In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the clas...In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers’ equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers’ equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers’ equations.展开更多
The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent...The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.展开更多
To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformati...To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each classification.Besides,a new conception called invariance set is raised.Moreover,this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.展开更多
We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core...We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.展开更多
For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, the infinite dimensional Lie algebra of the classical symmetry group is found and the one-dimensional optimal system of an 8-dimensional subalgebra o...For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, the infinite dimensional Lie algebra of the classical symmetry group is found and the one-dimensional optimal system of an 8-dimensional subalgebra of the infinite Lie algebra is constructed. The reduced equations of the equations with respect to the optimal system are derived. Furthermore, the one-dimensional optimal systems of the Lie algebra admitted by the reduced equations are also constructed. Consequently, the classification of the twice optimal symmetry reductions of the equations with respect to the optimal systems is presented. The reductions show that the (1 + 2)-dimensional nonlinear Schrodinger equations can be reduced to a group of ordinary differential equations which is useful for solving the related problems of the equations.展开更多
A symmetrical one-dimensional(1D)photonic crystal structure with a Dirac-emimetal-defected layer is proposed.The material properties of the Dirac semimetal are governed by three key parameters:Fermi level,Fermi veloci...A symmetrical one-dimensional(1D)photonic crystal structure with a Dirac-emimetal-defected layer is proposed.The material properties of the Dirac semimetal are governed by three key parameters:Fermi level,Fermi velocity,and degeneracy factor.Simulation results demonstrate that the proposed structure generates multiple photonic bandgaps within the THz frequency range.In the low-THz region,pronounced resonant transmission peaks emerge,enabling near-perfect filtering performance.The positions of these defect modes can be dynamically tuned by adjusting the Fermi level and degeneracy factor.In mid-and high-THz frequency bands,the Dirac semimetal begins to exhibit metallic behavior,leading to attenuation of the transmission peaks and the appearance of absorption.The elevation of the Fermi level delays the critical threshold for the transition from the dielectric state to the metallic state,while an increase in Fermi velocity suppresses metallic behavior.Therefore,enhancing both the Fermi level and Fermi velocity contributes to strengthening the defect peak intensity.Conversely,increasing the degeneracy factor strengthens the metallic characteristics,thereby disrupting the high-frequency photonic bandgap.Notably,the defect layer thickness and incident angle exert significant influence on the transmission behavior:a larger incident angle causes the defect peak to shift toward higher frequencies and reduces its intensity,whereas a thicker defect layer shifts the defect peak toward lower frequencies.The modulation effects of both parameters become more pronounced as frequency increases.Compared with conventional photonic crystals,our work can provide a tunable structure over transmission properties,offering novel strategies for designing tunable filters and optical sensors.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
In recent years,three-dimensional reconstruction technologies that employ multiple cameras have continued to evolve significantly,enabling remote collaboration among users in extended Reality(XR)environments.In additi...In recent years,three-dimensional reconstruction technologies that employ multiple cameras have continued to evolve significantly,enabling remote collaboration among users in extended Reality(XR)environments.In addition,methods for deploying multiple cameras for motion capture of users(e.g.,performers)are widely used in computer graphics.As the need to minimize and optimize the number of cameras grows to reduce costs,various technologies and research approaches focused on Optimal Camera Placement(OCP)are continually being proposed.However,as most existing studies assume homogeneous camera setups,there is a growing demand for studies on heterogeneous camera setups.For instance,technical demands keep emerging in scenarios with minimal camera configurations,especially regarding cost factors,the physical placement of cameras given the spatial structure,and image capture strategies for heterogeneous cameras,such as high-resolution RGB cameras and depth cameras.In this study,we propose a pre-visualization and simulation method for the optimal placement of heterogeneous cameras in XR environments,accounting for both the specifications of heterogeneous cameras(e.g.,field of view)and the physical configuration(e.g.,wall configuration)in real-world spaces.The proposed method performs a visibility analysis of cameras by considering each camera’s field-of-view volume,resolution,and unique characteristics,along with physicalspace constraints.This approach enables the optimal position and rotation of each camera to be recommended,along with the minimum number of cameras required.In the results of our study conducted in heterogeneous camera combinations,the proposed method achieved 81.7%~82.7%coverage of the target visual information using only 2~3 cameras.In contrast,single(or homogeneous)-typed cameras were required to use 11 cameras for 81.6%coverage.Accordingly,we found that camera deployment resources can be reduced with the proposed approaches.展开更多
