esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods
### Study Area and Data Processing
#### 2.2.2 Data Processing
In addition, the MODIS LAI, FPAR, and EVI time-series data were preprocessed with the Savitzky-Golay filter model (SG) due to noise. The UofT LAI algorithm, developed from the four-scale geometrical optical model (FSGOM) [78], and the Spatial and Temporal Nonlocal Filter-Based Data Fusion Method (STNLFFM) [79] were adopted to generate high spatiotemporal resolution LAI maps. In this study, the UofT LAI algorithm was used to retrieve an LAI map at the 30 m resolution from the cloud-free Landsat-8 image, and then the STNLFFM was adopted to generate LAI maps at the resolutions of 30 m and 8-days from the 30-m LAI map and time-series MODIS LAI maps. Similar to the above generation of LAI maps, time-series EVI maps at 30 m resolution were also obtained from an EVI image from the Landsat-8 data and MODIS EVI data using SG and STNLFFM. Based on the method in [51], time-series FPAR maps at 30 m resolution were obtained by fusing an NDVI image from the Landsat-8 data and time-series MODIS FPAR data in conjunction with topographic features. * Topographic maps Several topographic maps, including elevation, slope, aspect, watershed boundary, and sky-view factor (SVF), were obtained from SRTM DEM. In the derivation of the watershed boundary map, the threshold value of flow-accumulation was set as 2500 to retain the 1 km\({}^{2}\) footprint area of the three observation towers. SVF was calculated using the method of [PERSON] et al. (2011) [68]:  
\[SVF=\frac{1}{n}{\sum\limits_{i=1}^{n}(1-\sin h_{i})} \tag{33}\]  
where \(n\) and \(h_{i}\) are the number of directions and the vertical altitude angle, respectively. More descriptions about the calculation of SVF can be found in the online service ([[https://iaps.zrc-sazu.si/en/rvt#v](https://iaps.zrc-sazu.si/en/rvt#v)]([https://iaps.zrc-sazu.si/en/rvt#v](https://iaps.zrc-sazu.si/en/rvt#v)), accessed on 1 December 2020).
## 1 Introduction
The main advantages of the FPGA technology are reduced engineering cost, reduced time-to-market, high performance due to the exploitation of fine-grained hardware parallelism, and adaptation to control system requirements. Especially for control systems that use demanding computational intelligence techniques, the advanced performance of FPGAs combined with their low-cost and high adaptability render them an attractive computing platform. Taking also into consideration the real-time requirements of our HVAC system, we propose the FPGA-based acceleration of the BB-BC optimization algorithm and the PID controller to speed up the parameters tuning process, and consequently, improve system performance. The BB-BC, PID controller and register transfer level (RTL) models have been described using the VHDL language and implemented in the Xilinx Zybo (Zynq) development board from Xilinx Corporation (San Jose, CA, USA). Built around the Xilinx Zynq XC7Z010 FPGA device. Moreover, the FPGA-in-the-loop (FIL) technique has been used to enable the emulation of the plant (HVAC) in MATLAB/Simulink environment in conjunction with the execution of the PID controller and the optimization process in the real hardware; this way, the FIL technique facilitates the evaluation of the entire system in higher abstraction layers [15]. In order to demonstrate the efficiency of the proposed approach, we run various experiments in a second order system with two sec time delay and compared it with GA and PSO optimization algorithms in terms of PID tuning speed and convergence speed. The experimental results showed that the FPGA-BB-BC algorithm tunes the PID controller parameters \(\sim\)430X faster than the software version of GA algorithm, \(\sim\)539X faster than the software version of PSO algorithm, and \(\sim\)270X faster than the software version of BB-BC algorithm. Furthermore, the proposed approach was tested under various fitness functions (error) for different number of iterations, and the integral time absolute error (_ITAE_) was chosen. The organization of this paper is given as follows. Section 2 shortly describes the basics of PID controllers and BB-BC optimization algorithm. Section 3 presents the HVAC optimization problem and the proposed BB-BC-based tuning process of the PID parameters. Section 4 describes the FPGA implementation of the PID and BB-BC subsystems and the FIL approach. Section 5 presents the experimental results and demonstrates the efficiency of the proposed approach, while Section 6 concludes the paper.
# Improved Safety Analysis Integration in a Systems Engineering Approach
## 5 Improved System Behavior Based on DFT Recommendation
### Step 3: Automatic Generation of DFT from SysML Diagrams and Redundancy Profile
#### 5.1.3 Redundancy Profile  
To model the behavior of the system and the redundancy, additional information is needed. For this reason, we create an UML extension called \"Redundancy Profile\" in order to integrate redundancy information into SysML models. Figure 3 represents the created profile diagram.  
