esa-sceva/satcom-chunk-collection huggingface dataset:
# Modeling of Fuzzy Systems Based on the Competitive Neural Network
## 3 Proposed Method
### Design Process of the Fuzzy Inference Systems
#### 3.2.3 Trapezoidal Membership Functions  
Trapezoidal MF comprises four points \(a,b,\ c\), and \(d\), with the mathematical restriction that \(a<b\leq c<d\), as expressed in Equation (12).  
\[\textit{Trapezoidal}(x;a,b,c,d)=\left\{\begin{array}{c}0,\ x\leq a.\\ \frac{x-a}{b-a},\ a\leq x\leq b.\\ 1,\ b\leq x\leq c.\\ \frac{d-x}{d-c},\ c\leq x\leq d.\\ 0,\ d\leq x.\\ \end{array}\right. \tag{12}\]  
In this approach, we incorporate the statistical method, specifically a summary of the five numbers, to generate the graphic known as Box-and-Whisker [34]. This process enables the automatic design of a Trapezoidal MF, as illustrated in Figure 5. Table 3 details how the parameters \(a_{n},\ b_{n},\ c_{n}\), and \(d_{n}\) are calculated.  
Figure 4: Design of a Gaussian MF.  
Figure 5: Trapezoidal MF.  
\begin{table}
\begin{tabular}{l l l} \hline \hline \multicolumn{1}{c}{_MembershipFunction\({}_{\mathbf{1}}\)_} & \multicolumn{1}{c}{_MembershipFunction\({}_{\mathbf{2}}\)\(\ldots\)_} & \multicolumn{1}{c}{_MembershipFunction\({}_{\mathbf{n}}\)_} \\ \hline \(a_{1}=min(Cluster_{1})\) & \(a_{2}=min(Cluster_{2})\ldots\) & \(a_{n}=min(Cluster_{n})\) \\ \(b_{1}=Quartile\ 1(Cluster_{1})\) & \(b_{2}=Quartile\ 1(Cluster_{2})\ldots\) & \(b_{n}=Quartile\ 1(Cluster_{n})\) \\ \(c_{1}=Quartile\ 3(Cluster_{1})\) & \(c_{2}=Quartile\ 3(Cluster_{2})\ldots\) & \(c_{n}=Quartile\ 3(Cluster_{n})\) \\ \(d_{1}=max(Cluster_{1})\) & \(d_{2}=max(Cluster_{2})\ldots\) & \(d_{n}=max(Cluster_{n})\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Points for a Trapezoidal MF.
## 2 Materials and Methods  
### Biodiesel Production from Date Seeds  
The fine date-seed powder was obtained from Sharjah Dates Factory, a domestic date facility, and used as feedstock for oil extraction using a Soxhlet extractor (B 811 BUCHI, Flawil, Switzerland). The following conditions and parameters for obtaining the optimum extraction yield were obtained from the literature [25; 31; 32; 33; 34; 35]: Hexane solvent (S D Fine-Chem Limited); a temperature of 60 \({}^{\circ}\)C; 4 h time; and a solvent/seed weight ratio of six. The gums formed in the resulting oil were eliminated via a degumming process in which they were hydrated by small amounts of water and then separated by centrifugation. The resulting DSO had phosphorus (P), and magnesium (Mg) plus calcium (Ca) concentrations of 9.08 and 14.16 ppm, respectively, both higher than the limits accepted under ASTM D6751 (5 and 10 ppm for P and for Mg plus Ca, respectively). To reduce these levels to tolerable concentrations, the DSO was subjected to the \"_phosphoric acid treatment procedure._\" [36]. The measured free fatty acid content of the resulting DSO of 0.42 wt.% (using the titration method) was compliant with the level specified by ASTM D6751, justifying the use of a one-step transesterification process. The final product had an oil yield of 10.74%, and the fatty acid profile is as shown in Table 1 (gas chromatography with flame-ionization detection (GC/FID)). The biodiesel were produced using a standard transesterification process using the following parameters and conditions for optimum oil conversion based on previous research [19; 31; 32; 35; 37]: Methanol (Fisher Chemical, Pittsburgh, PA, USA), NaOH (Sigma-Aldrich, MO, USA) as catalyst, methanol/DSO molar ratio of 9/1, catalyst/DSO mass fraction of 1/100; 1 h time; and a temperature of 55 \({}^{\circ}\)C, respectively. The resulting DSO biodiesel were purified using distilled water, dried, tested, and finally characterized for conformity with the standards. Table 2 summarizes the properties of the DSO biodiesel along with those of the fossil-based diesel and other second-generation biodiesel. Four of the biodiesel-diesel blends, which are labeled B5, B10, B15, and B20, respectively, were then assessed in terms of their impact on engine tailpipe emissions and performance.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fatty Acid** & **Chemical Structure** & **Content in DSO (wt.