In this paper,an analysis-definition-processing(ADP)framework is proposed to search positive-incentive noise in continuous action iterated dilemma(CAID).We analyze the influence of communication noise on the cooperati...In this paper,an analysis-definition-processing(ADP)framework is proposed to search positive-incentive noise in continuous action iterated dilemma(CAID).We analyze the influence of communication noise on the cooperative behavior of players in the system and introduce the concept of positive-incentive noise in CAID.We design a global cost function to ensure convergence of the system can be achieved and strive to improve the final level of cooperation.An optimal CAID control method is proposed to derive the deterministic optimal learning rate in analytical form,avoiding the variability and uncertainty brought about by neural network fitting or parameter adjustment.On this basis,the convergence of the dynamic model is further analyzed by using the Lyapunov function instead of the Jacobian matrix.Additionally,an adaptive filtering mechanism is designed to dynamically ensure that only positive-incentive noise affects the system,effectively reducing the impact of negative noise and enhancing system stability.The framework is validated through simulations involving triple classical game models,including the hawk-dove game,the stag hunt game,the chicken game on networks,and a straightforward illustrative example.展开更多
The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical pe...The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.展开更多
Virtual power plant(VPP)integrates a variety of distributed renewable energy and energy storage to participate in electricity market transactions,promote the consumption of renewable energy,and improve economic effici...Virtual power plant(VPP)integrates a variety of distributed renewable energy and energy storage to participate in electricity market transactions,promote the consumption of renewable energy,and improve economic efficiency.In this paper,aiming at the uncertainty of distributed wind power and photovoltaic output,considering the coupling relationship between power,carbon trading,and green cardmarket,the optimal operationmodel and bidding scheme of VPP in spot market,carbon trading market,and green card market are established.On this basis,through the Shapley value and independent risk contribution theory in cooperative game theory,the quantitative analysis of the total income and risk contribution of various distributed resources in the virtual power plant is realized.Moreover,the scheduling strategies of virtual power plants under different risk preferences are systematically compared,and the feasibility and accuracy of the combination of Shapley value and independent risk contribution theory in ensuring fair income distribution and reasonable risk assessment are emphasized.A comprehensive solution for virtual power plants in the multi-market environment is constructed,which integrates operation strategy,income distribution mechanism,and risk control system into a unified analysis framework.Through the simulation of multi-scenario examples,the CPLEXsolver inMATLAB software is used to optimize themodel.The proposed joint optimization scheme can increase the profit of VPP participating in carbon trading and green certificate market by 29%.The total revenue of distributed resources managed by VPP is 9%higher than that of individual participation.展开更多
Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are o...Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are often effective for stabilization but may not directly optimize long-term performance.To address this limitation,this study develops an integrated framework that combines optimal control principles with reinforcement learning for a single-link robotic manipulator.The proposed scheme adopts an actor–critic structure,where the critic network approximates the value function associated with the Hamilton–Jacobi–Bellman equation,and the actor network generates near-optimal control signals in real time.This dual adaptation enables the controller to refine its policy online without explicit system knowledge.Stability of the closed-loop system is analyzed through Lyapunov theory,ensuring boundedness of the tracking error.Numerical simulations on the single-link manipulator demonstrate that themethod achieves accurate trajectory followingwhile maintaining lowcontrol effort.The results further showthat the actor–critic learning mechanism accelerates convergence of the control policy compared with conventional optimization-based strategies.This work highlights the potential of reinforcement learning integrated with optimal control for robotic manipulators and provides a foundation for future extensions to more complex multi-degree-of-freedom systems.The proposed controller is further validated in a physics-based virtual Gazebo environment,demonstrating stable adaptation and real-time feasibility.展开更多
Realizing optimal control performance for continuum robots(CRs) poses huge challenges on traditional modelbased optimal control approaches due to their high degrees of freedom,complex nonlinear dynamics and soft conti...Realizing optimal control performance for continuum robots(CRs) poses huge challenges on traditional modelbased optimal control approaches due to their high degrees of freedom,complex nonlinear dynamics and soft continuum morphologies which are difficult to explicitly model.This paper proposes a model-free adaptive optimal control algorithm(ADAPT)for CRs.In our strategy,we consider CRs as a class of nonlinear continuous-time dynamical systems in the state space,wherein the position of the end-effector is considered as the state and the input torque is mapped as the control input.Then,the optimized Hamilton-Jacobi-Bellman(HJB) equation is derived by optimal control principles,and subsequently solved by the proposed ADAPT algorithm without requiring knowledge of the original system dynamics.Under some mild assumptions,the global stability and convergence of the closed-loop control approach are guaranteed.Several simulation experiments are conducted on a magnetic CR(MCR) to demonstrate the practicality and effectiveness of the ADAPT algorithm.展开更多
