In radiology,magnetic resonance imaging(MRI)is an essential diagnostic tool that provides detailed images of a patient’s anatomical and physiological structures.MRI is particularly effective for detecting soft tissue...In radiology,magnetic resonance imaging(MRI)is an essential diagnostic tool that provides detailed images of a patient’s anatomical and physiological structures.MRI is particularly effective for detecting soft tissue anomalies.Traditionally,radiologists manually interpret these images,which can be labor-intensive and time-consuming due to the vast amount of data.To address this challenge,machine learning,and deep learning approaches can be utilized to improve the accuracy and efficiency of anomaly detection in MRI scans.This manuscript presents the use of the Deep AlexNet50 model for MRI classification with discriminative learning methods.There are three stages for learning;in the first stage,the whole dataset is used to learn the features.In the second stage,some layers of AlexNet50 are frozen with an augmented dataset,and in the third stage,AlexNet50 with an augmented dataset with the augmented dataset.This method used three publicly available MRI classification datasets:Harvard whole brain atlas(HWBA-dataset),the School of Biomedical Engineering of Southern Medical University(SMU-dataset),and The National Institute of Neuroscience and Hospitals brain MRI dataset(NINS-dataset)for analysis.Various hyperparameter optimizers like Adam,stochastic gradient descent(SGD),Root mean square propagation(RMS prop),Adamax,and AdamW have been used to compare the performance of the learning process.HWBA-dataset registers maximum classification performance.We evaluated the performance of the proposed classification model using several quantitative metrics,achieving an average accuracy of 98%.展开更多
In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimizatio...In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.展开更多
Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precurs...Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precursorswas conducted in a typical light industrial city in the YRD region from 1 May to 25 July in 2021.Alkanes were the most abundant VOC group,contributing to 55.0%of TVOCs concentration(56.43±21.10 ppb).OVOCs,aromatics,halides,alkenes,and alkynes contributed 18.7%,9.6%,9.3%,5.2%and 1.9%,respectively.The observational site shifted from a typical VOC control regime to a mixed regime from May to July,which can be explained by the significant increase of RO_(x)production,resulting in the transition of environment from NOx saturation to radical saturation with respect to O_(3)production.The optimal O_(3)control strategy should be dynamically changed depending on the transition of control regime.Under NOx saturation condition,minimizing the proportion of NOx in reduction could lead to better achievement of O_(3)alleviation.Under mixed control regime,the cut percentage gets the top priority for the effectiveness of O_(3)control.Five VOCs sources were identified:temperature dependent source(28.1%),vehicular exhausts(19.9%),petrochemical industries(7.2%),solvent&gasoline usage(32.3%)and manufacturing industries(12.6%).The increase of temperature and radiation would enhance the evaporation related VOC emissions,resulting in the increase of VOC concentration and the change of RO_(x)circulation.Our results highlight determination of the optimal control strategies for O_(3)pollution in a typical YRD industrial city.展开更多
The work takes a new liquid-cooling plate in a power battery with pin fins inside the channel as the object.A mathematical model is established via the central composite design of the response surface to study the rel...The work takes a new liquid-cooling plate in a power battery with pin fins inside the channel as the object.A mathematical model is established via the central composite design of the response surface to study the relationships among the length,width,height,and spacing of pin fins;the maximum temperature and temperature difference of the battery module;and the pressure drop of the liquid-cooling plate.Model accuracy is verified via variance analysis.The new liquid-cooling plate enables the power battery to work within an optimal temperature range.Appropriately increasing the length,width,and height and reducing the spacing of pin fins could reduce the temperature of the power battery module and improve the temperature uniformity.However,the pressure drop of the liquid-cooling plate increases.The structural parameters of the pin fins are optimized to minimize the maximum temperature and the temperature difference of the battery module as well as the pressure drop of the liquid-cooling plate.The errors between the values predicted and actual by the simulation test are 0.58%,4%,and 0.48%,respectively,which further verifies the model accuracy.The results reveal the influence of the structural parameters of the pin fins inside the liquid-cooling plate on its heat dissipation performance and pressure drop characteristics.A theoretical basis is provided for the design of liquid-cooling plates in power batteries and the optimization of structural parameters.展开更多
In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy sys...In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.展开更多
Two-dimensional double-layer honeycomb(DLHC)materials are known for their diverse physical properties,but superconductivity has been a notably absent characteristic in this structure.We address this gap by investigati...Two-dimensional double-layer honeycomb(DLHC)materials are known for their diverse physical properties,but superconductivity has been a notably absent characteristic in this structure.We address this gap by investigating M_(2)N_(2)(M=Nb,Ta)with DLHC structure using first-principles calculations.Our results show that M_(2)N_(2)are stable and metallic,exhibiting superconducting behavior.Specifically,Nb_(2)N_(2)and Ta_(2)N_(2)display superconducting transition temperatures of 6.8 K and 8.8 K,respectively.Their electron-phonon coupling is predominantly driven by the coupling between metal d-orbitals and low-frequency metal-dominated vibration modes.Interestingly,two compounds also exhibit non-trivial band topology.Thus,M_(2)N_(2)are promising platforms for studying the interplay between topology and superconductivity and fill the gap in superconductivity research for DLHC materials.展开更多