\%)** & **Molar Mass (g/mole)** \\ \hline Lignoocier & C24:0 & 0.24 & 368.65 \\ Erucic & C22:1 & 0.38 & 338.58 \\ Behenic & C22:0 & 0.46 & 340.59 \\ Arachidic & C20:0 & 0.21 & 312.54 \\ Linolenic & C18:3 & 0.11 & 278.44 \\ Linoleic & C18:2 & 9.95 & 280.45 \\ Oleic & C18:1 & 44.73 & 282.47 \\ Stearic & C18:0 & 4.54 & 284.48 \\ Palmitoleic & C16:1 & 0.09 & 254.41 \\ Palmitic & C16:0 & 12.01 & 256.43 \\ Myristic & C14:0 & 10.14 & 228.38 \\ Lauric & C12:0 & 16.14 & 200.32 \\ Capric & C10:0 & 0.47 & 172.27 \\ Caprylic & C8:0 & 0.34 & 144.21 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fatty acid profile of date-seed oil (DSO).
## 4 Discussion
However, many VECs-based approaches could not work effectively in clinical trials, which was not surprising as they lacked the proper delivery system of multiple growth factors due to the failure of recruiting and transplanting VECs [34; 35]. Here, the synergistic effects of VECs and different simultaneous delivery systems of VEGF and MCP-1 on new vessel formation were primarily evaluated through in vivo animal experiments. The star-shaped PLGA-mPEG block copolymer solution with an incorporation of the delivery system and VECs could be injected into a necrosis site of the femur head in Japanese rabbit. The composite hydrogel was formed in time with the help of animal body temperature. This technique was not only operated easily by researchers compared to traditional engineered scaffold replacement but also provided a new therapeutic strategy for treating chronic femoral head necrosis at an early stage instead of a total hip replacement [23; 27]. Being benefited from the good histocompatibility of the composite (Figure 4), the composite hydrogel treatment did not affect the bodily functions of rabbits, and abnormal signs such as infection, host reaction were not detected. On the other hand, in the clinic, although magnetic resonance imaging showed many advantages at an early stage compared to X-rays, such as a high image quality, considering the lost-cost of the X-rays for patients, X-ray combined with a histological analysis were used in this study [36]. We previously explored the effect of the sustained release of VEGF on vessel formation [23]. In this study, we expanded single VEGF to the simultaneous release of VEGF and MCP-1. MCP-1 showed a distinct behavior in three delivery systems, thus, leading to observable differences at different delivery systems (* \(p\) < 0.05), and significant differences compared to control group without intervention (*** \(p\) < 0.001). So, the release profile of MCP-1 played an important role in new vessel formation [7]. At week 8, the vessel density and mean average diameter of vessels both increased. The data showed that the simultaneous release of VEGF and MCP-1 promoted mature vessels formation in comparison to a single VEGF release. Although new bones have emerged, some old bones and necrotic bones might still exist, above phenomena might cause the resurgence of diseases, and then increased second surgical risk. Thus, the sequential delivery of multiple growth factors still needs to be explored in the future. In addition, besides VECs, other types of cells such as stem cells and macrophages need to be loaded into composites with multiple growth factors delivery system for angiogenesis and osteogenesis for bone regeneration [34; 35; 37].
# Toward SDM-Based Submarine Optical Networks: A Review of Their Evolution and Upcoming Trends
## 4 Submarine Amplifiers
### Pump Recycling (SDM) Technology  
Pump-recycling technology is a promising candidate to enhance optical amplification efficiency of cladding-pumped MC-EDFAs. This technique reuses part of the pump-amplification light (after being separated from the signal light) and, by doing so, achieves higher amplification efficiency. As a higher volume of pump optical power inserts into the outer cladding of the double-cladding MC-EDFA, it is egressed, and thus it does not take part in SDM signal amplification. More recently, a variety of schemes based on pump-recycling technology have been proposed and experimentally studied supporting 7-core [24, 46], and 19-core MC-EDFAs, respectively.  