The redundancy profile decomposes components in three different types. These components extend \"Class\" meta-class of UML and represent extensions of SysML blocks. The first category is the Redundant Component that describes duplicated and linked components. The second category is the Non Redundant Component, which describes the non duplicated components that do not have a redundancy link. Finally, the Switch Component is used in the case of standby or mixed redundancy  
Figure 3: Profile diagram.  
and it describes components that allow switching from the main component to the standby component. In addition, three additional stereotypes will extend the \"Association Class\" meta-class of UML. The redundancy association class aims at defining the relation between two redundant components. Hence, the redundancy type is specified and it can be active, standby, or mixed. Then, the sparing type will be defined and it can be cold, warm, or hot. Furthermore, \"Switch From\" and \"Switch To\" are used to define the activation order of the different redundant components. In the case of standby and mixed redundancy, some additional information like the type of redundant component (primary, secondary, etc.) are used.
## 3 Orbit Determination with ISL Measurements
\[\mathbf{x}(t_{k}) =\mathbf{X}(t_{k})-\mathbf{X}^{\star}(t_{k}) \tag{19}\] \[\mathbf{y}(t_{k}) =\mathbf{Y}(t_{k})-\mathbf{Y}^{\star}(t_{k}) \tag{20}\]  
The state deviations, \(\mathbf{x}(t_{k})\), can be mapped back to the initial epoch, \(t_{0}\), with the state transition matrix, \(\mathbf{\Phi}\), as follows:  
\[\mathbf{x}(t_{k})=\mathbf{\Phi}(t_{k},t_{0})\mathbf{x}(t_{0}) \tag{21}\]  
The state transition matrix is obtained by numerical integration, and its differential function is:  
\[\mathbf{\dot{\Phi}}(t_{k},t_{0})=\mathbf{A}(t_{k})\mathbf{\Phi}(t_{k},t_{0}) \tag{22}\]  
where:  
\[\mathbf{A}(t_{k})=[(\partial\mathbf{F}(\mathbf{X}^{\star},t_{k}))/(\partial \mathbf{X}(t_{k}))]^{\ast} \tag{23}\]  
where \(\left\|{}^{\ast}\right.\) means computed on the reference trajectory. Considering the case of \(N\) spacecraft, \(\mathbf{A}\) has the following formulation \(\mathbf{A}=diag(\mathbf{A}_{1},\dots,\mathbf{A}_{N})\), where:  
\[\mathbf{A}_{i}=\left[ \begin{array}{cccccc}0&0&0&1&0&0\\ 0&0&0&0&1&0\\ 0&0&0&0&0&1\\ \partial^{2}U_{i}/\partial^{2}X&\partial^{2}U_{i}/(\partial X\partial Y)& \partial^{2}U_{i}/(\partial X\partial Z)&0&2&0\\ \partial^{2}U_{i}/(\partial Y\partial X)&\partial^{2}U_{i}/(\partial^{2}Y)& \partial^{2}U_{i}/(\partial Y\partial Z)&-2&0&0\\ \partial^{2}U_{i}/(\partial Z\partial X)&\partial^{2}U_{i}/(\partial Z \partial Y)&\partial^{2}U_{i}/(\partial^{2}Z)&0&0&0\end{array} \right] \tag{24}\]  
The same approach can be used to map back all the measurements to the initial time \(t_{0}\), exploiting the observation residuals, defining the \(\hat{\mathbf{H}}\) matrix as:  
\[\hat{\mathbf{H}}=[\partial\mathbf{G}/\partial\mathbf{X}]^{\ast} \tag{25}\]  
where \(\mathbf{G}\) is the function that relates the observations to the state vector in the following way:  
\[\mathbf{Y}=\mathbf{G}(\mathbf{X},t)+\mathbf{\epsilon} \tag{26}\]  
as given in Equations (3) and (6). Therefore, it is possible to move the set of observations at time \(t_{k}\) back to the initial epoch \(t_{0}\) defining the matrix \(\mathbf{H}_{k}\):  
\[\mathbf{H}_{k}=\hat{H}\mathbf{\Phi}(t_{k},t0) \tag{27}\]  
When the total number of observations is larger than the number of unknowns, a solution for \(\mathbf{x}(t_{0})\) can be found by exploiting the normal equation:  
\[\mathbf{\Lambda}\mathbf{x}=\mathbf{N} \tag{28}\]  
where \(\mathbf{\Lambda}=\mathbf{H}^{T}\mathbf{W}\mathbf{H}\) is the information matrix, and \(\mathbf{N}=\mathbf{H}^{T}\mathbf{W}\mathbf{y}\) is the reduced residual vector, where \(\mathbf{H}\) is the block matrix containing the observation-state relationship matrices \(\mathbf{H}_{k}\) for all the epochs, and is given by:  
\[\mathbf{H}=\left[ \begin{array}{c}\mathbf{H}_{1}\\ \vdots\\ \mathbf{H}_{N}\end{array} \right] \tag{29}\]  
and \(\mathbf{W}\) is the weighting matrix:\[\mathbf{W}=\left[ \begin{array}{ccc}W_{1}&\dots&0\\ &\ddots&\\ 0&\dots&W_{l}\end{array} \right] \tag{30}\]  
assuming that the observation errors can be modeled as white Gaussian noise, and the standard deviation in the observation noise can be denoted as \(\sigma_{p}\), \(W_{p}=1/\sigma_{p}\).