In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and the...In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.展开更多
Metaheuristic optimization methods are iterative search processes that aim to efficiently solve complexoptimization problems. These basically find the solution space very efficiently, often without utilizing the gradi...Metaheuristic optimization methods are iterative search processes that aim to efficiently solve complexoptimization problems. These basically find the solution space very efficiently, often without utilizing the gradientinformation, and are inspired by the bio-inspired and socially motivated heuristics. Metaheuristic optimizationalgorithms are increasingly applied to complex feature selection problems in high-dimensional medical datasets.Among these, Teaching-Learning-Based optimization (TLBO) has proven effective for continuous design tasks bybalancing exploration and exploitation phases. However, its binary version (BTLBO) suffers from limited exploitationability, often converging prematurely or getting trapped in local optima, particularly when applied to discrete featureselection tasks. Previous studies reported that BTLBO yields lower classification accuracy and higher feature subsetvariance compared to other hybrid methods in benchmark tests, motivating the development of hybrid approaches.This study proposes a novel hybrid algorithm, BTLBO-Cheetah Optimizer (BTLBO-CO), which integrates the globalexploration strength of BTLBO with the local exploitation efficiency of the Cheetah Optimization (CO) algorithm. Theobjective is to enhance the feature selection process for cancer classification tasks involving high-dimensional data. Theproposed BTLBO-CO algorithm was evaluated on six benchmark cancer datasets: 11 tumors (T), Lung Cancer (LUC),Leukemia (LEU), Small Round Blue Cell Tumor or SRBCT (SR), Diffuse Large B-cell Lymphoma or DLBCL (DL), andProstate Tumor (PT).The results demonstrate superior classification accuracy across all six datasets, achieving 93.71%,96.12%, 98.13%, 97.11%, 98.44%, and 98.84%, respectively.These results validate the effectiveness of the hybrid approachin addressing diverse feature selection challenges using a Support Vector Machine (SVM) classifier.展开更多
Restructuring of power market not only introduces competition but also brings complexity which increases overloading of Transmission Lines(TL).To obviate this complexity,this paper aims to mitigate the overloading and...Restructuring of power market not only introduces competition but also brings complexity which increases overloading of Transmission Lines(TL).To obviate this complexity,this paper aims to mitigate the overloading and estimate the optimal location of Static Synchronous Compensator(STATCOM) by reducing congestion for a deregulated power system.The proposed method is based on the use of Locational Marginal Price(LMP) difference technique and congestion cost.LMPs are obtained as a by-product of Optimal Power Flow(OPF),whereas Congestion Cost(CC) is a function of difference in LMP and power flows.The effiectiveness of this approach is demonstrated by reducing the CC and solution space which can identify the TLs more suitable for placement of STATCOM.Importantly,total real power loss,reactive power loss and total CC are the three main objective functions in this optimization process.The process is implemented by developing an IEEE-69 bus test system which verifies and validates the effectiveness of proposed optimization technique.Additionally,a comparative analysis is enumerated by implementing two optimization techniques:Flower Pollination Algorithm(FPA) and Particle Swarm Optimization(PSO).The comparative analysis is sufficient to demonstrate the superiority of FPA technique over PSO technique in estimating an optimal placement of a STATCOM.The results from the load-flow analysis illustrate the reduction in CC,total real and reactive power loss using FPA technique compared to PSO technique.Overall,satisfactory results are obtained without using complex calculations which verify the effectiveness of optimization techniques.展开更多
Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly effi...Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly efficient calculations for O-CNOPs are still challenging in the field of ensemble forecasting.In this study,we combine a gradient-based iterative idea with the Gram‒Schmidt orthogonalization,and propose an iterative optimization method to compute O-CNOPs.This method is different from the original sequential optimization method,and allows parallel computations of O-CNOPs,thus saving a large amount of computational time.We evaluate this method by using the Lorenz-96 model on the basis of the ensemble forecasting ability achieved and on the time consumed for computing O-CNOPs.The results demonstrate that the parallel iterative method causes O-CNOPs to yield reliable ensemble members and to achieve ensemble forecasting skills similar to or even slightly higher than those produced by the sequential method.Moreover,the parallel method significantly reduces the computational time for O-CNOPs.Therefore,the parallel iterative method provides a highly effective and efficient approach for calculating O-CNOPs for ensemble forecasts.Expectedly,it can play an important role in the application of the O-CNOPs to realistic ensemble forecasts for high-impact weather and climate events.展开更多
