To solve the finite-time error-tracking problem in mis-sile guidance,this paper presents a unified design approach through error dynamics and free-time convergence theory.The proposed approach is initiated by establis...To solve the finite-time error-tracking problem in mis-sile guidance,this paper presents a unified design approach through error dynamics and free-time convergence theory.The proposed approach is initiated by establishing a desired model for free-time convergent error dynamics,characterized by its independence from initial conditions and guidance parameters,and adjustable convergence time.This foundation facilitates the derivation of specific guidance laws that integrate constraints such as leading angle,impact angle,and impact time.The theoretical framework of this study elucidates the nuances and synergies between the proposed guidance laws and existing methodologies.Empirical evaluations through simulation comparisons underscore the enhanced accuracy and adaptability of the proposed laws.展开更多
In this research article,we introduce a numerical investigation through artificial neural networks(ANN)integrated with evolutionary algorithm especially Archimedean optimization algorithm(AOA)hybrid with the water cyc...In this research article,we introduce a numerical investigation through artificial neural networks(ANN)integrated with evolutionary algorithm especially Archimedean optimization algorithm(AOA)hybrid with the water cycle algorithm(WCA)to address and enhance the analysis of the non-linear magneto-hydrodynamic(MHD)Jeffery-Hamel problem,especially stretching/shrinking in convergent and divergent channel.This combined technique is referred to as ANN-AOA-WCA.The complex nonlinear magneto-hydrodynamic Jeffery-Hamel problem based partial differential equations are transformed into non-linear system of ordinary differential equations for velocity and temperature.We formulate the ANN based fitness function to find the solution of non-linear differential.Subsequently,we employ a novel hybridization of AOA and WCA(AOA-WCA)to optimize the ANN based fitness function and identify the best optimal weights and biases for ANN.To demonstrate the effectiveness and versatility of our proposed hybrid method,we explore MHD models across a range of Reynolds numbers,channel angles and stretchable boundary value leading to the development of two distinct cases.ANN-AOA-WCA numerical results closely align with reference solutions(NDSOLVE)and the absolute error between NDSOLVE and ANN-AOA-WCA is up to 3.35´10^(-8),particularly critical to the understanding of stretchable convergent and divergent channel.Furthermore,to validate the ANN-AOA-WCA technique,we conducted a statistical analysis over 150 independence runs to find the fitness value.展开更多
In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice ...In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice matrix under unfold operator,and then the fold operator is used to form the next iteration tensor such that the computing time can be decreased.In theory,we analyze the global convergence of the algorithm.In numerical experiment,the simulation data and real image inpainting are carried out.Experiment results show the parallel algorithm outperform its original algorithm in CPU times under the same precision.展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradien...In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.展开更多
This paper presents an investigation on the target-guided coordinated control(TACC)of unmanned surface vehicles(USVs).In the scenario of tracking non-cooperative targets,the status information of the target can only b...This paper presents an investigation on the target-guided coordinated control(TACC)of unmanned surface vehicles(USVs).In the scenario of tracking non-cooperative targets,the status information of the target can only be obtained by some USVs.In order to achieve semi-encirclement tracking of noncooperative targets under maritime security conditions,a fixed-time tracking control method based on dynamic surface control(DSC)is proposed in this paper.Firstly,a novel TACC architecture with decoupled kinematic control law and decoupled kinetic control law was designed to reduce the complexity of control system design.Secondly,the proposed DSC-based target-guided kinematic control law including tracking points pre-allocation strategy and sigmoid artificial potential functions(SigAPFs)can avoid collisions during tracking process and optimize kinematic control output.Finally,a fixed-time TACC system was proposed to achieve fast convergence of kinematic and kinetics errors.The effectiveness of the proposed TACC approach in improving target tracking safety and reducing control output chattering was verified by simulation comparison results.展开更多
In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the...The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.展开更多
In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergen...In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.展开更多