In the wireless energy transmission service composition optimization problem,a key challenge is accurately capturing users’preferences for service criteria under complex influencing factors,and optimally selecting a ...In the wireless energy transmission service composition optimization problem,a key challenge is accurately capturing users’preferences for service criteria under complex influencing factors,and optimally selecting a composition solution under their budget constraints.Existing studies typically evaluate satisfaction solely based on energy transmission capacity,while overlooking critical factors such as price and trustworthiness of the provider,leading to a mismatch between optimization outcomes and user needs.To address this gap,we construct a user satisfaction evaluation model for multi-user and multi-provider scenarios,systematically incorporating service price,transmission capacity,and trustworthiness into the satisfaction assessment framework.Furthermore,we propose a Budget-Aware Preference Adjustment Model that predicts users’baseline preference weights from historical data and dynamically adjusts them according to budget levels,thereby reflecting user preferences more realistically under varying budget constraints.In addition,to tackle the composition optimization problem,we develop a ReflectiveEvolutionary Large Language Model—Guided Ant Colony Optimization algorithm,which leverages the reflective evolution capability of large language models to iteratively generate and refine heuristic information that guides the search process.Experimental results demonstrate that the proposed framework effectively integrates personalized preferences with budget sensitivity,accurately predicts users’preferences,and significantly enhances their satisfaction under complex constraints.展开更多
In real industrial microgrids(MGs),the length of the primary delivery feeder to the connection point of the main substation is sometimes long.This reduces the power factor and increases reactive power absorption along...In real industrial microgrids(MGs),the length of the primary delivery feeder to the connection point of the main substation is sometimes long.This reduces the power factor and increases reactive power absorption along the primary delivery feeder from the external network.Besides,the giant induction electro-motors as the working horse of industries requires remarkable amounts of reactive power for electro-mechanical energy conversions.To reduce power losses and operating costs of the MG as well as to improve the voltage quality,this study aims at providing an insightful model for optimal placement and sizing of reactive power compensation capacitors in an industrial MG.In the presented model,the objective function considers voltage profile and network power factor improvement at the MG connection point.Also,it realizes power flow equations within which all operational security constraints are considered.Various reactive power compensation strategies including distributed group compensation,centralized compensation at the main substation,and distributed compensation along the primary delivery feeder are scrutinized.A real industrial MG,say as Urmia Petrochemical plant,is considered in numerical validations.The obtained results in each scenario are discussed in depth.As seen,the best performance is obtained when the optimal location and sizing of capacitors are simultaneously determined at the main buses of the industrial plants,at the main substation of the MG,and alongside the primary delivery feeder.In this way,74.81%improvement in power losses reduction,1.3%lower active power import from the main grid,23.5%improvement in power factor,and 37.5%improvement in network voltage deviation summation are seen in this case compared to the base case.展开更多
Thermal storage electric heating(TSEH),as a prevalent variable load resource,offers significant potential for enhancing system flexibility when aggregated into a cluster.To address the uncertainties of renewable energ...Thermal storage electric heating(TSEH),as a prevalent variable load resource,offers significant potential for enhancing system flexibility when aggregated into a cluster.To address the uncertainties of renewable energy and load forecasting in active distribution networks(ADN),this paper proposes a multi-timescale coordinated optimal dispatch strategy that incorporates TSEH clusters.It utilizes the thermal storage characteristics and short-term regulation capabilities of TSEH,along with the rapid and gradual response characteristics of resources in active distribution grids,to develop a coordinated optimization dispatch mechanism for day-ahead,intraday,and real-time stages.It provides a coordinated optimized dispatch technique across several timescales for active distribution grids,taking into account the integration of TSEH clusters.The proposed method is validated on a modified IEEE 33-node system.Simulation results demonstrate that the participation of TSEH in collaborative optimization significantly reduces the total system operating cost by 8.71%compared to the scenario without TSEH.This cost reduction is attributed to a 10.84%decrease in interaction costs with the main grid and a 47.41%reduction in network loss costs,validating effective peak shaving and valley filling.The multi-timescale framework further enhances economic efficiency,with overall operating costs progressively decreasing by 3.91%(intraday)and 4.59%(real-time),and interaction costs further reduced by 5.34%and 9.25%,respectively.Moreover,the approach enhances system stability by effectively suppressing node voltage fluctuations and ensuring all voltages remain within safe operating limits during real-time operation.Therefore,the proposed approach achieves rational coordination of diverse resources,significantly improving the economic efficiency and stability of ADNs.展开更多
Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the...Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the coordination with virtual power plants(VPPs).The proposed strategy improves systemflexibility and responsiveness by optimizing the power adjustment of flexible resources.In the proposed strategy,theGaussian Process Regression(GPR)is firstly employed to determine the adjustable range of aggregated power within the VPP,facilitating an assessment of its potential contribution to power supply support.Then,an optimal dispatch model based on a leader-follower game is developed to maximize the benefits of the VPP and flexible resources while guaranteeing the power balance at the same time.To solve the proposed optimal dispatch model efficiently,the constraints of the problem are reformulated and resolved using the Karush-Kuhn-Tucker(KKT)optimality conditions and linear programming duality theorem.The effectiveness of the strategy is illustrated through a detailed case study.展开更多
Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in a...Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in an algebra,then the solution(and also the control gain in many cases)is also in the same algebra.The main result is verified by a numerical simulation.展开更多
The Brief Interactive Optimism Scale (BIOS-G), recently published, was developed to measure optimism based on the interactive personality styles theory in the general population of Mexican adults. It has been validate...The Brief Interactive Optimism Scale (BIOS-G), recently published, was developed to measure optimism based on the interactive personality styles theory in the general population of Mexican adults. It has been validated in both the general population in Mexico and other Latin American countries. This study aims to further consolidate the validity of the BIOS-G in a specific population. The objectives are to assess the psychometric properties of its items, validate its unidimensional structure, describe its distribution, verify its internal consistency, and examine its direct relationship with affective balance and positive affect, as well as its inverse relationship with emotional exhaustion and negative affect among Mexican university teachers. The BIOS-G, the CESQT emotional exhaustion subscale, and Scale of Positive and Negative Experience (SPANE) were administered to a non-probability sample of 213 Mexican university teachers. All items demonstrated discriminative power and internal consistency. The scale showed internal consistency (Green-Yang ordinal ω = 0.74 and McDonald ordinal ω = 0.88). The one-factor model presented good to acceptable fit to the data, with an average variance extracted of 0.65. Its distribution was negatively skewed and mesokurtic. The BIOS-G correlated directly with SPANE’s affective balance and positive emotional experiences and inversely with negative emotional experiences and emotional exhaustion, with moderate strengths of association. Its mean score was higher in men than in women and correlated positively with age. It is concluded that the BIOS-G demonstrates internal consistency and validity evidence among Mexican university teachers, and its use in this specific population is recommended.展开更多
In-situ heating conversion is the most practical recovery method for lacustrine low-to-medium maturity shale oil.However,the energy output-input ratio must exceed the economic threshold to achieve commercial developme...In-situ heating conversion is the most practical recovery method for lacustrine low-to-medium maturity shale oil.However,the energy output-input ratio must exceed the economic threshold to achieve commercial development.This paper systematically investigates the mechanism of super-rich accumulation of organic matter in continental shale,sweet spot evaluation,optimal heating windows,and appropriate well types and patterns from the perspectives of enhancing energy output and reducing energy input.(1)The super-rich accumulation of organic matter in lacustrine shale is primarily controlled by the intensity,frequency,and preservation of external material inputs,and is related to moderate volcanic and hydrothermal activities,marine transgressions,with total organic carbon content greater than or equal to 6%.(2)The quality of organic-rich intervals is related to the type of source material and hydrocarbon generation potential.The in-situ conversion-derived hydrocarbon quality index(HQI)is established,and the zones exhibiting HQI>450 are defined as sweet spots.(3)Considering the characteristics of the organic matter conversion material field and seepage field,the temperature interval 300-370℃is recommended as the optimal heating window for the Chang 7_(3)sub-member of the Triassic Yanchang Formation in the Ordos Basin.Based on the advantages of thermal conductivity,permeability,and hydrocarbon expulsion efficiency along the bedding direction during in-situ heating,the“horizontal well heating+vertical well development”scheme is proposed,which has demonstrated significant enhancement in both recovery factor and energy output-input ratio,making it the optimal in-situ conversion process.The research findings provide a theoretical and technical foundation for the economical and efficient development of low-to-medium maturity shale oil.展开更多
文摘In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers’ equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers’ equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers’ equations.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of China under Grant Nos.11375090,11275072 and 11435005+3 种基金Research Fund for the Doctoral Program of Higher Education of China under Grant No.20120076110024the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No.61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY14A010005
文摘The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.
