

Figure 4(d). "r_{2}" instead of "R2.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The authors presented methods for weight optimization for nonlinear model predictive controller based on genetic algorithm, which seems to have practical value for ship trajectory tracking. Overall the paper quality is good. The introduction is informative. Methods are described with details. Results look promising. Suggestions to modify the plots. In some plots, e.g. Figure 2, and Figure 3, the axis labels are confusing. Please consider using standard units. Change "t/s" to second. Change "x/m" to "meter".

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Dear Editor,

The article Real-time weight optimization of nonlinear model predictive controller using genetic algorithm for ship trajectory tracking is an original work and extremely correctly written. The Authors described in Abstract the value of their research in the words: This paper presents a weight optimization method for a nonlinear model predictive controller (NMPC) based on the genetic algorithm (GA) for ship trajectory tracking. In the introduction section, the authors describe the suggestions presented in the article: … this paper proposes a novel real-time weight optimization method of a nonlinear model predictive controller using a genetic algorithm for ship trajectory tracking, and the main contributions are as follows. (1) NMPC is applied to the ship trajectory tracking control, and the genetic algorithm is used to optimize the weight coefficients of the objective function in NMPC in real time. (2) The crossover operator, mutation operator, crossover rate, and mutation rate in the genetic algorithm are improved to enhance the performance of the genetic algorithm.

Despite such presentation, this section lacks an explicit purpose of the article, which is recommended by MDPI in Type of the Paper (Article, Review, Communication, etc.).

The review focuses on the formal side of the article and does not engage in polemics and discussions on the considerations adopted by the Authors because it determines the originality of the issue in the article. Considering the proposed solutions I accept it with appreciation.

The following observation require to draw attention and response from the Authors:

1.       As noted above, in the introduction section, the main aim of the work should be described.

I highly appreciate the editorial form of the article.

According to the reviewer, the article is exceptionally well written with good writing practice. In my review, I do not include more comments other than those presented in the review form. In the article, the Authors have used 32 items of references. All of the publications included in the References are mostly contemporary publications. The text of the article is clear.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have done great work and have addressed all my comments. The manuscript looks solid, and the results are well presented. I strongly support the publication of this work.

One last comment, the header on Table 2 has a lot of repeated words, i.e., Sine trajectory and under X% Gaussian noise. I would suggest the authors use one header as "Sine trajectory", over the last four columns and replace the header "under X% Gaussian noise" with "no GN", "1% GN" etc, and add an explanation of the label "GN" in the table's caption.