Improved precise integration method for differential Riccati equation

doi:10.1007/s10483-013-1648-8

Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (1): 1-14.doi: https://doi.org/10.1007/s10483-013-1648-8

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Improved precise integration method for differential Riccati equation

高强¹，谭述君²，钟万勰¹，张宏斌¹

1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China;
2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China

收稿日期:2012-09-20 修回日期:2012-10-18 出版日期:2013-01-03 发布日期:2013-01-03
通讯作者: Hong-wu ZHANG E-mail:zhanghw@dlut.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 10902020 and 10721062)

Improved precise integration method for differential Riccati equation

Qiang GAO¹, Hu-jun TAN², Wan-xie ZHONG¹, Hong-wu ZHANG¹

1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China;
2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China

Received:2012-09-20 Revised:2012-10-18 Online:2013-01-03 Published:2013-01-03
Contact: Hong-wu ZHANG E-mail:zhanghw@dlut.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 10902020 and 10721062)

摘要/Abstract

摘要： An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method (PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples show that the IPIM is stable and gives the machine accuracy solutions.

关键词: best approximation, coincidence, fixed point, topological vectorspace

Abstract: An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method (PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples show that the IPIM is stable and gives the machine accuracy solutions.

Key words: best approximation, coincidence, fixed point, topological vectorspace

高强;谭述君;钟万勰;张宏斌. Improved precise integration method for differential Riccati equation[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 1-14.

Qiang GAO;Shu-jun TAN;Wan-xie ZHONG;Hong-wu ZHANG. Improved precise integration method for differential Riccati equation[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 1-14.

参考文献

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Improved precise integration method for differential Riccati equation

Improved precise integration method for differential Riccati equation

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