基金Supported by the Global Change Research Program of China under Grant No.2015CB95390National Natural Science Foundation of China under Grant Nos.11675054 and 11435005Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213
文摘To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each classification.Besides,a new conception called invariance set is raised.Moreover,this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,11275072,61021004National High Technology Research and Development Program under Grant No.2011AA010101+1 种基金Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213Talent Fund and K.C.Wong Magna Fund in Ningbo University
文摘We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.
基金supported by the Natural science foundation of China(NSF),under grand number 11071159.
文摘For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, the infinite dimensional Lie algebra of the classical symmetry group is found and the one-dimensional optimal system of an 8-dimensional subalgebra of the infinite Lie algebra is constructed. The reduced equations of the equations with respect to the optimal system are derived. Furthermore, the one-dimensional optimal systems of the Lie algebra admitted by the reduced equations are also constructed. Consequently, the classification of the twice optimal symmetry reductions of the equations with respect to the optimal systems is presented. The reductions show that the (1 + 2)-dimensional nonlinear Schrodinger equations can be reduced to a group of ordinary differential equations which is useful for solving the related problems of the equations.
文摘A symmetrical one-dimensional(1D)photonic crystal structure with a Dirac-emimetal-defected layer is proposed.The material properties of the Dirac semimetal are governed by three key parameters:Fermi level,Fermi velocity,and degeneracy factor.Simulation results demonstrate that the proposed structure generates multiple photonic bandgaps within the THz frequency range.In the low-THz region,pronounced resonant transmission peaks emerge,enabling near-perfect filtering performance.The positions of these defect modes can be dynamically tuned by adjusting the Fermi level and degeneracy factor.In mid-and high-THz frequency bands,the Dirac semimetal begins to exhibit metallic behavior,leading to attenuation of the transmission peaks and the appearance of absorption.The elevation of the Fermi level delays the critical threshold for the transition from the dielectric state to the metallic state,while an increase in Fermi velocity suppresses metallic behavior.Therefore,enhancing both the Fermi level and Fermi velocity contributes to strengthening the defect peak intensity.Conversely,increasing the degeneracy factor strengthens the metallic characteristics,thereby disrupting the high-frequency photonic bandgap.Notably,the defect layer thickness and incident angle exert significant influence on the transmission behavior:a larger incident angle causes the defect peak to shift toward higher frequencies and reduces its intensity,whereas a thicker defect layer shifts the defect peak toward lower frequencies.The modulation effects of both parameters become more pronounced as frequency increases.Compared with conventional photonic crystals,our work can provide a tunable structure over transmission properties,offering novel strategies for designing tunable filters and optical sensors.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金supported by the 2024 Research Fund of University of Ulsan.
文摘In recent years,three-dimensional reconstruction technologies that employ multiple cameras have continued to evolve significantly,enabling remote collaboration among users in extended Reality(XR)environments.In addition,methods for deploying multiple cameras for motion capture of users(e.g.,performers)are widely used in computer graphics.As the need to minimize and optimize the number of cameras grows to reduce costs,various technologies and research approaches focused on Optimal Camera Placement(OCP)are continually being proposed.However,as most existing studies assume homogeneous camera setups,there is a growing demand for studies on heterogeneous camera setups.For instance,technical demands keep emerging in scenarios with minimal camera configurations,especially regarding cost factors,the physical placement of cameras given the spatial structure,and image capture strategies for heterogeneous cameras,such as high-resolution RGB cameras and depth cameras.In this study,we propose a pre-visualization and simulation method for the optimal placement of heterogeneous cameras in XR environments,accounting for both the specifications of heterogeneous cameras(e.g.,field of view)and the physical configuration(e.g.,wall configuration)in real-world spaces.The proposed method performs a visibility analysis of cameras by considering each camera’s field-of-view volume,resolution,and unique characteristics,along with physicalspace constraints.This approach enables the optimal position and rotation of each camera to be recommended,along with the minimum number of cameras required.In the results of our study conducted in heterogeneous camera combinations,the proposed method achieved 81.7%~82.7%coverage of the target visual information using only 2~3 cameras.In contrast,single(or homogeneous)-typed cameras were required to use 11 cameras for 81.6%coverage.Accordingly,we found that camera deployment resources can be reduced with the proposed approaches.