The Sine and Wormhole Energy Whale Optimization Algorithm(SWEWOA)represents an advanced solution method for resolving Optimal Power Flow(OPF)problems in power systems equipped with Flexible AC Transmission System(FACT...The Sine and Wormhole Energy Whale Optimization Algorithm(SWEWOA)represents an advanced solution method for resolving Optimal Power Flow(OPF)problems in power systems equipped with Flexible AC Transmission System(FACTS)devices which include Thyristor-Controlled Series Compensator(TCSC),Thyristor-Controlled Phase Shifter(TCPS),and Static Var Compensator(SVC).SWEWOA expands Whale Optimization Algorithm(WOA)through the integration of sine and wormhole energy features thus improving exploration and exploitation capabilities for efficient convergence in complex non-linear OPF problems.A performance evaluation of SWEWOA takes place on the IEEE-30 bus test system through static and dynamic loading scenarios where it demonstrates better results than five contemporary algorithms:Adaptive Chaotic WOA(ACWOA),WOA,Chaotic WOA(CWOA),Sine Cosine Algorithm Differential Evolution(SCADE),and Hybrid Grey Wolf Optimization(HGWO).The research shows that SWEWOA delivers superior generation cost reduction than other algorithms by reaching a minimum of 0.9%better performance.SWEWOA demonstrates superior power loss performance by achieving(P_(loss,min))at the lowest level compared to all other tested algorithms which leads to better system energy efficiency.The dynamic loading performance of SWEWOA leads to a 4.38%reduction in gross costs which proves its capability to handle different operating conditions.The algorithm achieves top performance in Friedman Rank Test(FRT)assessments through multiple performance metrics which verifies its consistent reliability and strong stability during changing power demands.The repeated simulations show that SWEWOA generates mean costs(C_(gen,min))and mean power loss values(P_(loss,min))with small deviations which indicate its capability to maintain cost-effective solutions in each simulation run.SWEWOA demonstrates great potential as an advanced optimization solution for power system operations through the results presented in this study.展开更多
Efficient resource management within Internet of Things(IoT)environments remains a pressing challenge due to the increasing number of devices and their diverse functionalities.This study introduces a neural network-ba...Efficient resource management within Internet of Things(IoT)environments remains a pressing challenge due to the increasing number of devices and their diverse functionalities.This study introduces a neural network-based model that uses Long-Short-Term Memory(LSTM)to optimize resource allocation under dynam-ically changing conditions.Designed to monitor the workload on individual IoT nodes,the model incorporates long-term data dependencies,enabling adaptive resource distribution in real time.The training process utilizes Min-Max normalization and grid search for hyperparameter tuning,ensuring high resource utilization and consistent performance.The simulation results demonstrate the effectiveness of the proposed method,outperforming the state-of-the-art approaches,including Dynamic and Efficient Enhanced Load-Balancing(DEELB),Optimized Scheduling and Collaborative Active Resource-management(OSCAR),Convolutional Neural Network with Monarch Butterfly Optimization(CNN-MBO),and Autonomic Workload Prediction and Resource Allocation for Fog(AWPR-FOG).For example,in scenarios with low system utilization,the model achieved a resource utilization efficiency of 95%while maintaining a latency of just 15 ms,significantly exceeding the performance of comparative methods.展开更多
We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of ...We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and,unlike the state of the art,requires neither weakcoupling Lamb-Dicke approximation nor perturbation treatment.With the application of gradient-based optimal control,it enables finding amplitude-and phase-modulated laser control protocols that work without the Lamb-Dicke approximation,promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies.Also,robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections.Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation,and thus can find applications in near-future experiments.展开更多
Finding an optimal isolator arrangement for asymmetric structures using traditional conceptual design methods that can significantly minimize torsional response while ensuring efficient horizontal seismic isolation is...Finding an optimal isolator arrangement for asymmetric structures using traditional conceptual design methods that can significantly minimize torsional response while ensuring efficient horizontal seismic isolation is cumbersome and inefficient.Thus,this work develops a multi-objective optimization method to enhance the torsional resistance of asymmetric base-isolated structures.The primary objective is to simultaneously minimize the interstory rotation of the superstructure,the rotation of the isolation layer,and the interstory displacement of the superstructure without exceeding the isolator displacement limits.A fast non-dominated sorting genetic algorithm(NSGA-Ⅱ)is employed to satisfy this optimization objective.Subsequently,the isolator arrangement,encompassing both positions and categories,is optimized according to this multi-objective optimization method.Additionally,an optimization design platform is developed to streamline the design operation.This platform integrates the input of optimization parameters,the output of optimization results,the finite element analysis,and the multi-objective optimization method proposed herein.Finally,the application of this multi-objective optimization method and its associated platform are demonstrated on two asymmetric base-isolated structures of varying heights and plan configurations.The results indicate that the optimal isolator arrangement derived from the optimization method can further improve the control over the lateral and torsional responses of asymmetric base-isolated structures compared to conventional conceptual design methods.Notably,the interstory rotation of the optimal base-isolated structure is significantly reduced,constituting only approximately 33.7%of that observed in the original base-isolated structure.The proposed platform facilitates the automatic generation of the optimal design scheme for the isolators of asymmetric base-isolated structures,offering valuable insights and guidance for the burgeoning field of intelligent civil engineering design.展开更多