The learning algorithms of causal discovery mainly include score-based methods and genetic algorithms(GA).The score-based algorithms are prone to searching space explosion.Classical GA is slow to converge,and prone to...The learning algorithms of causal discovery mainly include score-based methods and genetic algorithms(GA).The score-based algorithms are prone to searching space explosion.Classical GA is slow to converge,and prone to falling into local optima.To address these issues,an improved GA with domain knowledge(IGADK)is proposed.Firstly,domain knowledge is incorporated into the learning process of causality to construct a new fitness function.Secondly,a dynamical mutation operator is introduced in the algorithm to accelerate the convergence rate.Finally,an experiment is conducted on simulation data,which compares the classical GA with IGADK with domain knowledge of varying accuracy.The IGADK can greatly reduce the number of iterations,populations,and samples required for learning,which illustrates the efficiency and effectiveness of the proposed algorithm.展开更多
In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distri...In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.展开更多
To solve the problem that multiple missiles should simultaneously attack unmeasurable maneuvering targets,a guidance law with temporal consistency constraint based on the super-twisting observer is proposed.Firstly,th...To solve the problem that multiple missiles should simultaneously attack unmeasurable maneuvering targets,a guidance law with temporal consistency constraint based on the super-twisting observer is proposed.Firstly,the relative motion equations between multiple missiles and targets are established,and the topological model among multiple agents is considered.Secondly,based on the temporal consistency constraint,a cooperative guidance law for simultaneous arrival with finite-time convergence is derived.Finally,the unknown target maneuver-ing is regarded as bounded interference.Based on the second-order sliding mode theory,a super-twisting sliding mode observer is devised to observe and track the bounded interfer-ence,and the stability of the observer is proved.Compared with the existing research,this approach only needs to obtain the sliding mode variable which simplifies the design process.The simulation results show that the designed cooperative guidance law for maneuvering targets achieves the expected effect.It ensures successful cooperative attacks,even when confronted with strong maneuvering targets.展开更多
Aerocapture is one of the key technologies for low-cost transportation,with high demands of autonomy,accuracy,and robustness of guidance and control,due to its high reliability requirements for only one chance of tryi...Aerocapture is one of the key technologies for low-cost transportation,with high demands of autonomy,accuracy,and robustness of guidance and control,due to its high reliability requirements for only one chance of trying.A unified numerical predictor-corrector guidance method based on characteristic models for aerocapture is proposed.The numerical predictor-corrector guidance method is used to achieve autonomy and high accuracy,and the characteristic model control method is introduced to achieve robustness.At the same time,by transforming path constraints,characteristic model equations including apogee deviation and altitude differentiation are established.Based on the characteristic model equations,a unified guidance law which can satisfy path constraints and guidance objectives simultaneously is designed.In guidance problems,guidance deviation is not directly obtained from the output of the dynamics at present,but is calculated through integral and algebraic equations.Therefore,the method of directly discretizing differential equations cannot be used to establish characteristic models,which brings great difficulty to characteristic modeling.A method for characteristic modeling of guidance problems is proposed,and convergence analysis of the proposed guidance law is also provided.Finally,a joint numerical simulation of guidance and control considering navigation deviation and various uncertainties is conducted to verify the effectiveness of the proposed method.The proposed unified method can be extended to general aerodynamic entry guidance designs,providing theoretical and methodological support for them.展开更多
In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates...In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.展开更多
This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired...This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired terminal impact angle constraint.To address this issue,the problem formulation including 3-D nonlinear mathematical model description,and communication topology are built firstly.Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight(LOS)which satisfies the impact time constraint.However,the normal accelerations are designed to guarantee the convergence of the LOS angular rate.Furthermore,consider the terminal impact angle constraints,a nonsingular terminal sliding mode(NTSM)control is introduced,and a finite time convergent control law of normal acceleration is proposed.The convergence of the proposed guidance law is proved by using the second Lyapunov stability method,and numerical simulations are also conducted to verify its effectiveness.The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.展开更多
基金supported by the National Natural Science Foundation of China(12002370).