基金supported by the National Science Fund for Distinguished Young Scholars(62025602)the National Natural Science Foundation of China(62373302,U22B2036)+2 种基金the National Key Research and Development Program of China(2024YFF0509600)the Fundamental Research Funds for the Central Universities(G2024WD0151,D5000240309)the Tencent Foundation and XPLORER PRIZE。
文摘In this paper,an analysis-definition-processing(ADP)framework is proposed to search positive-incentive noise in continuous action iterated dilemma(CAID).We analyze the influence of communication noise on the cooperative behavior of players in the system and introduce the concept of positive-incentive noise in CAID.We design a global cost function to ensure convergence of the system can be achieved and strive to improve the final level of cooperation.An optimal CAID control method is proposed to derive the deterministic optimal learning rate in analytical form,avoiding the variability and uncertainty brought about by neural network fitting or parameter adjustment.On this basis,the convergence of the dynamic model is further analyzed by using the Lyapunov function instead of the Jacobian matrix.Additionally,an adaptive filtering mechanism is designed to dynamically ensure that only positive-incentive noise affects the system,effectively reducing the impact of negative noise and enhancing system stability.The framework is validated through simulations involving triple classical game models,including the hawk-dove game,the stag hunt game,the chicken game on networks,and a straightforward illustrative example.
基金supported by the National Nature Science Foundation of China under Grant No.11902332。
文摘The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.
基金funded by the Department of Education of Liaoning Province and was supported by the Basic Scientific Research Project of the Department of Education of Liaoning Province(Grant No.LJ222411632051)and(Grant No.LJKQZ2021085)Natural Science Foundation Project of Liaoning Province(Grant No.2022-BS-222).
文摘Virtual power plant(VPP)integrates a variety of distributed renewable energy and energy storage to participate in electricity market transactions,promote the consumption of renewable energy,and improve economic efficiency.In this paper,aiming at the uncertainty of distributed wind power and photovoltaic output,considering the coupling relationship between power,carbon trading,and green cardmarket,the optimal operationmodel and bidding scheme of VPP in spot market,carbon trading market,and green card market are established.On this basis,through the Shapley value and independent risk contribution theory in cooperative game theory,the quantitative analysis of the total income and risk contribution of various distributed resources in the virtual power plant is realized.Moreover,the scheduling strategies of virtual power plants under different risk preferences are systematically compared,and the feasibility and accuracy of the combination of Shapley value and independent risk contribution theory in ensuring fair income distribution and reasonable risk assessment are emphasized.A comprehensive solution for virtual power plants in the multi-market environment is constructed,which integrates operation strategy,income distribution mechanism,and risk control system into a unified analysis framework.Through the simulation of multi-scenario examples,the CPLEXsolver inMATLAB software is used to optimize themodel.The proposed joint optimization scheme can increase the profit of VPP participating in carbon trading and green certificate market by 29%.The total revenue of distributed resources managed by VPP is 9%higher than that of individual participation.
基金supported in part by the National Science and Technology Council under Grant NSTC 114-2221-E-027-104.
文摘Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are often effective for stabilization but may not directly optimize long-term performance.To address this limitation,this study develops an integrated framework that combines optimal control principles with reinforcement learning for a single-link robotic manipulator.The proposed scheme adopts an actor–critic structure,where the critic network approximates the value function associated with the Hamilton–Jacobi–Bellman equation,and the actor network generates near-optimal control signals in real time.This dual adaptation enables the controller to refine its policy online without explicit system knowledge.Stability of the closed-loop system is analyzed through Lyapunov theory,ensuring boundedness of the tracking error.Numerical simulations on the single-link manipulator demonstrate that themethod achieves accurate trajectory followingwhile maintaining lowcontrol effort.The results further showthat the actor–critic learning mechanism accelerates convergence of the control policy compared with conventional optimization-based strategies.This work highlights the potential of reinforcement learning integrated with optimal control for robotic manipulators and provides a foundation for future extensions to more complex multi-degree-of-freedom systems.The proposed controller is further validated in a physics-based virtual Gazebo environment,demonstrating stable adaptation and real-time feasibility.
基金supported in part by the Innovation and Technology Commission of Hong Kong,China(ITS/136/20,ITS/234/21,MHP/096/22,ITS/235/22)Multi-Scale Medical Robotics Center,InnoHK,China(8312051)+1 种基金Research Grants Council(RGC) of Hong Kong,China(CUHK 14217822,CUHK14207823,AoE/E-407/24-N)The Chinese University of Hong Kong(CUHK) Direct Grant。
文摘Realizing optimal control performance for continuum robots(CRs) poses huge challenges on traditional modelbased optimal control approaches due to their high degrees of freedom,complex nonlinear dynamics and soft continuum morphologies which are difficult to explicitly model.This paper proposes a model-free adaptive optimal control algorithm(ADAPT)for CRs.In our strategy,we consider CRs as a class of nonlinear continuous-time dynamical systems in the state space,wherein the position of the end-effector is considered as the state and the input torque is mapped as the control input.Then,the optimized Hamilton-Jacobi-Bellman(HJB) equation is derived by optimal control principles,and subsequently solved by the proposed ADAPT algorithm without requiring knowledge of the original system dynamics.Under some mild assumptions,the global stability and convergence of the closed-loop control approach are guaranteed.Several simulation experiments are conducted on a magnetic CR(MCR) to demonstrate the practicality and effectiveness of the ADAPT algorithm.