This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-d...This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-diffusion epidemic model with two strains.Furthermore,applying vaccines as a control strategy in the model,an optimal control problem is proposed to increase the number of healthy individuals while reducing control costs.By applying the truncation function technique and the operator semigroup methods,we prove the existence and uniqueness of a globally positive strong solution for the control model.The existence of the optimal control strategy is proven by using functional analysis theory and minimum sequence methods.The first-order necessary condition satisfied by the optimal control is established by employing the dual techniques.Finally,a specific example and its algorithm are provided.展开更多
Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this wor...Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations.展开更多
This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the ty...This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.展开更多
We have investigated the gauge dependence of physical observables in a quantum Rabi model under different potential fields arising from the Hilbert space truncation of the atomic degrees of freedom.In both the square-...We have investigated the gauge dependence of physical observables in a quantum Rabi model under different potential fields arising from the Hilbert space truncation of the atomic degrees of freedom.In both the square-well and harmonic potentials,the optimal gauge for the ground-state energy depends on the cavity frequency,which is optimal in the low-frequency limit,whereas the Coulomb gauge is optimal in the high-frequency limit.For a dynamic quantity,such as an out-of-time-order correlator,we have demonstrated the necessity of introducing an optimal dynamic gauge.This study provides deeper insight into the intricate relationship between gauge choice and the dynamics of quantum electrodynamics systems,resulting in more accurate theoretical frameworks.展开更多
Energy storage power plants are critical in balancing power supply and demand.However,the scheduling of these plants faces significant challenges,including high network transmission costs and inefficient inter-device ...Energy storage power plants are critical in balancing power supply and demand.However,the scheduling of these plants faces significant challenges,including high network transmission costs and inefficient inter-device energy utilization.To tackle these challenges,this study proposes an optimal scheduling model for energy storage power plants based on edge computing and the improved whale optimization algorithm(IWOA).The proposed model designs an edge computing framework,transferring a large share of data processing and storage tasks to the network edge.This architecture effectively reduces transmission costs by minimizing data travel time.In addition,the model considers demand response strategies and builds an objective function based on the minimization of the sum of electricity purchase cost and operation cost.The IWOA enhances the optimization process by utilizing adaptive weight adjustments and an optimal neighborhood perturbation strategy,preventing the algorithm from converging to suboptimal solutions.Experimental results demonstrate that the proposed scheduling model maximizes the flexibility of the energy storage plant,facilitating efficient charging and discharging.It successfully achieves peak shaving and valley filling for both electrical and heat loads,promoting the effective utilization of renewable energy sources.The edge-computing framework significantly reduces transmission delays between energy devices.Furthermore,IWOA outperforms traditional algorithms in optimizing the objective function.展开更多
This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optim...This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.展开更多
文摘In radiology,magnetic resonance imaging(MRI)is an essential diagnostic tool that provides detailed images of a patient’s anatomical and physiological structures.MRI is particularly effective for detecting soft tissue anomalies.Traditionally,radiologists manually interpret these images,which can be labor-intensive and time-consuming due to the vast amount of data.To address this challenge,machine learning,and deep learning approaches can be utilized to improve the accuracy and efficiency of anomaly detection in MRI scans.This manuscript presents the use of the Deep AlexNet50 model for MRI classification with discriminative learning methods.There are three stages for learning;in the first stage,the whole dataset is used to learn the features.In the second stage,some layers of AlexNet50 are frozen with an augmented dataset,and in the third stage,AlexNet50 with an augmented dataset with the augmented dataset.This method used three publicly available MRI classification datasets:Harvard whole brain atlas(HWBA-dataset),the School of Biomedical Engineering of Southern Medical University(SMU-dataset),and The National Institute of Neuroscience and Hospitals brain MRI dataset(NINS-dataset)for analysis.Various hyperparameter optimizers like Adam,stochastic gradient descent(SGD),Root mean square propagation(RMS prop),Adamax,and AdamW have been used to compare the performance of the learning process.HWBA-dataset registers maximum classification performance.We evaluated the performance of the proposed classification model using several quantitative metrics,achieving an average accuracy of 98%.
