为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式...为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式。首先,根据IESSRB的边界拓扑特性,构建系统的IESSR边界点搜索优化模型;然后,根据PCE,对IESSR边界点搜索优化模型进行参数化处理,构建IESSRB搜索的参数化优化模型;进一步地,根据IESSRB搜索的参数化优化模型的KKT条件,将IESSRB的参数化优化模型转化为高维参数化非线性方程组;在此基础上,借助广义Galerkin投影构建关于近似IESSRB的多项式逼近系数的Galerkin投影方程组,通过求解该方程组可得IESSRB的多项式逼近系数,从而获得IESSRB的多项式逼近表达式;为进一步降低Galerkin投影方程组求解复杂度,提出多项式分段近似IESSRB方法,在提高IESSRB近似精度的同时,提升了IESSRB近似的计算效率;最后,通过IES E39-G20测试系统和IES E118-G96测试系统对所提方法进行分析、验证。结果表明,所提方法可实现IESSR的准确、有效构建。展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
文摘为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式。首先,根据IESSRB的边界拓扑特性,构建系统的IESSR边界点搜索优化模型;然后,根据PCE,对IESSR边界点搜索优化模型进行参数化处理,构建IESSRB搜索的参数化优化模型;进一步地,根据IESSRB搜索的参数化优化模型的KKT条件,将IESSRB的参数化优化模型转化为高维参数化非线性方程组;在此基础上,借助广义Galerkin投影构建关于近似IESSRB的多项式逼近系数的Galerkin投影方程组,通过求解该方程组可得IESSRB的多项式逼近系数,从而获得IESSRB的多项式逼近表达式;为进一步降低Galerkin投影方程组求解复杂度,提出多项式分段近似IESSRB方法,在提高IESSRB近似精度的同时,提升了IESSRB近似的计算效率;最后,通过IES E39-G20测试系统和IES E118-G96测试系统对所提方法进行分析、验证。结果表明,所提方法可实现IESSR的准确、有效构建。
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
