Constrained Model Research Articles

Geologically constrained unsupervised dual-branch deep learning algorithm for geochemical anomalies identification

The identification of geochemical anomalies is crucial in mineral exploration. However, the limited sample size, high-dimensional features, and mixed geochemical information make identifying geochemical anomalies a significant challenge. Machine learning algorithms (MLAs), especially those with spatial and spectrum branches, have been proven to be a high efficiency tools for detecting geochemical anomalies related to mineralization. The spatial branch MLAs take two-dimensional images (pixel-patches) as input and mainly capture the spatial characteristics of geochemical patterns. The spectrum branch MLAs take one-dimensional sequence data (pixels) as input and mainly consider the elemental concentration and assemblies. Simultaneously considering the spatial patterns and geochemical concentrations of the geochemical survey data can mitigate geochemical concentration variations arising from objective factors and amplify subtle mineralization anomalies. This study proposes an unsupervised spatial-spectrum autoencoder (AE), namely dual-AE, which consists of a graph convolutional autoencoder (GCN-AE) and a long short-term memory network autoencoder (LSTM-AE) for geochemical anomalies identification. The spatial branch is constructed using the GCN-AE, which can effectively capture spatial geochemical patterns and extract spatial relationships between neighboring pixels. The spectrum branch consists of an LSTM-AE that can study geochemical elemental assemblies within a single pixel. A key ore-controlling factor was added into the dual-AE as a soft constraint to construct a geologically constrained dual-AE. A case study was conducted to recognize geochemical anomalies associated with iron polymetallic mineralization in Southwest Fujian Province, China. The obtained results demonstrated that (1) the unsupervised spatial-spectrum deep learning algorithm serves as a potent method for detecting geochemical anomalies related to mineralization, (2) the geologically constrained unsupervised spatial-spectrum dual-branch model can improve the accuracy and interpretability of geochemical anomaly identification, and (3) the identified anomalous areas can provide essential clues for further mineral exploration.

Power-Law Entanglement and Hilbert Space Fragmentation in Nonreciprocal Quantum Circuits.

Quantum circuits utilizing measurement to evolve a quantum wave function offer a new and rich playground to engineer unconventional entanglement dynamics. Here, we introduce a hybrid, nonreciprocal setup featuring a quantum circuit, whose updates are conditioned on the state of a classical dynamical agent. In our example the circuit is represented by a Majorana quantum chain controlled by a classical N-state Potts chain undergoing pair flips. The local orientation of the classical spins controls whether randomly drawn local measurements on the quantum chain are allowed or not. This imposes a dynamical kinetic constraint on the entanglement growth, described by the transfer matrix of an N-colored loop model. It yields an equivalent description of the circuit by an SU(N)-symmetric Temperley-Lieb Hamiltonian or by a kinetically constrained surface growth model for an N-component height field. For N=2, we find a diffusive growth of the half-chain entanglement toward a stationary profile S(L)∼L^{1/2} for L sites. For N≥3, the kinetic constraints impose Hilbert space fragmentation, yielding subdiffusive growth toward S(L)∼L^{0.57}. This showcases how the control by a classical dynamical agent can enrich the entanglement dynamics in quantum circuits, paving a route toward novel entanglement dynamics in nonreciprocal hybrid circuit architectures.

Random Pure Gaussian States and Hawking Radiation.

A black hole evaporates by Hawking radiation. Each mode of that radiation is thermal. If the total state is nevertheless to be pure, modes must be entangled. Estimating the minimum size of this entanglement has been an important outstanding issue. We develop a new theory of constrained random symplectic transformations, based on the assumptions that the total state is pure and Gaussian with given marginals. In the random constrained symplectic model we then compute the distribution of mode-mode correlations, from which we bound mode-mode entanglement. Modes of frequency much larger than [k_{B}T_{H}(t)/ℏ] are not populated at time t and drop out of the analysis. Among other relatively thinly populated modes (early-time high-frequency modes and/or late modes of any frequency), we find correlations and hence entanglement to be strongly suppressed. Relatively highly populated modes (early-time low-frequency modes) can, on the other hand, be strongly correlated, but a detailed analysis reveals that they are nevertheless very unlikely to be entangled. Our analysis hence establishes that restoring unitarity after a complete evaporation of a black hole does not require any significant quantum entanglement between any pair of Hawking modes. Our analysis further gives exact general expressions for the distribution of mode-mode correlations in random, pure, Gaussian states with given marginals, which may have applications beyond black hole physics.