基金supported by the National Natural Science Foundation of China under Grant 62472264the Natural Science Distinguished Youth Foundation of Shandong Province under Grant ZR2025QA13。
文摘In the wireless energy transmission service composition optimization problem,a key challenge is accurately capturing users’preferences for service criteria under complex influencing factors,and optimally selecting a composition solution under their budget constraints.Existing studies typically evaluate satisfaction solely based on energy transmission capacity,while overlooking critical factors such as price and trustworthiness of the provider,leading to a mismatch between optimization outcomes and user needs.To address this gap,we construct a user satisfaction evaluation model for multi-user and multi-provider scenarios,systematically incorporating service price,transmission capacity,and trustworthiness into the satisfaction assessment framework.Furthermore,we propose a Budget-Aware Preference Adjustment Model that predicts users’baseline preference weights from historical data and dynamically adjusts them according to budget levels,thereby reflecting user preferences more realistically under varying budget constraints.In addition,to tackle the composition optimization problem,we develop a ReflectiveEvolutionary Large Language Model—Guided Ant Colony Optimization algorithm,which leverages the reflective evolution capability of large language models to iteratively generate and refine heuristic information that guides the search process.Experimental results demonstrate that the proposed framework effectively integrates personalized preferences with budget sensitivity,accurately predicts users’preferences,and significantly enhances their satisfaction under complex constraints.
文摘In real industrial microgrids(MGs),the length of the primary delivery feeder to the connection point of the main substation is sometimes long.This reduces the power factor and increases reactive power absorption along the primary delivery feeder from the external network.Besides,the giant induction electro-motors as the working horse of industries requires remarkable amounts of reactive power for electro-mechanical energy conversions.To reduce power losses and operating costs of the MG as well as to improve the voltage quality,this study aims at providing an insightful model for optimal placement and sizing of reactive power compensation capacitors in an industrial MG.In the presented model,the objective function considers voltage profile and network power factor improvement at the MG connection point.Also,it realizes power flow equations within which all operational security constraints are considered.Various reactive power compensation strategies including distributed group compensation,centralized compensation at the main substation,and distributed compensation along the primary delivery feeder are scrutinized.A real industrial MG,say as Urmia Petrochemical plant,is considered in numerical validations.The obtained results in each scenario are discussed in depth.As seen,the best performance is obtained when the optimal location and sizing of capacitors are simultaneously determined at the main buses of the industrial plants,at the main substation of the MG,and alongside the primary delivery feeder.In this way,74.81%improvement in power losses reduction,1.3%lower active power import from the main grid,23.5%improvement in power factor,and 37.5%improvement in network voltage deviation summation are seen in this case compared to the base case.
基金supported by Integrated Distribution Network Planning and Operational Enhancement Using Flexibility Domains Under Deep Human-Vehicle-Charger-Road-Grid Coupling(U22B20105).
文摘Thermal storage electric heating(TSEH),as a prevalent variable load resource,offers significant potential for enhancing system flexibility when aggregated into a cluster.To address the uncertainties of renewable energy and load forecasting in active distribution networks(ADN),this paper proposes a multi-timescale coordinated optimal dispatch strategy that incorporates TSEH clusters.It utilizes the thermal storage characteristics and short-term regulation capabilities of TSEH,along with the rapid and gradual response characteristics of resources in active distribution grids,to develop a coordinated optimization dispatch mechanism for day-ahead,intraday,and real-time stages.It provides a coordinated optimized dispatch technique across several timescales for active distribution grids,taking into account the integration of TSEH clusters.The proposed method is validated on a modified IEEE 33-node system.Simulation results demonstrate that the participation of TSEH in collaborative optimization significantly reduces the total system operating cost by 8.71%compared to the scenario without TSEH.This cost reduction is attributed to a 10.84%decrease in interaction costs with the main grid and a 47.41%reduction in network loss costs,validating effective peak shaving and valley filling.The multi-timescale framework further enhances economic efficiency,with overall operating costs progressively decreasing by 3.91%(intraday)and 4.59%(real-time),and interaction costs further reduced by 5.34%and 9.25%,respectively.Moreover,the approach enhances system stability by effectively suppressing node voltage fluctuations and ensuring all voltages remain within safe operating limits during real-time operation.Therefore,the proposed approach achieves rational coordination of diverse resources,significantly improving the economic efficiency and stability of ADNs.
