Model Predictive Control for First-Order Hyperbolic System Based on Quasi-Shannon Wavelet Basis

Round 1

Reviewer 1 Report

There is a named " Assumption 1 " mentioned, related to eqn. 12,  which is not clear. It should we written as such ( "Assumption 1") in the appropritae place within the paper and discussed.

Author Response

Dear Reviewer:

        We thank the reviewer for carefully reading the paper and providing valuable
499 feedbacks. A proint-by-point response to the comments with the revised paper can be found in the attachment.

          Thank you very much again for your valuable suggestions!

 

The Author

Ling Ai, Kok Lay Teo, Liwei Deng, Desheng Zhang

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Referee report on “Model Predictive Control for First-order Hyperbolic System Based on Quasi-Shannon Wavelet Basis (Ling Ai, Kok Lay Teo, Liwei Deng and Desheng Zhang)”

The authors considered a class of first-order hyperbolic distributed parameter systems with particular emphasis on the design of a new class of model predictive control schemes using a quasi-Shannon wavelet basis. Generally, the paper is written quite well, and following the logic of the paper was not a problem. However, in order to help the reader it would be helpful if the authors could indicate the source of the software that was used to obtain the figures (for example, Fig 3) and the results of the simulation with some elaborations. There are many instances where full stop is missing after the equation(s). For instance, Equations (4, 5, 6), ‘.’ is missing (see also Equations (10, 13, 14 etc.)). Some of the formulas seem too complicated (Equation 18, for example) and have to be modified. On Page 7; Line 205/206: please revise the line starting with ‘Empirically, the parameter ?̃ should be chosen in the interval…’. Additionally, please the citations as well as the list of References should be consistent.

Author Response

Dear Reviewer:

We thank the reviewer for carefully reading the paper and providing valuable
499 feedbacks. A proint-by-point response to the comments with the revised paper can be found in the attachment.

Thank you very much again for your valuable suggestions!

 

The Author

Ling Ai, Kok Lay Teo, Liwei Deng, Desheng Zhang

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Accept 

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

A Review of
Model Predictive Control
for First-order Hyperbolic System
Based on Quasi-Shannon Wavelet Basis
submitted to
MDPI Processes
May 2020
General comments
The paper addresses a problem of predictive (optimising) control algorithm design utilising
model-based predictive control (MPC) approach. The designed algorithm is to serve to control
a class of plants described by non-linear hyperbolic partial dierential equations (PDEs). This
topic is considered relevant to the community and is in line with the scope of the journal.
The manuscript includes background knowledge, problem formulation, main result, case study
based experiments and conclusions sections. Although the manuscript macro-structure is well-
designed and concise, there are some deciencies and issues that need attention. The following
sections of the review discuss these issues.
Key concerns
1. The steps in the adopted problem-solving methodology indicated in the abstract do not
coincide with the description presented in the introduction and further sections of the
article. It is quite unexpected and surprising. Therefore, the substantive message is
unclear and inconsistent. It is therefore not possible to make a clear assessment of the
work.
2. The authors in their paper indicate that the key application case presented in the arti-
cle concerns research related to the ability of the control system to reject disturbances.
However, both the problem posed and the description of the case study does not take into
account the impact of disturbances. Therefore, it is not possible to conduct the postulated
research or experiments considering the aforementioned conditions.
Other issues
1. Concerning `Introduction'. The literature item introduced to illustrate the background of
the research should be introduced in a manner that explicitly highlights the contribution
of each of them. Moreover:

 Page 1 of 15, line 19: It seems that LPS should be used instead of DPS.
 Page 2 of 15, line 65: Is this the rst approach to use WCM? If not then an appro-
priate set of literature items that treat this problem in this manner should be included
in the background description.
 Page 2 of 15, lines 68{69: The sentence staring with `Nonlinear MPC . . . ' should be
rewritten to include explicitly the name of the method given in [32].
 Page 2 of 15, line 71: It might be considered benecial to change `will be given' to,
e.g., `has been ...'.
2. Concerning `Problem formulation':
 Page 3 of 15, line 81: Symbol R remains undened.
 Page 3 of 15, line 85: The domain and potentially important properties of u(x; t) have
not been dened.
 Page 3 of 15, line 87: It would be nice to have L2 or L2 type notation instead of L2.
 Page 3 of 15, line 88 (including (2)):
{ The statement (2) is not an objective function. It is an optimisation task. Only
J is an objective function. The nomenclature used is at least ambiguous.
{ Please provide explicitly the decision variables/control handles in the task (min
operator) subindex.
{ What are the arguments of J := J(?)?
{ he internal MPC model is missing in the provided formulation!
{ How do authors plan to achieve feasibility of control inputs if only control signal
increment is subject to constraints? This is an important aspect of the case study
provided in one of the following sections.
 Page 3 of 15, lines 92{95: It would be benecial to the reader to present this infor-
mation using Assumption environment and refer to the appropriate entry whenever
needed.
3. Concerning `Model predictive control using quasi-Shannon interpolating wavelet':
 The preamble of section 3 is empty. It could be used to guide the reader through the
section. For example, a general idea of the control system could be provided. Then
in the subsections, a detailed explanation of control system elements could be given.
 Page 3 of 15, lines 98{117: This part should be supplemented/enriched with references.
Also, the reviewer suggests using this information in the introductory part of the
manuscript for clarity of the overall presentation.
 Page 4 of 15, lines 122{123: Please consider addressing the domain of the system
rather than the solution which might imply actions in the solution space.
 Page 4 of 15, lines 122{123: Please consider addressing the domain of the system
rather than the solution which might imply actions in the solution space.
 Figure 1 | information on  and  might be included in the picture.
 Page 4 of 15, line 129: Since in introduction FDM and collocation method names are
stressed out this section should build on this fact. Hence the collocation method name
should be used here or an appropriate set of amendments and explanations given in
the introduction.
 Page 5 of 15, line 154: This title suggests dierent organisation of this subsection.
Also based on the provided description it might be found confusing for a reader at rst
is there an interval quasi-Shannon wavelet or interval and quasi-Shannon wavelet.
Please provide a proper introduction to this subsection.
 Page 5 of 15, lines 155{160: The overall paragraph is more suitable for the introduc-
tion. Here, please introduce the line of thought (logic behind the construction of this
subsection).
 Page 6 of 15, line 168: Explain/remind the reader why this condition is important
to the overall control design scheme. Also maybe the signicance of this condition is
such that this should be made an assumption in Section 2?
 It could be benecial to arrange elements in (11) into columns?
 Page 6 of 15, line 168: Explain/remind the reader why this condition is important
to the overall control design scheme. Also maybe the signicance of this condition is
such that this should be made an assumption in Section 2?
 Figure 4 seems to be misplaced.
 Page 7 of 15, lines 174{175: This fact has already been raised in Section 2. Introducing
a proper assumption would allow the Authors to refer to this fact elegantly.
 Page 7 of 15, line 180: Are there any consequences/drawbacks/benets considering
the selected discretisation methods? Why it has been selects?
 Page 8 of 15, line 185: Is it (15) or (16)?
 Page 8 of 15, line 187: Unnecessary white space.
 Page 8 of 15, line 195: What is the connection in between (20) and (17)?
 Page 8 of 15, line 197: The name `control law' is rather not applicable in this context.
It would be more accurate to describe this as an control actions over prediction horizon
or something similar? The control law includes the optimisation task and solver etc...
It is the entire algorithm, derived based on the MPC approach.
 Page 8 of 15, line 199{202: This is not a choice at the level of either. The enlisted
so-called intelligent optimisation algorithms are algorithms used only as last resort
algorithms. There needs to be a really good motivation to let go of SQP and consider
any of them later. Please deliberate on this topic as the current claim does not provide
a sucient level of details.
4. Concerning `Case study':
 Please make sure to provide all necessary parameter values required to recreate the
results.
 If this model is acquired e.g. from [21] please remind this fact here by giving a proper
reference.
 Page 9 of 15, line 220: The variables in (21) and in Fig. 5 have not been explained
as expected to be.
 Page 9 of 15, line 222: The n is not a point in x domain. The n is simply point
number so the description is imprecise.
 Page 9 of 15, lines 231{232: This needs to be explained to the reader in more detail
and justied why this fact occurs for this particular set of numbers. Is it connected
to the properties of the plant dynamics?
 Page 11 of 15, line 234: This statement is highly ambiguous. Please provide proper
explanation.
 Page 11 of 15, lines 237{238: The sentence is inconsistent. Please include a proper
reference for the second part of the sentence as well.
 Page 11 of 15, line 242: Isn't that to short to make an assessment? Please justify this
choice. It would be worth adding the same comparison after e.g. 10 units?
 Page 11 of 15, line 242: Isn't that to short to make an assessment? Please justify this
choice. It would be worth adding the same comparison after e.g. 10 units?
 Page 11 of 15, line 250: `The prediction of the performance. . . ' or `The prediction
performance. . . '?
 Page 11 of 15, lines 253{254: This brings us back to the `Key concerns' section of the
review.
5. Concerning `Conclusions' section:
 Page 13 of 15, lines 273{274: This claim is not in line with the abstract of the
manuscript. The reviewer is highly disturbed with this inconsistency.
6. Concerning References | the list is missing items (hints have been given in the former
points of this review).
7. Editorial issues:
 The punctuation used for the equations being introduced is faulty. Commas and dots
are missing or used incorrectly, e.g. (4){(6).
 The punctuation used in text, e.g. line 239.
 There are some language issues (missing `-s' in line 242, line 247: discontinuity =
discontinuous) and inconsistencies that need to be addressed. Please read the text
carefully.
Concluding remarks
In the reviewer's opinion, the research or its description was presented in a way that does not
provide convincing evidence for the claims made (please refer to the `Key concerns' section of
this review). Moreover, the text is in parts hard to follow (please refer to the `Other issues'
section of the review). The indicated serious deciencies of the manuscript do not allow the
manuscript to be considered for further evaluation.
Since the topic of the presented research is very interesting the Authors are encouraged to
make the required amendments and resubmit this work as it shows potential.

Reviewer 2 Report

In Figure 7 there is the presentation of the simulation results of analyzing method is non readable because of its size and most of them the used colors. They are very weathered and practically non visible at the computer screen. In this picture we can see the results obtained for assuming parameters. The question is, What decide about the choosing of discretization interval value in the compared example? The same question related to parameters of WCM basis functions and the interval interpolation wavelets integer exponent of the inner wavelet scale function. In my opinion, it should be a few words of explanation of this parameters choice.
At the fig.8 left should be the flow velocity while the axis are described as alteration of parameter u, moreover, it is cutted by the set limits what makes this picture not clear. It looks more like a control error than flow velocity.
Conclusions are more like a summary because of its generality. In my opinion Authors should be more detailed in relation to its research. Here should be included the detailed description of the presented method advanteges over others with extension on other systems where its application may give similar results. Many people before read the paper starts to read the abstract and conclusions to see what interesting and innovative the Authors achieved.