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

作     者：Hossein Mirinejad Tamer Inanc Jacek M.Zurada Hossein Mirinejad;Tamer Inanc;Jacek M.Zurada

作者机构：College of Aeronautics and EngineeringKent State UniversityKentOH 44242 USA Department of Electrical and Computer EngineeringUniversity of LouisvilleLouisvilleKY 40292 USA LouisvilleLouisvilleKY 40292 USAand also with the Information Technology InstituteUniversity of Social Science90-113ŁódźPoland 

出 版 物：《IEEE/CAA Journal of Automatica Sinica》 (自动化学报（英文版）)

年 卷 期：2021年第8卷第8期

页      面：1380-1388页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

主　　题：Costate estimation direct trajectory optimization Galerkin projection numerical optimal control radial basis function interpolation 

摘      要：This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control *** 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 *** 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 *** 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 *** 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 *** 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.