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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.
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篇名 Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation
来源期刊 自动化学报(英文版) 学科
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年,卷(期) 2021,(8) 所属期刊栏目 PAPERS
研究方向 页码范围 1380-1388
页数 9页 分类号
字数 语种 英文
DOI 10.1109/JAS.2021.1004081
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引文网络交叉学科
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期刊影响力
自动化学报(英文版)
双月刊
2329-9266
10-1193/TP
大16开
北京市海淀区中关村东路95号
80-604
2014
eng
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