An MC-EDFA compared to a single-core EDFA (SC-EDFA) implements a pump splitter, and there is a multiplex between the re-injected recycled pump in the spatial dimension with the original signal. The pump splitter has a major role for the pump-recycling process due to the fact that the optical power of the recycled pump light relies on its efficiency. A variety of both fiber-type [46, 47] and free space optics-type [24] pump splitters have already been evaluated. Another difference concerns the pump combiners of SC-EDFA and MC-EDFA because coupling loss due to the pump combiner for the cladding-pumped EDFA is much smaller than its counterpart, the SC-EDFA.  
A new investigation in pump-recycling technology, called the turbo cladding pumping scheme (TCP) is presented in [24]. It improves the optical amplification performance by 3.5 dB of cladding-pumping MC-EDFAs by implementing a paired free-optics combiner and splitters [17]. Finally, an improvement of the pump recycling ratio of the turbo cladding-pumped MC-EDFA from 12% to 42% by using paired prototypes of a spatial pump combiner and splitter achieved a 1-dB greater optical gain, as studied in [48].  
Figure 23: \(\times\) Tb/s schematic of a fully integrated SDM EDFA amplifier.
## 2 Materials and Methods
### Mathematical Models  
The Langmuir model represents the monolayer adsorption that assumes the adsorbent surface is homogeneous, and there is no transfer movement between the adsorbed metal ions. The Freundlich model describes the heterogeneous adsorption behavior of the adsorbent surface. The Ni\({}^{2+}\) adsorption by the soil colloids and sand was simulated by the Langmuir model Equation (1) and Freundlich model Equation (2); the related equations are shown below:  
\[Q=\frac{bC_{e}Q_{m}}{1+bC_{e}} \tag{1}\]  
\[Q=K_{f}C_{e}^{1/n} \tag{2}\]  
where \(Q\) (mg:g\({}^{-1}\)) and \(C_{e}\) (mg:L\({}^{-1}\)) are the solid-phase and solution-phase equilibrium concentrations, respectively; \(b\) is the Langmuir constant (L\(\cdot\)mg\({}^{-1}\)); \(Q_{m}\) is the maximum adsorption capacity (mg:g\({}^{-1}\)); \(K_{f}\) (mg:kg\({}^{-1}\cdot\)mg\({}^{-1}\cdot\)L\({}^{n}\)) is the Freundlich affinity coefficient, and \(n\) is the Freundlich adsorption strength parameter.  
The value of \(Q\) can be calculated by the equation as follows; Equation (3):  
\[Q=\frac{(C_{0}-C_{1})V_{0}}{m} \tag{3}\]  
where \(C_{0}\) is the initial Ni2+ concentration (mg:L\({}^{-1}\)); \(C_{1}\) is the final concentration after the equilibrium of Ni2+ in the solution (mg:L\({}^{-1}\)); \(V_{0}\) is the solution volume (mL), and \(m\) is the dry weight of the soil colloids (g).
# Seasonal Shifts and Smart Stats: Improving Biodrying in Waste Management
## 4 Results
### Biobox Performance Variability  
Figure 3 presents a boxplot illustrating the distribution of drying efficiency across the 12 bioboxes, offering a detailed visualization of their individual performance.  
While the range of drying efficiencies shows slight variations between bioboxes, statistical analysis using an Analysis of Variance (ANOVA) test confirms that these differences are not statistically significant (\(p\) value = 0.188). Thus, the observed variability in drying efficiency across the bioboxes can be attributed to random fluctuations rather than any systemic differences in performance. This finding suggests that all 12 bioboxes operate with comparable efficiency under similar conditions, emphasizing the consistency of the biodrying process across the system. Such consistency is critical for ensuring reliable performance in waste management operations and underscores the effectiveness of the system design in maintaining uniformity across the bioboxes.  
Figure 2: Control chart showing drying efficiency across observations for individual bioboxes. The range of 0–500 on the x-axis represents the sequential numbering of recorded observations, where each observation corresponds to a biodrying cycle for a specific biobox. The green dashed line indicates the mean drying efficiency (\(\sim\)28%), while the red dashed lines mark the upper and lower control limits (\(\pm\)3\(\sigma\)). Outliers exceeding the control limits are highlighted with red “X” markers.
# Strategies for Scaleable Communication and Coordination in Multi-Agent (UAV) Systems
## 3 Multi-Agent Planning and Control
### Locally Interactive State Spaces  
Every state space typically has a restricted set of legitimate transitions between individual states. This property is present in the simple gridworld system for example, with one robot on a \(10\times 10\) grid. Suppose the robot has four possible actions: \"up\", \"down\", \"left\", and \"right\". There are 100 possible states in the system corresponding to unique squares on the gird where the robot could be located. However, the robot can only reach (at most) four adjacent squares on the grid in the next time-step.  