Multi-Objective Constrained Optimization Model and Molten Iron Allocation Application Based on Hybrid Archimedes Optimization Algorithm

The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace’s production capacity and the steelmaking converter’s consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods.

PCSGAN: A Perceptual Constrained Generative Model for Railway Defect Sample Expansion From a Single Image

PCSGAN: A Perceptual Constrained Generative Model for Railway Defect Sample Expansion From a Single Image

Modeling residual-vehicle effects on uncertainty estimation of the connected vehicle penetration rate

In the transition to full deployment of connected vehicles (CVs), the CV penetration rate plays a key role in bridging the gap between partial and complete traffic information. Several innovative methods have been proposed to estimate the CV penetration rate using only CV data. However, these methods, as point estimators, may lead to biased estimations or suboptimal solutions when applied directly in modeling or system optimization. To avoid these problems, the uncertainty and variability in the CV penetration rate must be considered. Recently, a probabilistic penetration rate (PPR) model was developed for estimating such uncertainties. The key model input is a constrained queue length distribution composed exclusively of queues formed by red signals in undersaturation conditions with no residual vehicles. However, in real-world scenarios, due to random arrivals, residual vehicles are commonly carried over from one cycle to another in temporary overflow cycles in undersaturation conditions, which seriously restricts the applicability of the PPR model. To address this limitation, this paper proposes a Markov-constrained queue length (MCQL) model that can model the complex effects of residual vehicles on the CV penetration rate uncertainty. A constrained queue with residual vehicles is decomposed into four vehicle groups: observable constrained residual vehicles, unobservable constrained residual vehicles, unconstrained residual vehicles, and new arrivals. Although the first vehicle group is observable in the former cycle, the focus of this work is to model the residual vehicles from the second and third vehicle groups in combination with the new arrivals. The MCQL model includes four sub-models, namely, the residual-vehicle model, convolutional constrained queue model, constrained residual queue model, and observable residual queue model, to isolate and derive the distribution of the constrained vehicle set formed by the three latter vehicle groups. This distribution is then substituted into the PPR model to estimate the uncertainty. Comprehensive VISSIM simulations and applications to real-world datasets demonstrate that the proposed MCQL model can accurately model the residual-vehicle effect and estimate the uncertainty. Thus, the applicability of the PPR model is truly extended to real-world settings, regardless of the presence of residual vehicles. A simple stochastic CV-based adaptive signal control example illustrates the potential of the proposed model in real-world applications.

Startup drift compensation of RLG based on monotone constrained RBF neural network

Serious startup drift of the Ring Laser Gyroscope (RLG) is observed during cold startup process, which will dramatically degrade the performances of the corresponding Inertial Navigation System (INS). In this paper, correlation analysis method, which analyzes the relationship between the startup drift of the RLG and the temperature change, is used to determine the significant temperature-related terms during gyroscope startup. Based on the significant temperature-related terms and the startup time length, a startup drift compensation model for RLG based on monotonicity-constrained Radial Basis Function (RBF) neural network is proposed and validated. Compared with the raw RLG data without compensation, the standard deviation of the RLG output with the proposed constrained RBF network model is decreased by more than 46%, and the peak-to-peak value is decreased by more than 35%. Compared with the traditional multiple regression model, the standard deviation and peak-to-peak value of the RLG output are decreased by more than 10% and 6%, respectively. Compared with the common RBF network model, the standard deviation and peak-to-peak value of the RLG output are decreased by more than 8% and 3%, respectively. Navigation experiments also validate the effectiveness of the compensation model.

Facial feature point detection under large range of face deformations

Facial Feature Point Detection (FFPD) plays a significant role in several face analysis tasks such as feature extraction and classification. This paper presents a Fully Automatic FFPD system using the application of Random Forest Regression Voting in a Constrained Local Model (RFRV-CLM) framework. A global detector is used to find the approximate positions of the facial region and eye centers. A sequence of local RFRV-CLMs are used to locate a detailed set of points around the facial features. Both global and local models use Random Forest Regression to vote for optimal positions. The system is evaluated in the task of facial expression localization using five different facial expression databases of different characteristics including age, intensity, 6-basic expressions, 22 compound expressions, static and dynamic images, and deliberate and spontaneous expressions. Quantitative results of the evaluation of automatic point localization against manual points (ground truth) demonstrated that the results of the proposed approach are encouraging and outperform the results of alternative techniques tested on the same databases.

