Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation

doi:10.1109/JAS.2021.1004081

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	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	被引频次：5[WOS] [WOS记录] [WOS相关记录]
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.

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