基金sponsored by R&D Program of Beijing Municipal Education Commission(KM202410009013).
文摘In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.
基金supported by the National Natural Science Foundation of China(Nos.42005086,91844301,and 41805100)the National Key Research and Development Programof China(No.2022YFC3703500)+2 种基金China Postdoctoral Science Foundation(No.2023M733028)the Key Research and Development Program of Zhejiang Province(Nos.2021C03165 and 2022C03084)the Ecological and Environmental Scientific Research and Achievement Promotion Project of Zhejiang Province(No.2020HT0048).
文摘Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precursorswas conducted in a typical light industrial city in the YRD region from 1 May to 25 July in 2021.Alkanes were the most abundant VOC group,contributing to 55.0%of TVOCs concentration(56.43±21.10 ppb).OVOCs,aromatics,halides,alkenes,and alkynes contributed 18.7%,9.6%,9.3%,5.2%and 1.9%,respectively.The observational site shifted from a typical VOC control regime to a mixed regime from May to July,which can be explained by the significant increase of RO_(x)production,resulting in the transition of environment from NOx saturation to radical saturation with respect to O_(3)production.The optimal O_(3)control strategy should be dynamically changed depending on the transition of control regime.Under NOx saturation condition,minimizing the proportion of NOx in reduction could lead to better achievement of O_(3)alleviation.Under mixed control regime,the cut percentage gets the top priority for the effectiveness of O_(3)control.Five VOCs sources were identified:temperature dependent source(28.1%),vehicular exhausts(19.9%),petrochemical industries(7.2%),solvent&gasoline usage(32.3%)and manufacturing industries(12.6%).The increase of temperature and radiation would enhance the evaporation related VOC emissions,resulting in the increase of VOC concentration and the change of RO_(x)circulation.Our results highlight determination of the optimal control strategies for O_(3)pollution in a typical YRD industrial city.
基金supported by the Education and Teaching Research Project of Universities in Fujian Province(FBJY20230167).
文摘The work takes a new liquid-cooling plate in a power battery with pin fins inside the channel as the object.A mathematical model is established via the central composite design of the response surface to study the relationships among the length,width,height,and spacing of pin fins;the maximum temperature and temperature difference of the battery module;and the pressure drop of the liquid-cooling plate.Model accuracy is verified via variance analysis.The new liquid-cooling plate enables the power battery to work within an optimal temperature range.Appropriately increasing the length,width,and height and reducing the spacing of pin fins could reduce the temperature of the power battery module and improve the temperature uniformity.However,the pressure drop of the liquid-cooling plate increases.The structural parameters of the pin fins are optimized to minimize the maximum temperature and the temperature difference of the battery module as well as the pressure drop of the liquid-cooling plate.The errors between the values predicted and actual by the simulation test are 0.58%,4%,and 0.48%,respectively,which further verifies the model accuracy.The results reveal the influence of the structural parameters of the pin fins inside the liquid-cooling plate on its heat dissipation performance and pressure drop characteristics.A theoretical basis is provided for the design of liquid-cooling plates in power batteries and the optimization of structural parameters.
基金supported by the Central Government Guides Local Science and Technology Development Fund Project(2023ZY0020)Key R&D and Achievement Transformation Project in InnerMongolia Autonomous Region(2022YFHH0019)+3 种基金the Fundamental Research Funds for Inner Mongolia University of Science&Technology(2022053)Natural Science Foundation of Inner Mongolia(2022LHQN05002)National Natural Science Foundation of China(52067018)Metallurgical Engineering First-Class Discipline Construction Project in Inner Mongolia University of Science and Technology,Control Science and Engineering Quality Improvement and Cultivation Discipline Project in Inner Mongolia University of Science and Technology。
文摘In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12074213 and 11574108)the National Key R&D Program of China(Grant No.2022YFA1403103)+2 种基金the Major Basic Program of Natural Science Foundation of Shandong Province(Grant No.ZR2021ZD01)the Natural Science Foundation of Shandong Province(Grant No.ZR2023MA082)the Project of Introduction and Cultivation for Young Innovative Talents in Colleges and Universities of Shandong Province。
文摘Two-dimensional double-layer honeycomb(DLHC)materials are known for their diverse physical properties,but superconductivity has been a notably absent characteristic in this structure.We address this gap by investigating M_(2)N_(2)(M=Nb,Ta)with DLHC structure using first-principles calculations.Our results show that M_(2)N_(2)are stable and metallic,exhibiting superconducting behavior.Specifically,Nb_(2)N_(2)and Ta_(2)N_(2)display superconducting transition temperatures of 6.8 K and 8.8 K,respectively.Their electron-phonon coupling is predominantly driven by the coupling between metal d-orbitals and low-frequency metal-dominated vibration modes.Interestingly,two compounds also exhibit non-trivial band topology.Thus,M_(2)N_(2)are promising platforms for studying the interplay between topology and superconductivity and fill the gap in superconductivity research for DLHC materials.