By definition, the state \(s\in\mathcal{S}\) and the subset \(X\subseteq\mathcal{S}\) are locally interactive if \(\sum_{x\in X}p(x|s)=1\), where \(\mathcal{S}\) is the set of all possible states. Locally interactive states are reachable in the next time-step, and transitions between any pair of states occur exclusively through sequences of local interactions. It is difficult to find formal methods of identifying and exploiting locally interactive structure in general state spaces, but there have been attempts in the literature to do so [20]. Examples include the \"factored\" MDP (F-MDP) [7; 10] and POMDP (F-POMDP) [8]. Both require an explicit locally interactive structure in the state-space.
# Optimal Control for a Three-Rotor Unmanned Aerial Vehicle in Programmed Flights
## 2 Control Object
### Mathematical Model  
The tricopter is treated as a rigid body with a mass m, and the total force acting on it is the sum of the force generated by the rotors and the force due to gravity. The equations of motion derived using the Newton-Euler method derived by reference [20], only for a tricopter-type object are:  
\[\ddot{x}=\frac{1}{m}\big{[}U_{y}(sin(\phi)\sin(\theta)\cos(\psi)-cos(\phi)\sin (\psi))+U_{z}(\sin(\theta)cos(\phi)\cos(\psi)+ \tag{12}\]  
\[\ddot{y}=\frac{1}{m}\big{[}U_{y}(sin(\phi)\sin(\theta)\sin(\psi)+cos(\phi)\cos (\psi))+U_{z}(\sin(\theta)cos(\phi)\sin(\psi)- \tag{13}\]  
\[\ddot{z}=\frac{1}{m}\big{[}U_{y}sin(\phi)cos(\theta)+U_{z}cos(\phi)\cos(\theta )+mg\bigg{]}, \tag{14}\]  
\[\ddot{\phi}=\frac{1}{J_{xx}}\Big{[}\big{(}J_{yy}-I_{zz}\big{)}\dot{\theta}\dot {\psi}+U_{\phi}\Big{]}, \tag{15}\]\[\ddot{\theta} =\frac{1}{J_{yy}}\Big{[}(J_{zz}-J_{xx})\dot{\phi}\dot{\psi}+U_{\theta }\Big{]}, \tag{16}\] \[\ddot{\psi} =\frac{1}{J_{zz}}\Big{[}(J_{xx}-J_{yy})\dot{\phi}\dot{\theta}+U_{ \psi}\Big{]}, \tag{17}\]  
where:  
\(J_{xx}\)--moment of inertia about the X-axis,  
\(J_{yy}\)--moment of inertia about the Y-axis,  
\(J_{zz}\)--moment of inertia about the Z-axis.  
Since the experiments generally involve the tricopter operating close to the hover point, the linear equations of motion (12)-(17) can be linearized. It is assumed that \(\phi\approx 0\), \(\theta\approx 0\), so \(\sin\,(\phi)\approx 0,\sin\,(\theta)\approx 0,\cos\,(\phi)\approx 0,\cos\,( \theta)\approx 1\). In addition, based on [20], it can be assumed that the initial speed of the motors is the speed at which the object is maintained at the desired altitude:  
\[U_{z}=-mg+\Delta U_{z}, \tag{18}\]  
where:  
\(\Delta U_{z}\)--required control to keep the UAV hovering.  