## 2 Wavelet Packet Transform  
### Wpt  
Compared with wavelet decomposition, wavelet packet (WPT) makes up for the shortcomings of high-frequency part decomposition of the measurement signal. It separates the frequency band of the signal in multiple levels and refines the fault features of the measurement signal in each frequency band [20; 21]. Suppose the original signal is \(x_{j}^{n}(t)\in u_{j}^{n}\), then \(x_{j}^{n}(t)\) can be decomposed by wavelet packet as:  
\[x_{j}^{n}(t)=\sum_{l}d_{l}^{j,n}u_{n}\Big{(}2^{l}t-l\Big{)} \tag{1}\]Among them, \(j\) represents the scale and \(l\) represents the translation factor. \(u_{n}\big{(}2^{j}t-l\big{)}\) represents the basis function in \(u_{j}^{n}\), and \(d_{l}^{j,n}\) represents the WPT coefficient. \(|d_{l}^{j,n}\big{)}\) can be decomposed into \(\{d_{l}^{j,\ 2n}\}\) and \(\{d_{l}^{j,\ 2n+1}\}\), namely:  
\[\left\{\begin{array}{l}d_{l}^{j,2n}=\sum\limits_{k}a_{k-2l}d_{k}^{j+1,n}\\ d_{l}^{j,2n+1}=\sum\limits_{k}a_{k-2l}d_{k}^{j+1,n}\end{array}\right. \tag{2}\]  
where \(k\) represents the translation parameter; \(n\) represents the oscillation parameter.
## 4 Formulation and Solution of the Optimization Problem
### Optimization Problem Formulation  
According to the equation of RACH success probability and power consumption, the multi-objective optimization problem can be formulated as follows:  
\[\begin{split}&(\text{P1}):\max_{N_{\text{rep}},W_{\text{Bo}}}P_{s} \\ &(\text{P2}):\min_{N_{\text{rep}},W_{\text{Bo}}}E\\ &\text{s.t.}\ \text{C1}:\ T_{\text{msg1}}+RTD+T_{0}+T_{\text{ RAR}}+T_{\text{CR}}\leq T_{\text{RAO}}<T_{\text{max}}\\ &\text{C2}:\ 0<N_{\text{rep}}\leq N_{\text{rep}}^{\text{max}}\\ &\text{C3}:\ T_{\text{pre}}\cdot N_{\text{rep}}+W_{\text{BO}} \big{(}N_{\text{rep}}-1\big{)}=T_{\text{msg1}}+RTD+\text{StartRAR}\end{split} \tag{25}\]  
The objective function P1 denotes the RACH access probability by configuring the number of repetitions and back-off windows. The objective function P2 denotes the power consumption of NB-IoT terminals. The constraint C1 is the time of access that is less than the size of a random access occasion \(T_{RAO}\) and the satellite beam coverage time \(T_{\text{max}}\) in 3 GPP's technical report TR 38.821. The constraint C2 is the number of repetitions \(\text{N}_{\text{rep}}\) and must be smaller than the maximum number of repetitions \(N_{\text{rep}}^{\text{max}}\). The constraint C3 is the total time of repetitions and back-off should be equal to the sum of the RTD, \(T_{\text{msg1}}\), and StartRAR.  
