In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solutio...An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.展开更多
To solve the inequality problem, an adjustable entropy method is proposed. An inequality problem can be transformed into a minimax problem which is nondifferentiable; then an adjustable entropy is used to smooth the m...To solve the inequality problem, an adjustable entropy method is proposed. An inequality problem can be transformed into a minimax problem which is nondifferentiable; then an adjustable entropy is used to smooth the minimax problem. The solution of inequalities can be approached by using a BFGS algorithm of the standard optimization method. Some properties of the new approximate function are presented and then the global convergence are given according to the algorithm. Two numerical examples illustrate that the proposed method is efficient and is superior to the former ones.展开更多
Income inequality among farmers living in different regions was an important form of territorial inequalities. Studying the territorial inequality of the net income per peasant was an emphasis of this paper, and Shand...Income inequality among farmers living in different regions was an important form of territorial inequalities. Studying the territorial inequality of the net income per peasant was an emphasis of this paper, and Shandong Province was pointed as the case study region. By the help of logistic regression, it could be found that the special distribution of the net income per peasant in Shandong Province was affected by three factors： distance to No.308 National Highway, distance to the coastline in the east of Shandong Province, and urbanization rates. Based on the decomposition of Gini index, the net income per peasant was divided into four parts, and it was found that the income from family business and salary were the two major sources of income. As to the mechanism for income inequality, it was proved that urbanization was still the key factor. In order to reduce income inequality, the local governments should promote urbanization through improving road networks, such as building highways, which could connect rural areas with the major nodes such as big cities and the port cities in the east.展开更多
In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.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
讨论一类不确定非线性分数阶非等阶(noncommensurate)的系统的控制问题。假设系统含的不确定包括正实不确定(positive real uncertainty)项和非线性函数完全未知,首先利用RBF神经网络近似未知非线性函数,再基于系统的连续频率分布模型...讨论一类不确定非线性分数阶非等阶(noncommensurate)的系统的控制问题。假设系统含的不确定包括正实不确定(positive real uncertainty)项和非线性函数完全未知,首先利用RBF神经网络近似未知非线性函数,再基于系统的连续频率分布模型将分数阶系统转化为等价的无穷维分布状态变量的整数阶系统,结合间接Lyapunov方法及线性矩阵不等式(LMI)方法,给出了系统鲁棒渐近稳定的充分条件。理论和实例仿真验证了方法的有效性。展开更多
This research focuses on detecting faults in flight vehicles with unstable subsystems operating asynchronously.By accounting for asynchronous switching,a switched model is established,and filters for fault detection(F...This research focuses on detecting faults in flight vehicles with unstable subsystems operating asynchronously.By accounting for asynchronous switching,a switched model is established,and filters for fault detection(FD)in unstable subsystems are developed.The FD challenge is then transformed into an H∞filtering issue.Utilizing the multiple discontinuous Lyapunov function(MDLF)approach and the mode-dependent average dwell time(MDADT)method,sufficient conditions are derived to ensure stability during both fast and slow switching.Furthermore,the existence and solutions for FD filters are provided through linear matrix inequalities(LMIs).The simulation outcomes demonstrated the excellent performance of the developed method in studied cases.展开更多
Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point,a new integrated guidance and control design scheme based on variable structure control approac...Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point,a new integrated guidance and control design scheme based on variable structure control approach for missile with terminal impact angle constraint is proposed.First,a mathematical model of an integrated guidance and control model in pitch plane is established,and then nonlinear transformation is employed to transform the mathematical model into a standard form suitable for sliding mode control method design.A sufficient condition for the existence of linear sliding surface is given in terms of linear matrix inequalities（LMIs）,based on which the corresponding reaching motion controller is also developed.To verify the effectiveness of the proposed integrated design scheme,the numerical simulation of missile is made.The simulation results demonstrate that the proposed guidance and control law can guide missile to hit the target with desired impact angle and desired flight attitude angle simultaneously.展开更多
A novel gain-scheduled switching control method for the longitudinal motion of a flexible air-breathing hypersonic vehicle （FAHV） is proposed. Firstly, velocity and altitude are selected as scheduling variables, a p...A novel gain-scheduled switching control method for the longitudinal motion of a flexible air-breathing hypersonic vehicle （FAHV） is proposed. Firstly, velocity and altitude are selected as scheduling variables, a polytopic linear parameter varying （LPV） model is developed to represent the complex nonlinear longitudinal dynamics of the FAHV. Secondly, based on the obtained polytopic LPV model, the flight envelope is divided into four smaller subregions, and four gain-scheduled controllers are designed for these parameter subregions. Then, by the defined switching characteristic function, these gain-scheduled controllers are switched in order to guarantee the closed-loop FAHV system to be asymptotically stable and satisfy a given tracking error performance criterion. The condition of gain-scheduled switching controller synthesis is given in terms of linear matrix inequalities （LMIs） which can be easily solved by using standard software packages. Finally, simulation results show the effectiveness of the presented method.展开更多
Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for dela...Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.展开更多
The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal syst...The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some free-weighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.展开更多
A kind of networked control system is studied; the networked control system with noise disturbance is modeled based on information scheduling and control co-design. Augmented state matrix analysis method is introduced...A kind of networked control system is studied; the networked control system with noise disturbance is modeled based on information scheduling and control co-design. Augmented state matrix analysis method is introduced, and robust fault-tolerant control problem of networked control systems with noise disturbance under actuator failures is studied. The parametric expression of the controller under actuator failures is given. Furthermore, the result is analyzed by simulation tests, which not only satisfies the networked control systems stability, but also decreases the data information number in network channel and makes full use of the network resources.展开更多
The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is propo...The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.展开更多
To investigate a class of nonlinear network control system, a robust fault diagnosis method is presented based on the robust state observer. To access the objective that the designed robust filter is maximally toleran...To investigate a class of nonlinear network control system, a robust fault diagnosis method is presented based on the robust state observer. To access the objective that the designed robust filter is maximally tolerant to disturbances and sensitive to fault, the robustness and stability properties of the fault diagnosis scheme are established rigorously. Using the residual vector, a fault tolerant controller is established in order to guarantee the stability of the closed-loop system, and the controller law can be obtained by solving a set of linear matrix inequalities. Then, some relevant sufficient conditions for the existence of a solution are given by applying Lyapunov stability theory. Finally, a simulation example is performed to show the effectiveness of the proposed approach.展开更多
The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and n...The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.展开更多
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
基金Supported by Scientific Research Fund of Hunan Provincial Education Departmen(t23A0361)。
文摘An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.
文摘To solve the inequality problem, an adjustable entropy method is proposed. An inequality problem can be transformed into a minimax problem which is nondifferentiable; then an adjustable entropy is used to smooth the minimax problem. The solution of inequalities can be approached by using a BFGS algorithm of the standard optimization method. Some properties of the new approximate function are presented and then the global convergence are given according to the algorithm. Two numerical examples illustrate that the proposed method is efficient and is superior to the former ones.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences (KZCX2-EW-304)National Natural Science Foundation of China(40635029,40871257)
文摘Income inequality among farmers living in different regions was an important form of territorial inequalities. Studying the territorial inequality of the net income per peasant was an emphasis of this paper, and Shandong Province was pointed as the case study region. By the help of logistic regression, it could be found that the special distribution of the net income per peasant in Shandong Province was affected by three factors： distance to No.308 National Highway, distance to the coastline in the east of Shandong Province, and urbanization rates. Based on the decomposition of Gini index, the net income per peasant was divided into four parts, and it was found that the income from family business and salary were the two major sources of income. As to the mechanism for income inequality, it was proved that urbanization was still the key factor. In order to reduce income inequality, the local governments should promote urbanization through improving road networks, such as building highways, which could connect rural areas with the major nodes such as big cities and the port cities in the east.
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
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.
文摘讨论一类不确定非线性分数阶非等阶(noncommensurate)的系统的控制问题。假设系统含的不确定包括正实不确定(positive real uncertainty)项和非线性函数完全未知,首先利用RBF神经网络近似未知非线性函数,再基于系统的连续频率分布模型将分数阶系统转化为等价的无穷维分布状态变量的整数阶系统,结合间接Lyapunov方法及线性矩阵不等式(LMI)方法,给出了系统鲁棒渐近稳定的充分条件。理论和实例仿真验证了方法的有效性。
基金the National Natural Science Foundation of China(Grant Nos.62303380,62176214,62101590,62003268)the Aeronautical Science Foundation of China(Grant No.201907053001).
