Adaptive Fault-Tolerant Control of Hypersonic Vehicles with Unknown Model Inertia Matrix and System Induced by Centroid Shift

Round 1

Reviewer 1 Report

The article is logically laid out and there are no major issues with the presented analysis (although it could have been shortened in some places). One concern with the submitted manuscript is the quality of English language, which can be improved in multiple areas.
- some erroneous phrases appear as soon as the abstract, for instance "those estimated information"
-parts of the text contain unwarranted repetition, such as the first paragraph of introduction
-there are question marks erroneously appearing at the beginning of multiple sentences, such as the proof of Theorem 1.

One minor concern I would like the Authors to clarify is the viability of Assumptions 1 through 4 listed in Section II.D. Particularly, is it always feasible to assume that all system are available during the control process, and that the unpredictable disturbance is always bounded by a constant?

Author Response

{\bf Comment 1}: {\it The article is logically laid out and there are no major issues with the presented analysis (although it could have been shortened in some places). One concern with the submitted manuscript is the quality of English language, which can be improved in multiple areas.}

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{\bf Answer}: Thanks for the your sincere suggestions. The English writing has been carefully modified, to make the revised version easy to follow.    

{\bf Comment 2}: {\it some erroneous phrases appear as soon as the abstract, for instance "those estimated information"} 

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{\bf Answer}: Thanks for your kindness comment. The error has been corrected in the revised work.   

{\bf Comment 3}: {\it parts of the text contain unwarranted repetition, such as the first paragraph of introduction. }

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{\bf Answer}: Thanks for your constructive comment. The problem of text contain unwarranted repetition has been modified in the revised version. 

 

{\bf Comment 4}: {\it there are question marks erroneously appearing at the beginning of multiple sentences, such as the proof of Theorem 1. }

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{\bf Answer}: Thanks for your detailed suggestion.  The problem of question marks have been carefully corrected. 

 

{\bf Comment 5}: {\it One minor concern I would like the Authors to clarify is the viability of Assumptions 1 through 4 listed in Section II.D. Particularly, is it always feasible to assume that all system are available during the control process, and that the unpredictable disturbance is always bounded by a constant? }

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{\bf Answer}: Thanks for the your detailed suggestion. For the Assumptions 1-4, Assumption 1 is made to assumed that we focus on the challenges caused by force arm in control torque. 

Under Assumption 2, the inertia matrix $(J^* + \Delta J)$ is an invertible matrix, which plays a crucial role in controller, however, the inverse function of $(J^* + {\Delta \hat J})$ may not exist because $ {\Delta \hat J}$ is estimated by the estimator. For this challenge, a special negative feedback control is developed in this work without resorting to the exact knowledge of $(J^* + {\Delta \hat J})^{-1}$. In addition, based on an auxiliary integrator or necessary gain, they can be another way to deal with this problem.

Assumptions 3-4 are usual in the design process of relevant control algorithm. When it comes to the feasible to assume that all system are available during the control process, this is not reasonable, and it has been removed in the revised version. The unpredictable disturbance being bounded is applied for theoretical analysis, to ensure that the adaptive law of this paper is worked.

Author Response File: Author Response.pdf

Reviewer 2 Report

The article is devoted to the development of an adaptive fault-tolerant method for controlling hypersonic vehicles. In general, the article seems to be significant and interesting. However, I have to make a few remarks:

1. The first paragraph looks strange: the same phrase is repeated twice

2. There is an unaligned reference in line 67

3. How the parameter T is chosen in formula (15), it cannot be arbitrary

Thus I recommend minor revision

Author Response

{\bf Comment 1}: {\it  The first paragraph looks strange: the same phrase is repeated twice.}

\medskip
{\bf Answer}: Thanks for your sincere detailed comment. The repeated problem in the first paragraph has been carefully modified in the revised version.

 

{\bf Comment 2}: {\it  There is an unaligned reference in line 67.}

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{\bf Answer}: Thank you for your sincere suggestion. The unaligned reference has been modified in the revised version.  

{\bf Comment 3}: {\it   How the parameter $T$ is chosen in formula (15), it cannot be arbitrary.}

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{\bf Answer}: Thanks for your constructive comment. In order to clarify this question, the Eq.(15) is written as follows
\begin{align}\label{s.1}
J = {{\int_0^T {{\hat e^T_s}\left( {t + \hbar } \right)\hat e_s\left( {t + \hbar } \right)d\hbar } } \mathord{\left/
 {\vphantom {{\int_0^T {{\hat e^T}\left( {t + \tau } \right)\hat e_s\left( {t + \tau } \right)d\tau } } 2}} \right.
 \kern-\nulldelimiterspace} 2}
\end{align}

The parameter $T$ can not be selected arbitrary. In the model predictive control, $T$ represents the step size of iteration, which should ensure the sustainability of model predictive control iteration, namely, guaranteeing the existence of solutions in the iteration period. The larger $T$ can reduce calculation load, resulting in decreasing the control effect. $T$ is usually used as a super parameter, which is selected according to the control effect. 

Author Response File: Author Response.pdf