基金supported by the National Natural Science Foundation of China(Grant No.12301603).
文摘In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.
基金funded by the Deanship of Research andGraduate Studies at King Khalid University through the Large Research Project under grant number RGP2/417/46.
文摘Metaheuristic optimization methods are iterative search processes that aim to efficiently solve complexoptimization problems. These basically find the solution space very efficiently, often without utilizing the gradientinformation, and are inspired by the bio-inspired and socially motivated heuristics. Metaheuristic optimizationalgorithms are increasingly applied to complex feature selection problems in high-dimensional medical datasets.Among these, Teaching-Learning-Based optimization (TLBO) has proven effective for continuous design tasks bybalancing exploration and exploitation phases. However, its binary version (BTLBO) suffers from limited exploitationability, often converging prematurely or getting trapped in local optima, particularly when applied to discrete featureselection tasks. Previous studies reported that BTLBO yields lower classification accuracy and higher feature subsetvariance compared to other hybrid methods in benchmark tests, motivating the development of hybrid approaches.This study proposes a novel hybrid algorithm, BTLBO-Cheetah Optimizer (BTLBO-CO), which integrates the globalexploration strength of BTLBO with the local exploitation efficiency of the Cheetah Optimization (CO) algorithm. Theobjective is to enhance the feature selection process for cancer classification tasks involving high-dimensional data. Theproposed BTLBO-CO algorithm was evaluated on six benchmark cancer datasets: 11 tumors (T), Lung Cancer (LUC),Leukemia (LEU), Small Round Blue Cell Tumor or SRBCT (SR), Diffuse Large B-cell Lymphoma or DLBCL (DL), andProstate Tumor (PT).The results demonstrate superior classification accuracy across all six datasets, achieving 93.71%,96.12%, 98.13%, 97.11%, 98.44%, and 98.84%, respectively.These results validate the effectiveness of the hybrid approachin addressing diverse feature selection challenges using a Support Vector Machine (SVM) classifier.
文摘Restructuring of power market not only introduces competition but also brings complexity which increases overloading of Transmission Lines(TL).To obviate this complexity,this paper aims to mitigate the overloading and estimate the optimal location of Static Synchronous Compensator(STATCOM) by reducing congestion for a deregulated power system.The proposed method is based on the use of Locational Marginal Price(LMP) difference technique and congestion cost.LMPs are obtained as a by-product of Optimal Power Flow(OPF),whereas Congestion Cost(CC) is a function of difference in LMP and power flows.The effiectiveness of this approach is demonstrated by reducing the CC and solution space which can identify the TLs more suitable for placement of STATCOM.Importantly,total real power loss,reactive power loss and total CC are the three main objective functions in this optimization process.The process is implemented by developing an IEEE-69 bus test system which verifies and validates the effectiveness of proposed optimization technique.Additionally,a comparative analysis is enumerated by implementing two optimization techniques:Flower Pollination Algorithm(FPA) and Particle Swarm Optimization(PSO).The comparative analysis is sufficient to demonstrate the superiority of FPA technique over PSO technique in estimating an optimal placement of a STATCOM.The results from the load-flow analysis illustrate the reduction in CC,total real and reactive power loss using FPA technique compared to PSO technique.Overall,satisfactory results are obtained without using complex calculations which verify the effectiveness of optimization techniques.
基金sponsored by the National Natural Science Foundation of China(Grant Nos.41930971,42330111,and 42405061)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(Earth Lab).