基金supported by the Science and Technology Project of Sichuan Electric Power Company“Power Supply Guarantee Strategy for Urban Distribution Networks Considering Coordination with Virtual Power Plant during Extreme Weather Event”(No.521920230003).
文摘Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the coordination with virtual power plants(VPPs).The proposed strategy improves systemflexibility and responsiveness by optimizing the power adjustment of flexible resources.In the proposed strategy,theGaussian Process Regression(GPR)is firstly employed to determine the adjustable range of aggregated power within the VPP,facilitating an assessment of its potential contribution to power supply support.Then,an optimal dispatch model based on a leader-follower game is developed to maximize the benefits of the VPP and flexible resources while guaranteeing the power balance at the same time.To solve the proposed optimal dispatch model efficiently,the constraints of the problem are reformulated and resolved using the Karush-Kuhn-Tucker(KKT)optimality conditions and linear programming duality theorem.The effectiveness of the strategy is illustrated through a detailed case study.
文摘Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in an algebra,then the solution(and also the control gain in many cases)is also in the same algebra.The main result is verified by a numerical simulation.
文摘The Brief Interactive Optimism Scale (BIOS-G), recently published, was developed to measure optimism based on the interactive personality styles theory in the general population of Mexican adults. It has been validated in both the general population in Mexico and other Latin American countries. This study aims to further consolidate the validity of the BIOS-G in a specific population. The objectives are to assess the psychometric properties of its items, validate its unidimensional structure, describe its distribution, verify its internal consistency, and examine its direct relationship with affective balance and positive affect, as well as its inverse relationship with emotional exhaustion and negative affect among Mexican university teachers. The BIOS-G, the CESQT emotional exhaustion subscale, and Scale of Positive and Negative Experience (SPANE) were administered to a non-probability sample of 213 Mexican university teachers. All items demonstrated discriminative power and internal consistency. The scale showed internal consistency (Green-Yang ordinal ω = 0.74 and McDonald ordinal ω = 0.88). The one-factor model presented good to acceptable fit to the data, with an average variance extracted of 0.65. Its distribution was negatively skewed and mesokurtic. The BIOS-G correlated directly with SPANE’s affective balance and positive emotional experiences and inversely with negative emotional experiences and emotional exhaustion, with moderate strengths of association. Its mean score was higher in men than in women and correlated positively with age. It is concluded that the BIOS-G demonstrates internal consistency and validity evidence among Mexican university teachers, and its use in this specific population is recommended.
基金Supported by the National Natural Science Foundation of China Enterprise Innovation and Development Joint Fund Project(U22B6004)National Natural Science Foundation of China and Youth Science Fund Project(4250021468)CNPC Changqing Oilfield Company Key Core Technology Research Project(KJZX2023-01)。
文摘In-situ heating conversion is the most practical recovery method for lacustrine low-to-medium maturity shale oil.However,the energy output-input ratio must exceed the economic threshold to achieve commercial development.This paper systematically investigates the mechanism of super-rich accumulation of organic matter in continental shale,sweet spot evaluation,optimal heating windows,and appropriate well types and patterns from the perspectives of enhancing energy output and reducing energy input.(1)The super-rich accumulation of organic matter in lacustrine shale is primarily controlled by the intensity,frequency,and preservation of external material inputs,and is related to moderate volcanic and hydrothermal activities,marine transgressions,with total organic carbon content greater than or equal to 6%.(2)The quality of organic-rich intervals is related to the type of source material and hydrocarbon generation potential.The in-situ conversion-derived hydrocarbon quality index(HQI)is established,and the zones exhibiting HQI>450 are defined as sweet spots.(3)Considering the characteristics of the organic matter conversion material field and seepage field,the temperature interval 300-370℃is recommended as the optimal heating window for the Chang 7_(3)sub-member of the Triassic Yanchang Formation in the Ordos Basin.Based on the advantages of thermal conductivity,permeability,and hydrocarbon expulsion efficiency along the bedding direction during in-situ heating,the“horizontal well heating+vertical well development”scheme is proposed,which has demonstrated significant enhancement in both recovery factor and energy output-input ratio,making it the optimal in-situ conversion process.The research findings provide a theoretical and technical foundation for the economical and efficient development of low-to-medium maturity shale oil.
