Title: Optimal control of satellite formations due to oblateness perturbations

Authors: F.A. Abd El-Salam

Addresses: Department of Mathematics, Faculty of Science, Taibah University, Madina, KSA; Department of Astronomy, Faculty of Science, Cairo University, 12613 Cairo, Egypt

Abstract: The nonlinear satellite dynamics, including gravitational perturbations of zonal harmonics up to is utilised to search for the optimal fuel cost for maintaining a formation is investigated. The system dynamics were developed in an Earth-centred inertial coordinate frame using the methods of Hamiltonian dynamics. Continuous dynamic optimisation theory was used to minimise fuel requirements, resulting in a continuous thrust. The uncontrolled reference trajectory of the formation was restricted to a circular inclined orbit. Additionally, further fuel savings are discussed with possible modifications to orbit altitude, formation radius, and variations in the defined performance index.

Keywords: optimal control; satellite formations; nonlinear dynamics; gravitational perturbations; oblateness perturbations; formation flying; zonal harmonics; fuel costs; system dynamics; Hamiltonian dynamics; continuous dynamic optimisation; continuous thrust; circular inclined orbit; fuel consumption; fuel savings; orbit altitude; formation radius; satellites.

DOI: 10.1504/IJSPACESE.2016.081571

International Journal of Space Science and Engineering, 2016 Vol.4 No.2, pp.138 - 165

Received: 10 Sep 2016
Accepted: 22 Oct 2016

Published online: 12 Jan 2017 *

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