Geological Modeling of Shale Oil in Member 7 of the Yanchang Formation, Heshui South Area, Ordos Basin

In recent years, the Chang 7 member of the Mesozoic Triassic Yanchang Formation in the Ordos Basin has emerged as a significant repository of abundant and distinctive unconventional oil resources. The Heshui area boasts substantial shale oil reserves, with reported third-level reserves surpassing 600 million tons. However, the region in the southern part of Heshui is marked by pronounced variability in reservoir quality, intricate oil–water dynamics, low formation energy, and suboptimal fluid properties, leading to divergent development outcomes for horizontal wells. There is an imperative need to devise and refine new geological models to underpin the efficient exploitation of shale oil in the southern Heshui area. This study focuses on the shale oil reservoir of the Chang 7 member in the southern Heshui area of the Ordos Basin, conducting detailed stratigraphic correlation and establishing a refined isochronous stratigraphic framework. Utilizing PetrelTM modeling software (version 2018), we integrate deterministic and stochastic modeling approaches, adhering to the principles of isochronous and phased modeling. By assessing the thickness of sand and mudstone layers and the overall stratigraphic sequence, we derive a geological probability surface. Subsequently, this surface is harnessed to constrain the lithofacies, yielding a constrained lithofacies model. Employing sequential indicator simulation and sequential Gaussian stochastic simulation, we develop a reservoir attribute model that is anchored in the lithofacies model and its controls, culminating in a robust and dependable static model. Employing the geological probability surface constraint method, we meticulously construct the reservoir matrix model, amalgamating individual well data with the inherent certainty and randomness of reservoir plane thickness. This approach further enhances the model’s accuracy and mitigates the uncertainty and randomness associated with inter-well interpolation to a significant degree.

Minimal model identification of drum brake squeal via SINDy

The industrial standard in the design and development process of NVH(Noise Vibration Harshness) characteristic of brakes is the application of Finite Element(FE) models with a high number of degrees of freedom in the range of one or several millions. Nevertheless, parallel experimental investigations are still indispensable. On the other hand, minimal models with, due to the inclusion of the self-excitation process, at least two degrees of freedom are well known to be capable to explain qualitatively phenomena as instability of the desired non-vibrating solution or limit cycle oscillation but are in general very inaccurate in predicting the dynamics of a specific real brake. This is because the underlying physical assumptions are already too restrictive and model parameters (especially those referring to nonlinearities) are widely unknown. To overcome this problem, the data-driven modeling approach SINDy(Sparse Identification of Nonlinear Dynamics) is applied to identify appropriate nonlinear functions for a brake squeal minimal model. A problem thereby is the limited database. It turns out that the naive implementation of the method yielding the lowest possible residuum does not necessarily provide physically meaningful models and results, respectively. Instead, a constrained model that incorporates physical knowledge is used to robustly identify parameters and reproduce realistic dynamic behavior. Thereby, several appropriate models with coexisting limit cycles and stationary equilibrium are identified. In particular, it was found that the angular position of the brake drum has a significant influence on the model parameters and therefore must be taken into account in a model with long-term validity.

Constrained model predictive control for networked jump systems under denial‐of‐service attacks and time delays

AbstractThis article addresses the problem of model predictive control of networked jump systems in the presence of DoS attacks and time delays. In the structural framework of the network predictive control system, we mathematically model the networked jump system by using Markov chains to describe the time delays and a polytope model to describe the jump system phenomenon, considering the properties of DoS attacks and time delays. Based on this, we propose a strategy to lessen the effect of network constraints on the control performance of the system. This strategy involves the corresponding control inputs from the control sequence for real‐time active compensation. It includes adjusting the control sequence application length variation based on the duration of the DoS attacks and time delays at each moment. In addition, we demonstrate the recursive feasibility of the control strategy and the global asymptotic stability of the control system from a theoretical perspective through the Lyapunov stability theory. Finally, the effectiveness of the proposed strategy is verified by simulation arithmetic.

