Planar tilting maneuver of a spacecraft: Singular arcs in the minimum time problem and chattering

Jiamin  Zhu; Emmanuel Trélat; Max  Cerf

doi:10.3934/dcdsb.2016.21.1347

Article Contents

2016, Volume 21, Issue 4: 1347-1388. Doi: 10.3934/dcdsb.2016.21.1347

This issue Previous Article A mathematical model for hepatitis B with infection-age structure Next Article

Planar tilting maneuver of a spacecraft: Singular arcs in the minimum time problem and chattering

1.
Sorbonne Universités, UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris
2.
Sorbonne Universités, UPMC Univ. Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, Institut Universitaire de France, F-75005, Paris

Received: April 2015

Published: June 2016

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Abstract

In this paper, we study the minimum time planar tilting maneuver of a spacecraft, from the theoretical as well as from the numerical point of view, with a particular focus on the chattering phenomenon. We prove that there exist optimal chattering arcs when a singular junction occurs. Our study is based on the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F. Borisov. We give sufficient conditions on the terminal values under which the optimal solutions do not contain any singular arc, and are bang-bang with a finite number of switchings. Moreover, we implement sub-optimal strategies by replacing the chattering control with a fixed number of piecewise constant controls. Numerical simulations illustrate our results.

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Mathematics Subject Classification: Primary: 49K15, 49M37, 65H20.

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