Singular Arcs in the Generalized Goddard’s Problem

F. Bonnans (), P. Martinon () and E. Trélat ()
Additional contact information
F. Bonnans: Ecole Polytechnique, and INRIA Futurs
P. Martinon: Ecole Polytechnique, and INRIA Futurs
E. Trélat: Ecole Polytechnique, and INRIA Futurs

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 2, No 15, 439-461

Abstract: Abstract We investigate variants of Goddard’s problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this article, performing an analysis based on the Pontryagin maximum principle, we prove that optimal trajectories may involve singular arcs (along which the norm of the thrust is neither zero nor maximal), that are computed and characterized. Numerical simulations are carried out, both with direct and indirect methods, demonstrating the relevance of taking into account singular arcs in the control strategy. The indirect method that we use is based on our previous theoretical analysis and consists in combining a shooting method with an homotopic method. The homotopic approach leads to a quadratic regularization of the problem and is a way to tackle the problem of nonsmoothness of the optimal control.

Keywords: Optimal control; Goddard’s problem; Singular trajectories; Shooting method; Homotopy; Direct methods (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-008-9387-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:139:y:2008:i:2:d:10.1007_s10957-008-9387-1

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-008-9387-1

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().