Using Equation (18), we can derive the following equations of linear and spherical motion:  
\[\ddot{x}=-g\cdot\theta, \tag{19}\]  
\[\ddot{y}=g\cdot\phi+\frac{U_{Y}}{m}, \tag{20}\]  
\[\ddot{z}=\frac{U_{z}}{m}+g, \tag{21}\]  
\[\ddot{\phi}=\frac{U_{\phi}}{J_{xx}}, \tag{22}\]  
\[\ddot{\theta}=\frac{U_{\theta}}{J_{yy}}, \tag{23}\]  
\[\ddot{\psi}=\frac{U_{\psi}}{J_{zz}}. \tag{24}\]
## 3 Results and Discussion
### Health-Promoting Properties of Wheat bread with Addition of G. Iederacea Infusion
\begin{table}
\begin{tabular}{c l c c c c c c c c} \hline \hline  & & & & & & & & & & & \\ \cline{3-10} No. & Compound & **Rt** & \(\lambda_{\text{max}}\) & **[M – HI]** & **\#/z** & **Control** & **A** & **B** & **C** \\ \cline{3-10}  & & **min** & **mm** & **MS** & **MSMS** & & & **mg/g.d.w.** & \\ \hline
1 & Chlorogenic acid & 2.93 & 299\(\pm\)33,324 & 333 & 191 & n.d. & n.d. & 337.1 \(\pm\) 0.30 & 84.66 \(\pm\) 0.74 \\
2 & Cryptochlorogenic acid & 3.05 & 299\(\pm\)33,324 & 335 & 191 & n.d. & 20.22\({}^{\pm}\) 0.18 & 100.68 \(\pm\) 0.88 & 223.50 \({}^{\pm}\) 1.36 \\
3 & Caffeyogenic acid & 3.37 & 299\(\pm\)33,324 & 297 & 179 & 1.06\(\pm\) 0.01 & 89.55\({}^{\pm}\) 0.04 & 154.27 \(\pm\) 1.36 & 298.43 \(\pm\) 2.62 \\
4 & Raffin & 4.43 & 255.326 & 690 & 301 & n.d. & 6461.8 \({}^{\pm}\) 5.40 & 150.564 \(\pm\) 13.22 & 297.33 \({}^{\pm}\) 2.281 \\
5 & Hypercoiled & 4.62 & 253,330 & 463 & 301 & n.d. & 112.42 \(\pm\) 0.99 & 234.04 \(\pm\) 2.06 & 467.41 \(\pm\) 4.11 \\
6 & Quercetin 3-O-(6\({}^{\prime\prime}\)-mallow)breoside & 4.89 & 255,337 & 549 & 301 & n.d. & 270.24 \({}^{\pm}\) 0.27 & 289.13 \({}^{\pm}\) 2.54 & 485.99 \({}^{\pm}\) 4.26 \\
7 & Kaempfer 3-O-debibioside & 4.95 & 262,341 & 993 & 285 & 566.14 \(\pm\) 0.50 & 400.088 \(\pm\) 5.31 & 843.99 \(\pm\) 7.33 & 511.54 \(\pm\) 3.36 \\
8 & Yunnan 2-O-Chumuoside & 5.18 & 267,333 & 577 & 203 & n.d. & 4483.4 \({}^{\pm}\) 0.29 & 122.45 \({}^{\pm}\) 0.24 & 100.28 \({}^{\pm}\) 2.04 \\
9 & Romaritonic acid & 5.60 & 329 & 359 & 161 & 21.36 \({}^{\pm}\) 0.19 & 1286.61 \({}^{\pm}\) 1.13 & 55.08 \(\pm\) 4.71 & 90.08 \(\pm\) 5.70 \\
10 & Appleton & 6.11 & 267,331 & 369 & 225 & n.d. & 36.0 \({}^{\pm}\) 0.32 & 93.41 \({}^{\pm}\) 0.82 \\
11 & 3-O-methyl-rosmaritonic acid & 6.73 & 328 & 373 & 129 & n.d. & 483.0 \({}^{\pm}\) 0.38 & 199.17 \({}^{\pm}\) 1.39 & 302.62 \({}^{\pm}\) 2.91 \\ Total & Total & & & & & & & & \\ \hline \multicolumn{7}{c}{Mean values from two repetitions : i SD. Values in columns followed by the same superscript letters do not significantly differ at a significance level of 0.05. Abbreviations R. retention time [M – H], negative ion values: m/z, nus-to-charge ratio: d.w. dry weight: n.d., dry weight: n.d., dry reduced.} \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Individual phenolic compounds identified by UPLC-PDA-MS/MS in bread with G. _beforeax_ L. infusion.