Shape Morphing of Re‐Entrant Honeycomb Metamaterials for Linear Auxetic Behaviors

A re‐entrant honeycomb structure stands out as one of the most prevalent auxetic metamaterials, characterized by its negative Poisson's ratio. While re‐entrant auxetic structures are capable of achieving tunable Poisson's ratios, they tend to vary with the magnitude of applied strain, thereby exhibiting nonlinear auxetic behaviors. This study proposes a novel re‐entrant structure aimed at achieving linear auxetic behavior by mathematically modifying the shape of a re‐entrant cell. To achieve this objective, a sigmoid‐based shape morphing function is introduced to modify the morphology of the hinge connections within the re‐entrant honeycomb cell. The deformation behavior of the shape‐morphed re‐entrant cell is investigated using finite element analysis (FEA), with variations in the morphing parameter. Two FEA models, namely the unconstrained and constrained models, are developed for fundamental analysis of cell deformation and experimental validation, respectively. Compared to the pure re‐entrant honeycomb structure, the proposed shape morphing reduces the relative variation of Poisson's ratio by 70%, while maintaining its magnitude higher than 1.0. This achievement of linear auxetics with a high Poisson's ratio has the potential to broaden the applications of the proposed auxetic structures to various functional components, including sensors with high linear sensitivity and soft actuators with tunable deformation characteristics.

Parameter estimation of PEM fuel cells using metaheuristic algorithms

Developing an accurate model for precise parameter estimation is crucial for the design of polymer electrolyte membrane fuel cells (PEMFC). While many studies can meet the evaluation criteria for parameter estimation, there is a significant physical inconsistency when applying the Generalized Steady State of Electrochemical Model (GSSEM) prediction in the optimization framework. This study aims to address this inconsistency by adding necessary constraints to the optimization model. It employs the Artificial Hummingbird Algorithm (AHA) and Lévy flight improvement to find unknown parameters by minimizing the sum of squared errors (SSE). The proposed method has been rigorously tested with seven PEMFC cases, demonstrating its robustness and superior accuracy compared to alternative approaches. Notably, the cathode charge transfer coefficient exhibits zero relative percent difference (RPD) between the two sources, confirming its physical consistency. Furthermore, the proposed constrained optimization model lays the groundwork for achieving consistent parameter estimation results for PEMFC when utilizing GSSEM.

Optimizing the management of multiple water resources in irrigation area under uncertainty: A novel scenario-based multi-objective fuzzy-credibility constrained programming model

Effective water resources management is vital for sustainable development, healthy ecosystems, stable socio-economic, and human well-being. However, managing water resources faces challenges due to the involvement of multiple stakeholders and uncertainties in various hydrologic fluxes. This complexity makes it rare for research to simultaneously address the hidden uncertainties in both objectives and constraints. Here, we developed a scenario-based multi-objective fuzzy-credibility constrained programming approach and applied it to the water resource management system (SMOFCP-WRMS) of the Zhaokou Yellow River Diversion Irrigation Area Phase II Project (ZKID-II). This method handles uncertainties represented by scenarios and fuzzy sets, while also resolving fuzzy uncertainty parameters within the multiple objectives and constraints of the model. We solve the SMOFCP-RWMS model by integrating the Nondominated sorting genetic algorithm III (NSGA-III) and compromise programming (CP) method. The results show that: (1) An increase in constraints violation risks (credibility level from 0.5 to 1.0) results in a decrease in water resources allocation and pollutant discharge by 25.95 × 106 m3 and 207.63 tonne, respectively, accompanied by a decline in net economic income by 68.04 × 106 CNY; (2) From extraordinary dry year to normal year (design frequencies from 95 % to 50 %) leads to a reduction in water shortage by 167.07 × 106 m3. Incorporating ‘credibility levels’ and ‘design frequencies’ would be beneficial for addressing uncertainties, including fuzzy information and discrete possibilities for the future; (3) Regarding the multi-objective model solution, the combined NSGA-III and CP approach demonstrates an average increase of 1.71 % in net economic benefits and 5.91 % in total pollution discharge, along with a 6.77 % reduction in the water deficit ration compared to the traditional CP method. Although the ecological benefits decrease slightly in the compromise-optimal solutions using the combined NSGA-III and CP method, the economic and social benefits are improved compared to those from the combined NSGA-II and CP method. This study provides valuable decision-making guidance for water resources managers in irrigated areas, aiding them in balancing economic, social, and ecological benefits, and enabling the section of an optimal water resources management scheme based on acceptable risk levels under various uncertain conditions.

