The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the ...The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.展开更多
A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstra...A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstrated where the gradient values are obeyed a simple relative error condition.展开更多
A new algorithm of trust region type is presented to minimize a differentiable function ofmany variables with nonlinear equality and linear inequality constraints. Under the milder conditions, theglobal convergence of...A new algorithm of trust region type is presented to minimize a differentiable function ofmany variables with nonlinear equality and linear inequality constraints. Under the milder conditions, theglobal convergence of the main algorithm is proved. Moreover, since any nonlinear inequality constraint can beconverted into an equation by introducing a slack variable, the trust region method can be used in solving general nonlinear programming problems.展开更多
Sliding polynomial modeling has undergone considerable development and has been widely applied to dynamic modeling. One focus of the polynomial model is to make efficient use of prior information, which can also be ca...Sliding polynomial modeling has undergone considerable development and has been widely applied to dynamic modeling. One focus of the polynomial model is to make efficient use of prior information, which can also be called additional or constrained information. Considering the fact that much additional information can be translated to equality constraints, we develop a new two-stage approach for sliding polynomial modeling with equality constraints. To maintain its compatibility with the polyno-mial model without this constraint, only a simple adjustment based on the constraint equation is involved in the algorithm. The approach is easy to implement and is superior in observability, convergence and accuracy. The results of a simulation study of spacecraft tracking are provided to confirm the theoretical development. As no special hypotheses are required, the approach presented here can be widely applied to dynamic modeling for nonlinear systems with equality constraints. Furthermore, per-formance predictions for other dynamic models can also draw lessons from this approach.展开更多
常规的精密单点定位(Precise Point Positioning,PPP)算法中尚未考虑附加先验信息约束的方法,当系统存在固有的先验信息时,不加以利用可能会导致信息的浪费。对此,本文重点研究了车辆直线运动轨迹所存在的约束信息,推导整理了空间直线...常规的精密单点定位(Precise Point Positioning,PPP)算法中尚未考虑附加先验信息约束的方法,当系统存在固有的先验信息时,不加以利用可能会导致信息的浪费。对此,本文重点研究了车辆直线运动轨迹所存在的约束信息,推导整理了空间直线斜截式约束方程,同时结合等式约束滤波方法中的准确测量法应用到PPP的参数估计过程中,形成附加直线轨迹约束的PPP方法。实验表明:在铁路直线轨道约束实验中,收敛时间最高减少60%,定位精度最高提升14.94%,不同实验结果均表明附加直线轨迹约束能提高PPP定位性能。展开更多
Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality an...Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality and inequality constraints and have given a generalized gradient projection algorithm. The global convergence of the algorithm has been proved and the problems have been solved completely by our algorithm.展开更多
A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） ...A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict： to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.展开更多
In this paper, we introduce a concept of substationary points and present a new trust region-based method for the optimization problems with general nonlinear equality constraints and simple bounds. Without the linear...In this paper, we introduce a concept of substationary points and present a new trust region-based method for the optimization problems with general nonlinear equality constraints and simple bounds. Without the linear independent assumption on the gradients of the equalitiy constraints, we prove the global convergence results for the main algorithm and indicate that they extend the results on SQP and those on trust region methods for equality constrained optimizstion and for optimization with simple bounds. Moreover, since any nonlinear programming problem can be converted into the standard nonlinear programming by introducing slack variables, the trust region method preseated in this paper can be used for solving general nonlinear programming problems.展开更多
Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, ...Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, opti-mal estimation leads to a simple solution. LQL control scheme, is further discussed to make it rational in the actual application.展开更多
基于荷电状态(state of charge,SOC)控制储能系统参与一次调频时,由于储能系统出力约束条件较为单一,因而限制了储能系统的性能。针对此问题提出一种基于储能系统多重约束的一次调频策略。首先,把通过双层模糊控制方法确定储能系统多时...基于荷电状态(state of charge,SOC)控制储能系统参与一次调频时,由于储能系统出力约束条件较为单一,因而限制了储能系统的性能。针对此问题提出一种基于储能系统多重约束的一次调频策略。首先,把通过双层模糊控制方法确定储能系统多时间尺度调频死区作为第1重约束条件,避免火电机组与储能电池频繁动作。其次,将SOC作为第2重约束条件,约束因子作为第3重约束条件,基于logistic曲线构建惯性与下垂综合控制模型,约束储能系统出力。最后,通过高精度SOC构建快速均衡函数,缩短SOC均衡时间。通过搭建仿真模型分别在阶跃负荷扰动和连续负荷扰动的工况下验证所提控制策略有效性。展开更多
In a composite-step approach, a step Sk is computed as the sum of two components Uk and hk. The normal component Vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential ...In a composite-step approach, a step Sk is computed as the sum of two components Uk and hk. The normal component Vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, Sk is a composite step composed of normal component Uk, and tangential component hk.展开更多
A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed. In this method, linear equality constraints are deleted with null space technique and the descending ...A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed. In this method, linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved. The numerical results show that the new method may be capable of processing some large scale problems.展开更多
基金supported by the National Natural Science Foundation of China,Grant Nos.42174011,41874001 and 41664001Innovation Found Designated for Graduate Students of ECUT,Grant No.DHYC-202020。
文摘The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.