文摘This research focuses on detecting faults in flight vehicles with unstable subsystems operating asynchronously.By accounting for asynchronous switching,a switched model is established,and filters for fault detection(FD)in unstable subsystems are developed.The FD challenge is then transformed into an H∞filtering issue.Utilizing the multiple discontinuous Lyapunov function(MDLF)approach and the mode-dependent average dwell time(MDADT)method,sufficient conditions are derived to ensure stability during both fast and slow switching.Furthermore,the existence and solutions for FD filters are provided through linear matrix inequalities(LMIs).The simulation outcomes demonstrated the excellent performance of the developed method in studied cases.
基金supported by the Nationa Natural Science Foundation of China(60434010)Outstanding Youth Fund of Heilongjiang Province(JC200606)
文摘Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point,a new integrated guidance and control design scheme based on variable structure control approach for missile with terminal impact angle constraint is proposed.First,a mathematical model of an integrated guidance and control model in pitch plane is established,and then nonlinear transformation is employed to transform the mathematical model into a standard form suitable for sliding mode control method design.A sufficient condition for the existence of linear sliding surface is given in terms of linear matrix inequalities（LMIs）,based on which the corresponding reaching motion controller is also developed.To verify the effectiveness of the proposed integrated design scheme,the numerical simulation of missile is made.The simulation results demonstrate that the proposed guidance and control law can guide missile to hit the target with desired impact angle and desired flight attitude angle simultaneously.
基金supported by the National Outstanding Youth Science Foundation(61125306)the National Natural Science Foundation of Major Research Plan(91016004+2 种基金61034002)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20110092110020)the Scientific Research Foundation of Graduate School of Southeast University(YBJJ1103)
文摘A novel gain-scheduled switching control method for the longitudinal motion of a flexible air-breathing hypersonic vehicle （FAHV） is proposed. Firstly, velocity and altitude are selected as scheduling variables, a polytopic linear parameter varying （LPV） model is developed to represent the complex nonlinear longitudinal dynamics of the FAHV. Secondly, based on the obtained polytopic LPV model, the flight envelope is divided into four smaller subregions, and four gain-scheduled controllers are designed for these parameter subregions. Then, by the defined switching characteristic function, these gain-scheduled controllers are switched in order to guarantee the closed-loop FAHV system to be asymptotically stable and satisfy a given tracking error performance criterion. The condition of gain-scheduled switching controller synthesis is given in terms of linear matrix inequalities （LMIs） which can be easily solved by using standard software packages. Finally, simulation results show the effectiveness of the presented method.
基金the National Natural Science Foundation of China (60574011)the National Natural Science Foundation of Liaoning Province (2050770).
文摘Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.
文摘The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some free-weighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.
基金Supported by the State Key Program of National Natural Science of China （60534010）, National Basic Research Program of China （973 Program）（2009CB320604）, National Natural Science Foundation of China （60674021）, the Funds for Creative Research Groups of China （60521003）, the 111 Project（B08015）, and the Funds of Ph.D. Program of Ministry of Eduction, China （20060145019）.
基金Hohai University Startup Outlay for Doctor Scientific Research (2084/40601136)
文摘A kind of networked control system is studied; the networked control system with noise disturbance is modeled based on information scheduling and control co-design. Augmented state matrix analysis method is introduced, and robust fault-tolerant control problem of networked control systems with noise disturbance under actuator failures is studied. The parametric expression of the controller under actuator failures is given. Furthermore, the result is analyzed by simulation tests, which not only satisfies the networked control systems stability, but also decreases the data information number in network channel and makes full use of the network resources.
基金supported by the National Natural Science Foundation of China(60774016).
文摘The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.
基金supported by the National Natural Science Foundation of China(90816023).
文摘To investigate a class of nonlinear network control system, a robust fault diagnosis method is presented based on the robust state observer. To access the objective that the designed robust filter is maximally tolerant to disturbances and sensitive to fault, the robustness and stability properties of the fault diagnosis scheme are established rigorously. Using the residual vector, a fault tolerant controller is established in order to guarantee the stability of the closed-loop system, and the controller law can be obtained by solving a set of linear matrix inequalities. Then, some relevant sufficient conditions for the existence of a solution are given by applying Lyapunov stability theory. Finally, a simulation example is performed to show the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China (60564001)the Program for New Century Excellent Talentsin University (NCET-06-0756)
文摘The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.
