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 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
为全面综合评价国内一线城市对人才的吸引力,选取9个典型城市作为研究对象,确定经济发展水平、社会因素、生活质量、教育资源、环境与公共服务5个因子作为1级指标,并派生出17个2级指标,构建人才吸引力指标评价体系;同时,利用优劣解距离...为全面综合评价国内一线城市对人才的吸引力,选取9个典型城市作为研究对象,确定经济发展水平、社会因素、生活质量、教育资源、环境与公共服务5个因子作为1级指标,并派生出17个2级指标,构建人才吸引力指标评价体系;同时,利用优劣解距离法(technique for order preference by similarity to an ideal solution, TOPSIS)-熵权法及聚类分析法对9个城市人才吸引力指数和城市间发展共性和特性进行分析。研究结果显示:规模以上工业企业数量指标占比最高。北京、上海、深圳和广州归为第一层次的城市,成都、杭州和武汉为第二层次城市,第三层次为宁波和西安。同时为不同类型的城市提出针对性建议:对第一层次城市,建议引入社会资本完善社区养老体系,同时优化基础教育资源分配;对第二层次城市,建议选择1~2个战略性产业重点突破;对第三层次城市,建议挖掘历史文化资源,打造特色人才文化IP。展开更多
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.
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.
文摘为全面综合评价国内一线城市对人才的吸引力,选取9个典型城市作为研究对象,确定经济发展水平、社会因素、生活质量、教育资源、环境与公共服务5个因子作为1级指标,并派生出17个2级指标,构建人才吸引力指标评价体系;同时,利用优劣解距离法(technique for order preference by similarity to an ideal solution, TOPSIS)-熵权法及聚类分析法对9个城市人才吸引力指数和城市间发展共性和特性进行分析。研究结果显示:规模以上工业企业数量指标占比最高。北京、上海、深圳和广州归为第一层次的城市,成都、杭州和武汉为第二层次城市,第三层次为宁波和西安。同时为不同类型的城市提出针对性建议:对第一层次城市,建议引入社会资本完善社区养老体系,同时优化基础教育资源分配;对第二层次城市,建议选择1~2个战略性产业重点突破;对第三层次城市,建议挖掘历史文化资源,打造特色人才文化IP。