This paper has established an optimization model of the NB-IoT CE mechanism and power consumption. It is important to note that \(N_{\text{rep}}\) is an integer type in this context. In the next subsection, we will solve this optimization problem and choose the corresponding parameters for different applications.
# A Review of Double-Walled and Triple-Walled Carbon Nanotube Synthesis and Applications
## 1 Introduction and Motivation  
Before starting with the Introduction and definitions, it is important to keep in mind that this manuscript is intended to briefly review and discuss the recent progress on the controlled growth of double-walled carbon nanotubes (DWNTs) and triple-walled carbon nanotubes (TWNTs), which are the few-walled versions of the single-walled carbon nanotubes (SWNTs). Namely, since they were first discovered [1], carbon nanotubes (CNTs) have undoubtedly been one of the most promising nano-materials to advance applications in mechanics, electronics, materials science, sensors, energy harvesting devices and much more [2; 3; 4].
## 4 Descriptors
### Descriptors Based on Superpixel Segmentation and Histogram  
In this section, three descriptors that use their histograms as features are described. Three images must be obtained to construct the required descriptors. Let \((R,G,B)\) be the channels red, green, and blue, respectively; the descriptors will be obtained from \(R-B\), \(R/B\), and \(RGB\) images. Cloud detection algorithms commonly use color to determine if a region of the image is a cloud. Cloud particles have a similar dispersion of B and R intensity, whereas clear sky presents more \(B\) than \(R\) intensity [12; 13].  
For \(N\) pixels, \(M\) superpixels will be generated based on color similarity and proximity using Simple Linear Iterative Clustering (SILC) [32] in CIELAB color space. SILC initializes \(M\) clusters centers \(C_{m}=[l_{m},a_{m},b_{m},x_{m},y_{m}]^{T}\) on a regular grid space, where \((l,a,b)\) is the color vector in CIELAB space and \((x,y)\) are the pixel coordinates. Each superpixel has an approximate size of \(N/M\) and the center will be located every \(S=\sqrt{N/M}\).  
SILC computes a distance \(D\) between pixel \(i\) and its nearest cluster center \(C_{m}\)  
\[D=\sqrt{d_{c}^{2}+\left(\frac{d_{s}}{s}\right)r^{2}}, \tag{3}\]  
where \(r\in[1,40]\) is a constant that allows pondering between color similarity and spatial proximity, \(d_{c}\) and \(d_{s}\) are defined by  
\[d_{c}=\sqrt{\left(l_{j}-l_{i}\right)^{2}+\left(a_{j}-a_{i}\right)^{2}+\left(b_{ j}-b_{i}\right)^{2}} \tag{4}\]  
\[d_{s}=\sqrt{\left(x_{j}-x_{i}\right)^{2}+\left(y_{j}-y_{i}\right)^{2}}. \tag{5}\]The clusters are adjusted to take the value of the main vector of the pixels in \(C_{m}\), and a residual error \(E\) between the new cluster center and previous centers is computed using \(L_{2}\) norm. The algorithm stops when \(E\) reaches a certain threshold.  
The descriptor \(\beta\) of the superpixel \(k\) is obtained from a histogram of 16 values for each superpixel in \(R-B\) and \(R/B\) images. The intensity value of pixel \(i\in k\) is divided by 16 and rounded downward to its nearest integer value. In the case of the \(RGB\) image, a histogram for each channel is obtained.
# Inhibitory Effect of Cold Atmospheric Plasma on Chronic Wound-Related Multispecies Biofilms
## 4 Discussion
In this study, all tested periods of treatments presented a DNA index between 1.2 and 1.33 (mean and median) which, according to the score, represents a slight ploidy, but taking into account that the CAP group was into the same score; median 1.24 and mean 1.27, we believe treatment was not genotoxic. Our results are coincident with others in the literature. [PERSON] et al. [70] observed no mutations, through EPRT assay, on V79 cells after 30 to 240 s of CAP treatment using a MiniFlatPlaSter device. Only a decrease in the proliferation rate was observed. [PERSON] et al. [71] and [PERSON] et al. [72] tested the KINPen(r) trough different methods of evaluation, and found no signals of genotoxicity due to plasma treatment. [PERSON] et al. [71] assays used up to 180 s of CAP in non-cancer cells (HaCat and MRC5 cells) and melanoma cells (SK-Mel-147 cells) and did not find mutagenic changes with CAP treatment as well. They used HPRT1 mutation assay, micronuclele formation assay, and clonogenic assay, to confirm their findings. [PERSON] et al. [73] used the KINPen MED(tm) to evaluate CAP genotoxicity using HET-MN model and also observed no genotoxic alterations on CAP treatment. In our study, static cytometry was chosen to calculate DNA index and, in that way, evaluate possible mutations caused by cold plasma treatment and found no genotoxic signals in cells expose up to 7 min (420 s). Different CAP sources, cell types, CAP treatment conditions, and assay models reported make it difficult to compare results, but it seems that CAP safety has been proven by literature. The inhibitory effect of CAP on wound-related multispecies biofilm with the low cytotoxicity and no genotoxicity observed in this wound-related multispecies biofilm study encourage in vivo studies to evaluate the effects of CAP on infected wounds that can also investigate additional anti-inflammatory and tissue repair inducing effects.
