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On the Radau pseudospectral method: theoretical and implementation advances

Sagliano, Marco and Theil, Stephan and Bergsma, Michiel and D’Onofrio, Vincenzo and Whittle, Lisa and Viavattene, Giulia (2017) On the Radau pseudospectral method: theoretical and implementation advances. CEAS Space Journal, 9 (3), pp. 313-331. Springer. DOI: 10.1007/s12567-017-0165-5 ISSN 1868-2502

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Official URL: https://link.springer.com/article/10.1007/s12567-017-0165-5

Abstract

In the last decades the theoretical development of more and more refined direct methods, together with a new generation of CPUs, led to a significant improvement of numerical approaches for solving optimal-control problems. One of the most promising class of methods is based on pseudospectral optimal control. These methods do not only provide an efficient algorithm to solve optimalcontrol problems, but also define a theoretical framework for linking the discrete numerical solution to the analytical one in virtue of the covector mapping theorem. However, several aspects in their implementation can be refined. In this framework SPARTAN, the first European tool based on flipped-Radau pseudospectral method, has been developed. This paper illustrates the aspects implemented for SPARTAN, which can potentially be valid for any other transcription. The novelties included in this work consist specifically of a new hybridization of the Jacobian matrix computation made of four distinct parts. These contributions include a new analytical formulation for expressing Lagrange cost function for open final-time problems, and the use of dual-number theory for ensuring exact differentiation. Moreover, a self-scaling strategy for primal and dual variables, which combines the projected-Jacobian rows normalization and the covector mapping, is described. Three concrete examples show the validity of the novelties introduced, and the quality of the results obtained with the proposed methods.

Item URL in elib:https://elib.dlr.de/117120/
Document Type:Article
Title:On the Radau pseudospectral method: theoretical and implementation advances
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Sagliano, MarcoMarco.Sagliano (at) dlr.dehttps://orcid.org/0000-0003-1026-0693
Theil, StephanStephan.Theil (at) dlr.dehttps://orcid.org/0000-0002-5346-8091
Bergsma, MichielUNSPECIFIEDUNSPECIFIED
D’Onofrio, VincenzoUNSPECIFIEDUNSPECIFIED
Whittle, LisaUNSPECIFIEDUNSPECIFIED
Viavattene, GiuliaUNSPECIFIEDUNSPECIFIED
Date:September 2017
Journal or Publication Title:CEAS Space Journal
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:9
DOI :10.1007/s12567-017-0165-5
Page Range:pp. 313-331
Publisher:Springer
ISSN:1868-2502
Status:Published
Keywords:Pseudospectral methods, Entry, descent, and landing
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Transport
DLR - Research area:Raumfahrt
DLR - Program:R RP - Raumtransport
DLR - Research theme (Project):R - Shefex III
Location: Bremen
Institutes and Institutions:Institute of Space Systems > Navigation and Control Systems
Deposited By: Sagliano, Marco
Deposited On:13 Dec 2017 10:57
Last Modified:14 Dec 2019 04:28

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