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

Hossein Mirinejad; Tamer Inanc; Jacek M. Zurada

doi:10.1109/JAS.2021.1004081

Volume 8 Issue 8

Aug. 2021

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2021 > 8(8): 1380-1388

H. Mirinejad, T. Inanc, and Jacek M. Zurada, "Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation," IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1380-1388, Aug. 2021. doi: 10.1109/JAS.2021.1004081

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H. Mirinejad, T. Inanc, and Jacek M. Zurada, "Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation," IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1380-1388, Aug. 2021. doi: 10.1109/JAS.2021.1004081

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

doi: 10.1109/JAS.2021.1004081

1.
College of Aeronautics and Engineering, Kent State University, Kent, OH 44242 USA
2.
Department of Electrical and Computer Engineering, University of Louisville, Louisville, KY 40292 USA
3.
Information Technology Institute, University of Social Science, 90-113 Łódź, Poland

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Author Bio:
Hossein Mirinejad (M’12) received the Ph.D. degree in electrical engineering from the University of Louisville, USA, in 2016. He is an Assistant Professor in the College of Aeronautics and Engineering at Kent State University, USA. Prior to joining Kent State, he was a Research Fellow at the Food and Drug Administration (2017–2019) and a Postdoctoral Fellow at the University of Michigan-Ann Arbor (2016–2017). His research interests include modeling and control of autonomous systems, optimal control theory and applications, healthcare automation, and biomedical control systems

Tamer Inanc (SM’16) received the B.S. degree in electrical engineering from Dokuz Eylul University, Turkey in 1991. He received the M.S. and Ph.D. degrees in electrical engineering from Penn State University in 1994 and 2002, respectively. He was a Postdoctoral Scholar at Control and Dynamical Systems Department at Caltech, USA, between 2002 and 2004. He is currently an Associate Professor at Department of Electrical and Computer Engineering at the University of Louisville, USA. His research interests include autonomous robotics, nonlinear trajectory generation for UAVs, robust active vision systems, robust control and identification, biometrics, and biomedical problems

Jacek M. Zurada (LF’15) received the Ph.D. degree in electrical engineering from Gdansk University of Technology, Poland, in 1975. He is a Professor of electrical and computer engineering at the University of Louisville, USA. He authored or coauthored several books and over 380 papers in computational intelligence, neural networks, machine learning, logic rule extraction, and bioinformatics, and delivered more than 100 presentations throughout the world. Prof. Zurada has been awarded numerous distinctions, including the 2013 Joe Desch Innovation Award, the 2015 Distinguished Service Award, and five honorary professorships. In 2014, he served as the IEEE V-President and Technical Activities (TAB Chair). He also chaired the IEEE TAB Periodicals Committee, and the TAB Periodicals Review and Advisory Committee. He was the Editor-in-Chief of the IEEE Transactions on Neural Networks from 1997 to 2003 and an Associate Editor of the IEEE Transactions on Circuits and Systems, Neural Networks, the Proceedings of the IEEE, Neurocomputing, and several other journals. From 2004 to 2005, he was the President of the IEEE Computational Intelligence Society. He has been a Board Member of IEEE, IEEE CIS, and IJCNN. He has been elected as a Member of Polish Academy of Sciences since 2005
Corresponding author: Hossein Mirinejad, e-mail: hmiri@kent.edu
Received Date: 2020-09-23
Revised Date: 2020-11-29
Accepted Date: 2021-03-28

Available Online: 2021-05-08

Abstract

Abstract

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.
- Costate estimation,
- direct trajectory optimization,
- Galerkin projection,
- numerical optimal control,
- radial basis function interpolation

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References(32)

References

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An accurate, direct method proposed for solving optimal control problems (especially nonsmooth)
RBF-Galerkin, the proposed method, offers a highly flexible framework for direct transcription
Any type of global RBFs (as interpolants) and any arbitrary discretization points can be used
RBF-Galerkin uses global RBF interpolation and Galerkin projection for trajectory optimization
Costate estimation provided via RBF-Galerkin Costate Mapping Theorem

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

doi: 10.1109/JAS.2021.1004081

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通讯作者: 陈斌, bchen63@163.com

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