# Early Ventricular Fibrillation Prediction Based on Topological Data Analysis of ECG Signal
## 4 Discussion
### Comparison with Previous Prediction Methods  
Previous ECG-based VF prediction methods were compared, and databases, features, and prediction performance corresponding to the selected literature are listed in Table 7.  
In terms of the data volume and databases used, 60 ECG records from three databases were used for our study. Among the listed literature, only [PERSON] et al. [7] and [PERSON] et al. [12] employ a larger amount of data, but both exhibit limitations in the length of forecast time, meaning that the predictions are too close to the onset of VF to provide an advantage in early prediction. In terms of forecast time, we predict VF 5 min before the onset. Studies conducted by [PERSON] et al. [5] and [PERSON] et al. [4] achieved longer forecast times, but both are limited by the small data volume. Also, the lack of diversity in databases makes the generalizability of the methods challenging, while the accuracy is lower than our proposed method. For the prediction performance, [PERSON] et al. [8], [PERSON] et al. [9], and [PERSON] et al. [6] achieve higher accuracy. However, the forecast time proposed by [6] is very close to the onset of VF. Although [8] is close to our work in terms of forecast time and accuracy, it uses a smaller amount of data from only two public databases, making the prediction result limited by the data. Compared to [9], we advance the forecast time by half a minute while guaranteeing the prediction accuracy, which proves the advantage of this work in relation to early VF prediction.
# Finite Difference/Collocation Method for a Generalized Time-Fractional KdV Equation
## 2 Preliminaries of Fractional Calculus and Jacobi Polynomials
### Numerical Discretization in the Time Direction  
To establish a numerical approximation scheme in the time direction, we divide the time domain into \(M\) equal parts, where \(M\) is a positive integer. Thus \(\Delta t=\frac{T}{M}\) is the time-grid size. We label the successive time nodes as \(t_{k}=k\cdot\left({\Delta t}\right)\), \(k=0,1,2,\cdots,M\), where \(t_{0}=0\) is the initial time. Assuming \(w(t)>0,\;\;0<\alpha<1\) and \(z\left(t\right)\) is strictly monotonic increasing on \(\left({0,T}\right]\), then \(s=z^{-1}(\eta)\) by setting \(\eta=z(s)\). The Caputo-type generalized fractional derivative of \(u(t)\) can be discretized as  
\[ \begin{array}{rcl}{{}^{*}D_{0+}^{\alpha}u(t_{k})}&=&{\frac{ \left[{w(t_{k})}\right]^{-1}}{\Gamma(1-\alpha)}\sum\limits_{i=1}^{k}\int_{t_{i -1}}^{t_{i}}\frac{\left[{w(s)u(s)}\right]^{\prime}}{[z(t_{k})-z(s)]^{\alpha}}ds }\\ &=&{\frac{\left[{w(t_{k})}\right]^{-1}}{\Gamma(1-\alpha)}\sum \limits_{i=1}^{k}\int_{z(t_{i-1})}^{z(t_{i})}\frac{1}{\left[{z(t_{k})-\eta} \right]^{\alpha}}\cdot\frac{d\left[{w(z^{-1}(\eta))u\left({z^{-1}(\eta)} \right)}\right]}{dz^{-1}(\eta)}dz^{-1}(\eta)}dz^{-1}(\eta)\\ &=&{\frac{\left[{w(t_{k})}\right]^{-1}}{\Gamma(1-\alpha)}\sum \limits_{i=1}^{k}\frac{w(t_{i})u(t_{i})-w(t_{i-1})u(t_{i-1})}{z(t_{i})-z(t_{i- 1})}\int_{z(t_{i-1})}^{z(t_{i})}\frac{1}{\left[{z(t_{k})-\eta}\right]^{\alpha}} d\eta+R_{k}}\\ &=&{\frac{\left[{w(t_{k})}\right]^{-1}}{\Gamma(2-\alpha)}\sum \limits_{i=1}^{k}a_{i}\left[{w(t_{i})u(t_{i})-w(t_{i-1})u(t_{i-1})}\right]+R_{ k}}\end{array}  \tag{12}\]  
where  