Weight bound constraints in mean-variance models: a robust control theory foundation via machine learning

Using an innovative representation of the weight bound constrained Markowitz's (Portfolio selection. J. Finance, 1952, 7, 77–91) mean-variance model, developed using the support vector data description, a machine learning algorithm introduced by Tax and Duin (Support vector data description. Mach. Learn., 2004, 54, 45–66), we provide an innovative interpretation of the robustness of these bound constraints in terms of robust control theory in the sense of Hansen and Sargent (Robust control and model uncertainty. Am. Econ. Rev., 2001, 91, 60–66). Building on these insights, firstly, we detail the method for quantifying the degree of misspecification in Markowitz's (1952) mean-variance model using its counterpart with weight upper bounds. Additionally, we show that this degree of misspecification is a decreasing piecewise linear function of the bound. Secondly, we empirically investigate two simulation-based methods, inspired by Michaud's (The Markowitz optimization enigma: Is ‘optimized’ optimal? Financ. Anal. J., 1989, 45, 31–42) resampling technique, for choosing the bound. Thirdly, we compare the robustness of the weight upper bound constrained mean-variance model with that of Goldfarb and Iyengar's (Robust portfolio selection problems. Math. Oper. Res., 2003, 28, 1–38) robust maximum return model.

Constrained hidden Markov models reveal further Hsp90 protein states

Time series of conformational dynamics in proteins are usually evaluated with hidden Markov models (HMMs). This approach works well if the number of states and their connectivity is known. However, for the multi-domain protein Hsp90, a standard HMM analysis with optimization of the BIC (Bayesian information criterion) cannot explain long-lived states well. Therefore, here we employ constrained HMMs, which neglect transitions between states by including assumptions. Gradually tuning a model with justified and focused changes allows us to improve its effectiveness and the score of the BIC. This became possible by analyzing time traces with several thousand observable transitions and, therefore, superb statistics. In this scheme, we also monitor the residences in the states reconstructed by the model, aiming to find exponentially distributed dwell times. We show how introducing new states can achieve these statistics but also point out limitations, e.g. for substantial similarity of two states connected to a common neighbor. One of the states displays the lowest free energy and could be the idle open ‘waiting state’, in which Hsp90 waits for the binding of nucleotides, cochaperones, or clients.

Model-based predictive greenhouse parameter control of aquaponic system.

The effectiveness of an aquaponic system significantly relies on the habitat provided for both the fish and plants. As an integral component of aquaponics, hydroponic cultivation benefits greatly from the controlled environment of a greenhouse. Within this environment, factors such as temperature, carbon dioxide levels, humidity, and light can be carefully adjusted to maximize plant growth and development. This precise regulation ensures an ideal growing environment, fostering the flourishing of plants and contributing to the overall success of the aquaponic ecosystem. This study presented a control approach for an aquaponic greenhouse system. It aims to keep the greenhouse climate parameters (temperature, CO2 concentration, and humidity) at their ideal levels. The proposed control strategy is a two-layered mechanism in which the first layer presents an optimization framework using particle swarm optimization (PSO) algorithm to give the setpoints for the controller, and the second layer demonstrates a constrained discrete model predictive control (CDMPC) strategy to maintain the desired trajectories received from the optimization layer. To validate the results obtained using PSO, this study incorporates genetic algorithms (GA) and assesses their performance in comparison. Given similar computational efficiency and low computational time for both algorithms, the optimal values identified by particle swarm optimization (PSO) are adopted as the setpoints. Two performance criteria, relative average deviation (RAD) and mean relative deviation (MRD), are derived to evaluate the tracking performance of the proposed CDMPC controller under external disturbances. A comparison of the proposed CDMPC with the PI controller is also offered. According to the comparison results, our proposed CDMPC performs better than the PI controller with lower RAD values (temperature, 1.1315; CO2 concentration, 0.9225; humidity, 2.547) and MRD values (temperature, 0.315; CO2 concentration, 0.25; humidity: 1.013). The controller is validated to be efficient by its strong control performance, highlighted by robustness, efficient setpoint tracking, and adequate disturbance rejection. This novel approach might prove to be a useful technique for developing environmental control strategies that can be used for potentially boosting production rates of aquaponic greenhouse systems, maximizing profitability, and reducing labor needs. By maintaining optimal conditions, it can enhance ecosystem health, improve yields, and streamline operations, paving the way for greater system performance and sustainability.