文摘To solve the finite-time error-tracking problem in mis-sile guidance,this paper presents a unified design approach through error dynamics and free-time convergence theory.The proposed approach is initiated by establishing a desired model for free-time convergent error dynamics,characterized by its independence from initial conditions and guidance parameters,and adjustable convergence time.This foundation facilitates the derivation of specific guidance laws that integrate constraints such as leading angle,impact angle,and impact time.The theoretical framework of this study elucidates the nuances and synergies between the proposed guidance laws and existing methodologies.Empirical evaluations through simulation comparisons underscore the enhanced accuracy and adaptability of the proposed laws.
文摘In this research article,we introduce a numerical investigation through artificial neural networks(ANN)integrated with evolutionary algorithm especially Archimedean optimization algorithm(AOA)hybrid with the water cycle algorithm(WCA)to address and enhance the analysis of the non-linear magneto-hydrodynamic(MHD)Jeffery-Hamel problem,especially stretching/shrinking in convergent and divergent channel.This combined technique is referred to as ANN-AOA-WCA.The complex nonlinear magneto-hydrodynamic Jeffery-Hamel problem based partial differential equations are transformed into non-linear system of ordinary differential equations for velocity and temperature.We formulate the ANN based fitness function to find the solution of non-linear differential.Subsequently,we employ a novel hybridization of AOA and WCA(AOA-WCA)to optimize the ANN based fitness function and identify the best optimal weights and biases for ANN.To demonstrate the effectiveness and versatility of our proposed hybrid method,we explore MHD models across a range of Reynolds numbers,channel angles and stretchable boundary value leading to the development of two distinct cases.ANN-AOA-WCA numerical results closely align with reference solutions(NDSOLVE)and the absolute error between NDSOLVE and ANN-AOA-WCA is up to 3.35´10^(-8),particularly critical to the understanding of stretchable convergent and divergent channel.Furthermore,to validate the ANN-AOA-WCA technique,we conducted a statistical analysis over 150 independence runs to find the fitness value.
基金Supported by National Nature Science Foundation(12371381)Nature Science Foundation of Shanxi(202403021222270)。
文摘In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice matrix under unfold operator,and then the fold operator is used to form the next iteration tensor such that the computing time can be decreased.In theory,we analyze the global convergence of the algorithm.In numerical experiment,the simulation data and real image inpainting are carried out.Experiment results show the parallel algorithm outperform its original algorithm in CPU times under the same precision.
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
基金Supported by the Science and Technology Project of Guangxi(Guike AD23023002)。
文摘In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.
文摘This paper presents an investigation on the target-guided coordinated control(TACC)of unmanned surface vehicles(USVs).In the scenario of tracking non-cooperative targets,the status information of the target can only be obtained by some USVs.In order to achieve semi-encirclement tracking of noncooperative targets under maritime security conditions,a fixed-time tracking control method based on dynamic surface control(DSC)is proposed in this paper.Firstly,a novel TACC architecture with decoupled kinematic control law and decoupled kinetic control law was designed to reduce the complexity of control system design.Secondly,the proposed DSC-based target-guided kinematic control law including tracking points pre-allocation strategy and sigmoid artificial potential functions(SigAPFs)can avoid collisions during tracking process and optimize kinematic control output.Finally,a fixed-time TACC system was proposed to achieve fast convergence of kinematic and kinetics errors.The effectiveness of the proposed TACC approach in improving target tracking safety and reducing control output chattering was verified by simulation comparison results.
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Re-accompanying Funding Project of Academic Achievements of Jingdezhen Ceramic University(Grant Nos.215/20506277,215/20506341)。
文摘The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.
基金supported by the National Social Science Fundation(Grant No.21BTJ040)the Project of Outstanding Young People in University of Anhui Province(Grant Nos.2023AH020037,SLXY2024A001).