文摘Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly efficient calculations for O-CNOPs are still challenging in the field of ensemble forecasting.In this study,we combine a gradient-based iterative idea with the Gram‒Schmidt orthogonalization,and propose an iterative optimization method to compute O-CNOPs.This method is different from the original sequential optimization method,and allows parallel computations of O-CNOPs,thus saving a large amount of computational time.We evaluate this method by using the Lorenz-96 model on the basis of the ensemble forecasting ability achieved and on the time consumed for computing O-CNOPs.The results demonstrate that the parallel iterative method causes O-CNOPs to yield reliable ensemble members and to achieve ensemble forecasting skills similar to or even slightly higher than those produced by the sequential method.Moreover,the parallel method significantly reduces the computational time for O-CNOPs.Therefore,the parallel iterative method provides a highly effective and efficient approach for calculating O-CNOPs for ensemble forecasts.Expectedly,it can play an important role in the application of the O-CNOPs to realistic ensemble forecasts for high-impact weather and climate events.
文摘The Sine and Wormhole Energy Whale Optimization Algorithm(SWEWOA)represents an advanced solution method for resolving Optimal Power Flow(OPF)problems in power systems equipped with Flexible AC Transmission System(FACTS)devices which include Thyristor-Controlled Series Compensator(TCSC),Thyristor-Controlled Phase Shifter(TCPS),and Static Var Compensator(SVC).SWEWOA expands Whale Optimization Algorithm(WOA)through the integration of sine and wormhole energy features thus improving exploration and exploitation capabilities for efficient convergence in complex non-linear OPF problems.A performance evaluation of SWEWOA takes place on the IEEE-30 bus test system through static and dynamic loading scenarios where it demonstrates better results than five contemporary algorithms:Adaptive Chaotic WOA(ACWOA),WOA,Chaotic WOA(CWOA),Sine Cosine Algorithm Differential Evolution(SCADE),and Hybrid Grey Wolf Optimization(HGWO).The research shows that SWEWOA delivers superior generation cost reduction than other algorithms by reaching a minimum of 0.9%better performance.SWEWOA demonstrates superior power loss performance by achieving(P_(loss,min))at the lowest level compared to all other tested algorithms which leads to better system energy efficiency.The dynamic loading performance of SWEWOA leads to a 4.38%reduction in gross costs which proves its capability to handle different operating conditions.The algorithm achieves top performance in Friedman Rank Test(FRT)assessments through multiple performance metrics which verifies its consistent reliability and strong stability during changing power demands.The repeated simulations show that SWEWOA generates mean costs(C_(gen,min))and mean power loss values(P_(loss,min))with small deviations which indicate its capability to maintain cost-effective solutions in each simulation run.SWEWOA demonstrates great potential as an advanced optimization solution for power system operations through the results presented in this study.
基金funding of the Deanship of Graduate Studies and Scientific Research,Jazan University,Saudi Arabia,through Project Number:ISP-2024.
文摘Efficient resource management within Internet of Things(IoT)environments remains a pressing challenge due to the increasing number of devices and their diverse functionalities.This study introduces a neural network-based model that uses Long-Short-Term Memory(LSTM)to optimize resource allocation under dynam-ically changing conditions.Designed to monitor the workload on individual IoT nodes,the model incorporates long-term data dependencies,enabling adaptive resource distribution in real time.The training process utilizes Min-Max normalization and grid search for hyperparameter tuning,ensuring high resource utilization and consistent performance.The simulation results demonstrate the effectiveness of the proposed method,outperforming the state-of-the-art approaches,including Dynamic and Efficient Enhanced Load-Balancing(DEELB),Optimized Scheduling and Collaborative Active Resource-management(OSCAR),Convolutional Neural Network with Monarch Butterfly Optimization(CNN-MBO),and Autonomic Workload Prediction and Resource Allocation for Fog(AWPR-FOG).For example,in scenarios with low system utilization,the model achieved a resource utilization efficiency of 95%while maintaining a latency of just 15 ms,significantly exceeding the performance of comparative methods.
基金supported by the National Natural Science Foundation of China(Grant Nos.12441502,12122506,12204230,and 12404554)the National Science and Technology Major Project of the Ministry of Science and Technology of China(2024ZD0300404)+6 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2021B1515020070)Shenzhen Science and Technology Program(Grant No.RCYX20200714114522109)China Postdoctoral Science Foundation(CPSF)(2024M762114)Postdoctoral Fellowship Program of CPSF(GZC20231727)supported by the National Natural Science Foundation of China(Grant Nos.92165206 and 11974330)Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301603)the Fundamental Research Funds for the Central Universities。
文摘We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and,unlike the state of the art,requires neither weakcoupling Lamb-Dicke approximation nor perturbation treatment.With the application of gradient-based optimal control,it enables finding amplitude-and phase-modulated laser control protocols that work without the Lamb-Dicke approximation,promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies.Also,robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections.Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation,and thus can find applications in near-future experiments.