Constrained Reinforcement Learning for Fair and Environmentally Efficient Traffic Signal Controllers

Traffic signal controller (TSC) has a crucial role in managing traffic flow in urban areas. Recently, reinforcement learning models have received a great attention for TSC with promising results. However, these RL-TSC models still need to be improved for real-world deployment due to limited exploration of different performance metrics such as fair traffic scheduling or air quality impact. In this work, we introduce a constrained multi-objective RL model that minimizes multiple constrained objectives while achieving a higher expected reward. Furthermore, our proposed RL strategy integrates the peak and average constraint models to the RL problem formulation with maximum entropy off-policy models. We applied this strategy to a single TSC and a network of TSCs. As part of this constrained RL-TSC formulation, we discuss fairness and air quality parameters as constraints for the close-loop control system optimization model at TSCs called FAirLight . Our experimental analysis shows that the proposed FAirLight achieves a good traffic flow performance in terms of average waiting time while being fair and environmentally friendly. Our method outperforms the baseline models and allows a more comprehensive view of RL-TSC regarding its applicability to the real world.

Design for early-age structural performance of 3D printed concrete structures: A parametric numerical modeling approach

This paper presents a design framework based on structural performance of 3D concrete printing (3DCP) that considers three strength criteria for early-age failure modes: plastic collapse, elastic buckling, and flexural collapse. A simulator of structural behavior during printing was developed to take any shell or linear model, slice it into layers, perform incremental structural analysis layer by layer, and assign the respective material properties by adjusting the age of each layer when a new one is added. Then, finite element analysis for each printing stage indicates whether collapse might occur based on rheological and mechanical material properties over time. Printing experiments validated the criteria based on collapse layer estimation for a solid cylinder (plastic collapse), a thin-wall structure (elastic buckling), and an overhang structure (flexural collapse). Plastic collapse was most accurately predicted by a Drucker-Prager yield criterion for an unrestrained base and by a Modified Lade and Mohr-Coulomb criterion for a partially restrained base, while elastic buckling was predicted by linear elastic analysis. Additionally, this paper introduces flexural collapse as a distinct failure mode in early age 3DCP, proposing design criteria for overhang structures based on printing experiments. Experimental lessons learned were used to establish design constraints to aid the design of 3DCP structures, which were tested in the design of a hollow column and a cantilever structure. This study advances computational design for 3DPC structures with a new design methodology that combines constrained design and parametric numerical modeling.

Adaptive fault-tolerant control of distributed electric propulsion aircraft based on multivariable model predictive control

Distributed Electric Propulsion (DEP) aircraft presents a highly promising technology aligned with the demands of green aviation due to its superior flight efficiency, reduced energy loss, and diminished noise. This paper firstly designs and establishes a flight dynamics model for DEP aircraft, followed by an analysis of flying qualities, thus laying the foundation for control method design. Secondly, addressing the challenge of detecting subtle control surface faults, a deep learning fault diagnosis method based on Data Dimensionality Reduction (DDR) structure is devised, achieving an accuracy rate of 99.8 %. Finally, an adaptive fault-tolerant control method for the lateral motion mode of DEP aircraft is introduced, utilizing Constrained Multivariable-multiobjective Model Predictive Control (CMMPC). Notably, for the rudder complete fault, adaptive fault-tolerant control is achieved by switching controllers and utilizing differential thrust from distributed redundant propulsion units to mitigate yaw channel anomalies, thus showcasing the advantages of DEP aircraft. Simulation results validate the theoretical soundness of the proposed method, providing a theoretical basis for the future engineering application and advancement of control systems for DEP aircraft.