\[a_{i}=\frac{\left[{z(t_{k})-z(t_{i-1})}\right]^{1-\alpha}-\left[{z(t_{k})-z(t _{i})}\right]^{1-\alpha}}{z(t_{i})-z(t_{i-1})},i=1,2,\cdots,k, \tag{13}\]  
and \(R_{k}\) is the truncation error given by  
\[ \begin{array}{l}R_{k}\\ =\frac{\left[{w(t_{k})}\right]^{-1}}{\Gamma\left({1-\alpha}\right)}\sum \limits_{i=1}^{k}\int_{z_{i-1}}^{z_{i}}\frac{1}{\left[{z(t_{k})-\eta}\right]^{ \alpha}}\left[{\frac{d\left[{w\left({z^{-1}\left(\eta\right)}\right)u\left({ x,z^{-1}\left(\eta\right)}\right)}\right]}{d\eta}-\frac{w(t_{i})u(t_{i})-w(t_{i-1})u(t_{i-1 })}{z(t_{i})-z(t_{i-1})}}\right]d\eta.\end{array}  \tag{14}\]  
**Lemma 1**. : _The coefficients \(a_{i}\), \(i=1,\cdots,k\), defined as (13), satisfy \(a_{k}>a_{k-1}>\cdots>a_{0}>0\)._Proof. : According to the mean-value theorem of integrals, there exist \(\zeta\in[z_{i-1},z_{i}]\) such that  
\[\frac{a_{i}}{1-\alpha} = \frac{1}{z_{i}-z_{i-1}}\int_{z_{i-1}}^{z_{i}}\frac{1}{(z_{k}-\eta)^ {\alpha}}d\eta\] \[= \frac{1}{(z_{k}-\zeta)^{\alpha}}.\]  
Since \(z(t)\) is monotonically increasing, it follows that \(a_{i}>0\) and \(a_{k}>a_{k-1}>\cdots>a_{0}\). **Remark 2**. : _To analyze the truncation error \(R_{k}\), we denote \(U\left(\eta\right)=w\left(z^{-1}\left(\eta\right)\right)u\left(z^{-1}\left( \eta\right)\right)\) for \(\eta\in[z_{i-1},z_{i}]\), \(w\left(t_{k}\right)=w_{k}\) and \(z\left(t_{k}\right)=z_{k}\) for convenience.
# Computationally Efficient Soft Detection Schemes for Coded Massive MIMO Systems +
## 5 Conclusions  
In this paper, we proposed an efficient method to reduce the computational complexity of the MMSE-PIC-based JIDD scheme for a massive MIMO system. The proposed method approximates the Gram matrix with a diagonal matrix composed of a universal value, and tailored it for efficient soft MIMO detection. The proposed method does not require a complex matrix inversion process and layer dependent PE-SINR estimation at every iteration, resulting in huge amount of complexity reduction. In addition, we derived compact equations to estimate soft-symbol values for the MMSE-PIC process. It was shown that the proposed method requires two orders less complexity than the conventional one. The simulation results demonstrated that the proposed method can achieve approximating performance to the conventional methods with a greatly reduced complexity.  
**Author Contributions:** Conceptualization, M.Z.; Data curation, Z.Z. and S.C.; Investigation, M.Z. and S.C.; Project administration, S.K.; Software, Z.Z. and S.C.; Writing-review & editing, S.K. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03027939) and National Natural Science Foundation of China (Grant No. 61601403).  
**Conflicts of Interest:** The authors declare no conflict of interest.
## 4 Simulations and Discussion
### Scenario 2: Rapid Deceleration of Leader Vehicle  
In this scenario, the leader car suddenly brakes sharply and decelerates from 30 m/s to 1 m/s with 5 m/s\({}^{2}\) deceleration at 15 s.  
Figure 4 shows the results of scenario 2. When the leader vehicle decelerates sharply, the distance-prescribed performance control algorithm can control the vehicle to brake with the leader vehicle within the preset safe spacing range to avoid collision and achieve emergency avoidance.  
**Remark 4**.: _Due to the controller constraining the range of the distance error variation, when the leader vehicle decelerates urgently, the following vehicle will also decelerate urgently without overshoot._