Knowledge Commons of Institute of Automation,CAS
Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation | |
Hossein Mirinejad; Tamer Inanc; Jacek M. Zurada | |
发表期刊 | IEEE/CAA Journal of Automatica Sinica |
ISSN | 2329-9266 |
2021 | |
卷号 | 8期号:8页码:1380-1388 |
摘要 | This work presents a novel approach combining radial basis function (RBF) interpolation with Galerkin projection to efficiently solve general optimal control problems. The goal is to develop a highly flexible solution to optimal control problems, especially nonsmooth problems involving discontinuities, while accounting for trajectory accuracy and computational efficiency simultaneously. The proposed solution, called the RBF-Galerkin method, offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points. The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush–Kuhn–Tucker (KKT) conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem, if a set of discrete conditions holds. The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem. In addition, the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency. |
关键词 | Costate estimation direct trajectory optimization Galerkin projection numerical optimal control radial basis function interpolation |
DOI | 10.1109/JAS.2021.1004081 |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.ia.ac.cn/handle/173211/44590 |
专题 | 学术期刊_IEEE/CAA Journal of Automatica Sinica |
推荐引用方式 GB/T 7714 | Hossein Mirinejad,Tamer Inanc,Jacek M. Zurada. Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation[J]. IEEE/CAA Journal of Automatica Sinica,2021,8(8):1380-1388. |
APA | Hossein Mirinejad,Tamer Inanc,&Jacek M. Zurada.(2021).Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation.IEEE/CAA Journal of Automatica Sinica,8(8),1380-1388. |
MLA | Hossein Mirinejad,et al."Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation".IEEE/CAA Journal of Automatica Sinica 8.8(2021):1380-1388. |
条目包含的文件 | ||||||
文件名称/大小 | 文献类型 | 版本类型 | 开放类型 | 使用许可 | ||
JAS-2020-1043.pdf(985KB) | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | 浏览 |
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