# A New Lightweight Watchdog-Based Algorithm for Detecting Sybil Nodes in Mobile WSNs
## 4 Proposed Algorithm
In each row (corresponding to a specific time step), the left most column illustrates the former IDs-co-presence status of the network shown by matrix \(A_{co-prs-1}^{k-1}\). The second column from the left illustrates the network topology after applying one-step movement. Figure 5: A pictorial representation of the advancement of the information collection phase in a typical watchdog, herein, \(W_{1}\). Similarly, the third column from the left shows the current (post-movement) IDs-co-presence status of the network presented by matrix \(A^{k}_{co-prs-1}\). By comparing \(A^{k-1}_{co-prs-1}\) and \(A^{k}_{co-prs-1}\), the scoring matrix \(C^{k}_{co-prs-1}\) is updated according to the state diagram of Figure 3, as shown in the forth column. This algorithm proceeds in the following row (corresponding to the next time step) starting with a \(A^{k-1}_{co-prs-1}\) generated from \(A^{k}_{co-prs-1}\) in the preceding row and manipulated by [7] in the flowchart of Figure 4. This phase is terminated by reaching the simulation step limit which is equal to 10 in this example. * Detection phase: The designated WD receives the \(C^{k}_{co-prs-2}\) matrices from the other three WDs. Then the designated WD uses the received information, and its own \(C^{k}_{co-prs-2}\) matrix to form the \(C_{co-prs-final}\) matrix according to Equation (2). Finally, each element of the \(C_{co-prs-final}\) matrix is compared against the Sybil threshold, \(T_{s}=1\), to detect and announce the Sybil IDs as illustrated in Figure 6.
## 3 Mathematical Model
### Governing Equations  
To emphasize the physical essence and facilitate the numerical calculation, we made the following assumptions:  
1. The temperature of the exterior building surface is uniformly distributed;
2. Indoor heat disturbance was ignored;
3. The air is a Newton fluid that satisfies the boussinesq assumption;
4. The thermal contact resistance between different layer of the exterior wall were ignored;
5. The change in thermal conductivity with temperature was ignored, and the thermal conductivity was constant.  
The Reynolds-averaged Navier-Stokes equations are used to describe the turbulent flow because they can excellently express the statistical average of the physical quantities and other statistical randomness in turbulence. With good convergence and a low memory footprint, the Standard k-\(\epsilon\) model can be used in the exterior flow with complex geometries as well as non-slip wall flow, which uses wall functions to analyze fluid velocities in the viscous sublayer near the wall. Therefore, the Standard k-\(\epsilon\) model was used to solve the Reynolds stress term in this study. The governing equations are given in Table 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Boundary Type** & **Boundary Condition Setting** \\ \hline \multirow{2}{*}{Inlet} & \multirow{2}{*}{Velocity inlet} & Velocity: 3 m/s, 5 m/s and 10 m/s [38; 39; 40] \\  & & Temperature: \(-10\) °C, \(-20\) °C, \(-27\) °C [38; 39; 40] \\ \hline Outlet & Pressure outlet & \\ \hline \multirow{2}{*}{Exterior building surface/gabion} & \multirow{2}{*}{Wall} & Temperature: Data from calculation \\  & & Non-slip \\ \hline Lateral and top side of the domain & Symmetry & \\ \hline Ground surface & Wall & Adiabatic \\ \hline \hline \end{tabular}
\end{table}
Table 2: Boundary conditions for simulation.  
Figure 4: Computational domain (H: height of the tallest building).
## 7 Practical Applications of NCS
### Quasi-Decentralized Control System  
In order to achieve robust stability for a wide range of power system operating conditions, there is a need to break the limit imposed by the decentralized controller structure by implementing a quasi-decentralized control structure. Figure 20 is a block diagram to represent such a scheme. Since time-synchronized phases of Alternating Current (AC) voltages and currents are essential for the coordinated control, synchronous sampling control units based on the Global Positioning System (GPS) are used for this purpose.  
Figure 19: Flow diagram of autonomous unmanned aerial vehicles (UAV).
## 4 Intraday MPC Rolling Optimization  
MPC is a model-based closed-loop control method that utilizes the system's dynamic model to forecast future behavior over a prediction horizon and determines the optimal control input by solving an online optimization problem. The principal variables involved in the MPC formulation include state variables, control variables, and disturbance variables. In this specific application, the output of each device at time \(t\) is represented as a state variable vector, denoted by \(x\). The control variables, denoted by \(u\), represent the decisions or actions applied from time \(t\) to \(t+1\) that govern the system's evolution. Both the state and control variables are structured into upper and lower layers, and their detailed expressions will be presented in the subsequent section on rolling optimization. Disturbance variables, denoted by \(\omega\), are employed to model uncertainties or external variations, such as fluctuations in renewable energy generation and load demand, at time \(t\). The formulation for these disturbances is given as follows:  
\[\omega=[P_{\text{pv}},P_{\text{wt}},P_{\text{load}},H_{\text{load}},C_{\text{ load}},G_{\text{load}},T_{\text{load}}] \tag{33}\]  
MPC consists of prediction models, rolling optimization, and feedback correction. The following section will establish mathematical models for each of these three components.