Enhanced moving finite element method based on error geometric estimation for simultaneous trajectory optimization
Enhanced moving finite element method based on error geometric estimation for simultaneous trajectory optimization
复制标题
基于误差几何估计的同步轨迹优化的增强移动有限元方法
DOI：
10.1016/j.automatica.2022.110711
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发表时间：
2023-01
期刊：
影响因子：
6.4
通讯作者：
Lorenz T. Biegler
中科院分区：
文献类型：
--
作者：
Yan Gao;Zhengyu Wei;Zhijiang Shao;Weifeng Chen;Zhengyu Song;Lorenz T. Biegler
由于需要优化受控动态系统的性能，直接法已广泛应用于轨迹优化的各个领域。直接法发展的一个重要问题是有限元网格的选择。尽管关于自适应网格细化的研究很多，但很少有工作关注细化之前的有限元布局优化。提出一种基于非搭配点误差（NCPE）和广义有限元长度（GFEL）几何估计的增强型移动有限元方法（EMFE），以每个有限元的长度为变量。 EMFE 的特点包括灵活的问题重构、稳定的数值计算以及为奇异控制问题定位断点（控制变量在问题中线性出现）和找到局部最小数值误差的能力。还研究了奇异控制问题断点定位能力的理论基础和NCPE估计的特点。三个数值例子，其中两个是月球着陆的奇异控制问题，另一个是运载火箭的多相非线性问题，展示了所提出的 EMFE 方法的性能和特点。
The direct method has been widely used in various fields of trajectory optimization due to the need to optimize the performance of a controlled dynamic system. An essential issue in the development of the direct method is the selection of the finite element mesh. Although there have been many pieces of research on adaptive mesh refinement, few works focused on finite element layout optimization before the refinement. This paper proposes an enhanced moving finite element method (EMFE), taking the length of each finite element as a variable, based on the geometric estimation of non-collocation-point error (NCPE) and generalized finite element length (GFEL). The features of EMFE include flexible problem reformulation, stable numerical calculation and the ability to locate breakpoints for singular control problems (the control variables appear linearly in the problems) and finding the local minimum numerical error. The theoretical basis of the ability to locate the breakpoints for singular control problems and the feature of NCPE estimate has also been investigated. Three numerical examples, two of which are singular control problems for lunar landing and the other is a multi-phase nonlinear problem for launch vehicles, demonstrated the performance and features of the proposed EMFE method.
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DOI：
10.1016/j.jfranklin.2015.05.028
发表时间：
2015-10
期刊：
J. Frankl. Inst.
影响因子：
--
作者：
Fengjin Liu;W. Hager;Anil V. Rao
通讯作者：
Fengjin Liu;W. Hager;Anil V. Rao
影响因子：
3.1
作者：
Gill, PE;Murray, W;Saunders, MA
通讯作者：
Saunders, MA
影响因子：
5.7
作者：
Luo Yazhong;Zhang Jin;Tang Guojin
通讯作者：
Tang Guojin
影响因子：
2.9
作者：
RUSSELL, RD;CHRISTIANSEN, J
通讯作者：
CHRISTIANSEN, J
影响因子：
1.8
作者：
Darby, Christopher L.;Hager, William W.;Rao, Anil V.
通讯作者：
Rao, Anil V.