基金National Natural Science Foundation of China under Grant No.52278490。
文摘Finding an optimal isolator arrangement for asymmetric structures using traditional conceptual design methods that can significantly minimize torsional response while ensuring efficient horizontal seismic isolation is cumbersome and inefficient.Thus,this work develops a multi-objective optimization method to enhance the torsional resistance of asymmetric base-isolated structures.The primary objective is to simultaneously minimize the interstory rotation of the superstructure,the rotation of the isolation layer,and the interstory displacement of the superstructure without exceeding the isolator displacement limits.A fast non-dominated sorting genetic algorithm(NSGA-Ⅱ)is employed to satisfy this optimization objective.Subsequently,the isolator arrangement,encompassing both positions and categories,is optimized according to this multi-objective optimization method.Additionally,an optimization design platform is developed to streamline the design operation.This platform integrates the input of optimization parameters,the output of optimization results,the finite element analysis,and the multi-objective optimization method proposed herein.Finally,the application of this multi-objective optimization method and its associated platform are demonstrated on two asymmetric base-isolated structures of varying heights and plan configurations.The results indicate that the optimal isolator arrangement derived from the optimization method can further improve the control over the lateral and torsional responses of asymmetric base-isolated structures compared to conventional conceptual design methods.Notably,the interstory rotation of the optimal base-isolated structure is significantly reduced,constituting only approximately 33.7%of that observed in the original base-isolated structure.The proposed platform facilitates the automatic generation of the optimal design scheme for the isolators of asymmetric base-isolated structures,offering valuable insights and guidance for the burgeoning field of intelligent civil engineering design.
基金Supported by the National Natural Science Foundation of China(Grant Nos.125610811246108612271147)。
文摘This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-diffusion epidemic model with two strains.Furthermore,applying vaccines as a control strategy in the model,an optimal control problem is proposed to increase the number of healthy individuals while reducing control costs.By applying the truncation function technique and the operator semigroup methods,we prove the existence and uniqueness of a globally positive strong solution for the control model.The existence of the optimal control strategy is proven by using functional analysis theory and minimum sequence methods.The first-order necessary condition satisfied by the optimal control is established by employing the dual techniques.Finally,a specific example and its algorithm are provided.
基金supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302100)the National Natural Science Foundation of China(Grant Nos.12361131576,92265205,and 92476205).
文摘Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations.
基金co-supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF21-BJ-J-1180)。
文摘This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.
基金supported by the National Natural Science Foundation of China(Grant Nos.12174194 and 12475033)the Fundamental Research Funds for the Central Universities。
文摘We have investigated the gauge dependence of physical observables in a quantum Rabi model under different potential fields arising from the Hilbert space truncation of the atomic degrees of freedom.In both the square-well and harmonic potentials,the optimal gauge for the ground-state energy depends on the cavity frequency,which is optimal in the low-frequency limit,whereas the Coulomb gauge is optimal in the high-frequency limit.For a dynamic quantity,such as an out-of-time-order correlator,we have demonstrated the necessity of introducing an optimal dynamic gauge.This study provides deeper insight into the intricate relationship between gauge choice and the dynamics of quantum electrodynamics systems,resulting in more accurate theoretical frameworks.
基金supported by the Changzhou Science and Technology Support Project(CE20235045)Open Subject of Jiangsu Province Key Laboratory of Power Transmission and Distribution(2021JSSPD12)+1 种基金Talent Projects of Jiangsu University of Technology(KYY20018)Postgraduate Research&Practice Innovation Program of Jiangsu Province(SJCX23_1633).
文摘Energy storage power plants are critical in balancing power supply and demand.However,the scheduling of these plants faces significant challenges,including high network transmission costs and inefficient inter-device energy utilization.To tackle these challenges,this study proposes an optimal scheduling model for energy storage power plants based on edge computing and the improved whale optimization algorithm(IWOA).The proposed model designs an edge computing framework,transferring a large share of data processing and storage tasks to the network edge.This architecture effectively reduces transmission costs by minimizing data travel time.In addition,the model considers demand response strategies and builds an objective function based on the minimization of the sum of electricity purchase cost and operation cost.The IWOA enhances the optimization process by utilizing adaptive weight adjustments and an optimal neighborhood perturbation strategy,preventing the algorithm from converging to suboptimal solutions.Experimental results demonstrate that the proposed scheduling model maximizes the flexibility of the energy storage plant,facilitating efficient charging and discharging.It successfully achieves peak shaving and valley filling for both electrical and heat loads,promoting the effective utilization of renewable energy sources.The edge-computing framework significantly reduces transmission delays between energy devices.Furthermore,IWOA outperforms traditional algorithms in optimizing the objective function.
基金supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF-21-BJ-J-1180).
文摘This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.