文摘In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.
基金supported by the National Social Science Fund of China(2022-SKJJ-B-084).
文摘The learning algorithms of causal discovery mainly include score-based methods and genetic algorithms(GA).The score-based algorithms are prone to searching space explosion.Classical GA is slow to converge,and prone to falling into local optima.To address these issues,an improved GA with domain knowledge(IGADK)is proposed.Firstly,domain knowledge is incorporated into the learning process of causality to construct a new fitness function.Secondly,a dynamical mutation operator is introduced in the algorithm to accelerate the convergence rate.Finally,an experiment is conducted on simulation data,which compares the classical GA with IGADK with domain knowledge of varying accuracy.The IGADK can greatly reduce the number of iterations,populations,and samples required for learning,which illustrates the efficiency and effectiveness of the proposed algorithm.
基金National Natural Science Foundation of China (Grant Nos.12061028, 71871046)Support Program of the Guangxi China Science Foundation (Grant No.2018GXNSFAA281011)。
文摘In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.
基金supported by the Funds for the Central Universities。
文摘To solve the problem that multiple missiles should simultaneously attack unmeasurable maneuvering targets,a guidance law with temporal consistency constraint based on the super-twisting observer is proposed.Firstly,the relative motion equations between multiple missiles and targets are established,and the topological model among multiple agents is considered.Secondly,based on the temporal consistency constraint,a cooperative guidance law for simultaneous arrival with finite-time convergence is derived.Finally,the unknown target maneuver-ing is regarded as bounded interference.Based on the second-order sliding mode theory,a super-twisting sliding mode observer is devised to observe and track the bounded interfer-ence,and the stability of the observer is proved.Compared with the existing research,this approach only needs to obtain the sliding mode variable which simplifies the design process.The simulation results show that the designed cooperative guidance law for maneuvering targets achieves the expected effect.It ensures successful cooperative attacks,even when confronted with strong maneuvering targets.
基金The National Key R&D Program of China(2018YFA0703800)。
文摘Aerocapture is one of the key technologies for low-cost transportation,with high demands of autonomy,accuracy,and robustness of guidance and control,due to its high reliability requirements for only one chance of trying.A unified numerical predictor-corrector guidance method based on characteristic models for aerocapture is proposed.The numerical predictor-corrector guidance method is used to achieve autonomy and high accuracy,and the characteristic model control method is introduced to achieve robustness.At the same time,by transforming path constraints,characteristic model equations including apogee deviation and altitude differentiation are established.Based on the characteristic model equations,a unified guidance law which can satisfy path constraints and guidance objectives simultaneously is designed.In guidance problems,guidance deviation is not directly obtained from the output of the dynamics at present,but is calculated through integral and algebraic equations.Therefore,the method of directly discretizing differential equations cannot be used to establish characteristic models,which brings great difficulty to characteristic modeling.A method for characteristic modeling of guidance problems is proposed,and convergence analysis of the proposed guidance law is also provided.Finally,a joint numerical simulation of guidance and control considering navigation deviation and various uncertainties is conducted to verify the effectiveness of the proposed method.The proposed unified method can be extended to general aerodynamic entry guidance designs,providing theoretical and methodological support for them.
基金supported by the National Natural Science Foundation of China(61873126)。
文摘In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.
文摘This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired terminal impact angle constraint.To address this issue,the problem formulation including 3-D nonlinear mathematical model description,and communication topology are built firstly.Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight(LOS)which satisfies the impact time constraint.However,the normal accelerations are designed to guarantee the convergence of the LOS angular rate.Furthermore,consider the terminal impact angle constraints,a nonsingular terminal sliding mode(NTSM)control is introduced,and a finite time convergent control law of normal acceleration is proposed.The convergence of the proposed guidance law is proved by using the second Lyapunov stability method,and numerical simulations are also conducted to verify its effectiveness.The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.
