A novel mesh discretization strategy for numerical solution of optimal control problems in aerospace engineering

作     者：Lv, Lu Xiao, Long Zou, Ruping Wang, Wenhai Chen, Shichao Hui, Junpeng Liu, Jiaqi Liu, Xinggao 

作者机构：Hubei Univ Technol Hubei Key Lab High Efficiency Utilizat Solar Energ Wuhan 430068 Hubei Peoples R China Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Peoples R China Xian Modern Control Technol Res Inst Xian 710065 Shanxi Peoples R China China Aerosp Sci & Technol Corp Res Inst 1 Beijing 100076 Peoples R China 

出 版 物：《JOURNAL OF THE FRANKLIN INSTITUTE》 (佛兰克林学会杂志)

年 卷 期：2023年第360卷第14期

页      面：10433-10456页

核心收录：

学科分类：0808[工学-电气工程] 07[理学] 08[工学] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：National Natural Science Foundation of China [12075212  12105246  11975207  62073288] 

主　　题：Nonlinear programming 

摘      要：An effective approach is proposed for optimal control problems in aerospace engineering. First, several interval lengths are treated as optimization variables directly to localize the switching points accurately. Second, the variable intervals are usually refined into more subintervals homogeneously to obtain the trajectories with high accuracy. To reduce the number of optimization variables and improve the efficiency, the control and the state vectors are parameterized using different meshes in this paper such that the control can be approximated asynchronously by fewer parameters where the trajectories change slowly. Then, the variables are departed as independent variables and dependent variables, the gradient formulae, based on the partial derivatives of dependent parameters with respect to independent parameters, are computed to solve nonlinear programming problems. Finally, the proposed approach is applied to the classic moon lander and hang glider problems. For the moon lander problem, the proposed approach is compared with CVP, Fast-CVP and GPM methods, respectively. For the hang glider problem, the proposed approach is compared with trapezoidal discretization and stopping criteria methods, respectively. The numerical results validate the effectiveness of the proposed approach.2023 Published by Elsevier Inc. on behalf of The Franklin Institute.