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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 103-125, 2018/05/29
The objectives of this work are to study and to apply the full-space quasi-Lagrange-Newton-Krylov (FQLNK) algorithm for solving trajectory optimization problems arising from aerospace industrial applications. As its name suggests, in this algorithm we first convert the constrained optimization problem into an unconstrained one by introducing the augmented Lagrangian parameters. The next step is to find the optimal candidate solution by solving the Karush-Kuhn-Tucker (KKT) system with a Newton-Krylov method. To reduce the computational cost of constructing the KKT system, we employ the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula to build an approximation of the (1,1) subblock of the KKT matrix, which is the most expensive part of the overall computation. The BFGS-based FQLNK algorithm exhibits a superior speedup compared to some of the alternatives. We demonstrate our FQLNK algorithm to be a practical approach for designing an optimal trajectory of a launch vehicle in space missions.
Keywords: launch vehicle mission, trajectory optimization, KKT system, BFGS, Lagrange-Newton-Krylov solver