文摘A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstrated where the gradient values are obeyed a simple relative error condition.
基金Project supported by the National Natural Science Foundation of China.
文摘A new algorithm of trust region type is presented to minimize a differentiable function ofmany variables with nonlinear equality and linear inequality constraints. Under the milder conditions, theglobal convergence of the main algorithm is proved. Moreover, since any nonlinear inequality constraint can beconverted into an equation by introducing a slack variable, the trust region method can be used in solving general nonlinear programming problems.
基金supported by the National Natural Science Foundation of China(Grant Nos.61072115and60901071)
文摘Sliding polynomial modeling has undergone considerable development and has been widely applied to dynamic modeling. One focus of the polynomial model is to make efficient use of prior information, which can also be called additional or constrained information. Considering the fact that much additional information can be translated to equality constraints, we develop a new two-stage approach for sliding polynomial modeling with equality constraints. To maintain its compatibility with the polyno-mial model without this constraint, only a simple adjustment based on the constraint equation is involved in the algorithm. The approach is easy to implement and is superior in observability, convergence and accuracy. The results of a simulation study of spacecraft tracking are provided to confirm the theoretical development. As no special hypotheses are required, the approach presented here can be widely applied to dynamic modeling for nonlinear systems with equality constraints. Furthermore, per-formance predictions for other dynamic models can also draw lessons from this approach.
文摘常规的精密单点定位(Precise Point Positioning,PPP)算法中尚未考虑附加先验信息约束的方法,当系统存在固有的先验信息时,不加以利用可能会导致信息的浪费。对此,本文重点研究了车辆直线运动轨迹所存在的约束信息,推导整理了空间直线斜截式约束方程,同时结合等式约束滤波方法中的准确测量法应用到PPP的参数估计过程中,形成附加直线轨迹约束的PPP方法。实验表明:在铁路直线轨道约束实验中,收敛时间最高减少60%,定位精度最高提升14.94%,不同实验结果均表明附加直线轨迹约束能提高PPP定位性能。
基金the National Natural Science Foundation of China
文摘Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality and inequality constraints and have given a generalized gradient projection algorithm. The global convergence of the algorithm has been proved and the problems have been solved completely by our algorithm.
基金supported by the National Natural Science Foundation of China(71202140)the Fundamental Research for the Central Universities(HUST:2013QN099)
文摘A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict： to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.
文摘In this paper, we introduce a concept of substationary points and present a new trust region-based method for the optimization problems with general nonlinear equality constraints and simple bounds. Without the linear independent assumption on the gradients of the equalitiy constraints, we prove the global convergence results for the main algorithm and indicate that they extend the results on SQP and those on trust region methods for equality constrained optimizstion and for optimization with simple bounds. Moreover, since any nonlinear programming problem can be converted into the standard nonlinear programming by introducing slack variables, the trust region method preseated in this paper can be used for solving general nonlinear programming problems.
文摘Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, opti-mal estimation leads to a simple solution. LQL control scheme, is further discussed to make it rational in the actual application.
文摘基于荷电状态(state of charge,SOC)控制储能系统参与一次调频时,由于储能系统出力约束条件较为单一,因而限制了储能系统的性能。针对此问题提出一种基于储能系统多重约束的一次调频策略。首先,把通过双层模糊控制方法确定储能系统多时间尺度调频死区作为第1重约束条件,避免火电机组与储能电池频繁动作。其次,将SOC作为第2重约束条件,约束因子作为第3重约束条件,基于logistic曲线构建惯性与下垂综合控制模型,约束储能系统出力。最后,通过高精度SOC构建快速均衡函数,缩短SOC均衡时间。通过搭建仿真模型分别在阶跃负荷扰动和连续负荷扰动的工况下验证所提控制策略有效性。
基金Supported partially by Chinese NNSF grants 19731010the knowledge innovation program of CAS.
文摘In a composite-step approach, a step Sk is computed as the sum of two components Uk and hk. The normal component Vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, Sk is a composite step composed of normal component Uk, and tangential component hk.
基金Supported by the National Natural Sicence Foundation of China(No.11071117)the Natural Science Foundation of Jiangsu Province(No.BK2006184)the Fundamental Research Funds for the Central Universities(No. 2010LKSX01)
文摘A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed. In this method, linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved. The numerical results show that the new method may be capable of processing some large scale problems.
