Abstract
Two aircraft exposed to illumination by a tracking radar are considered and the optimization problem of cooperatively steering them to a prespecified rendezvous point is addressed. First, the problem of a single aircraft exposed to illumination by a tracking radar is considered and the problem of determining an optimal planar trajectory connecting two prespecified points is addressed. The solution is shown to exist only if the angle θf formed by the lines connecting the radar to the two prespecified trajectory points, is less than 60°. In addition, expressions are given for the optimal path length, l*, and optimal cost. When the angle θf≥60° an unconstrained optimal solution does not exist, and in order to render the optimization problem well posed, a path length constraint is imposed. Numerical optimization techniques are used to obtain optimal aircraft trajectories for the constrained case. Finally, the problem of isochronous rendezvous of the two aircraft is addressed using an optimization argument and the analytic results previously derived for a single aircraft trajectory.
The views expressed in this article are those of the authors and do not reflect the official policy of the U.S. Air Force, Department of Defense, or the U.S. Government.
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References
Eves, H. (1991). Analytic geometry. In Beyer, W. H., editor, CRC Standard Mathematical Tables and Formulae. CRC Press, Boca Raton, Florida, 29th edition.
Milne-Thomson, L. (1970). Elliptic integrals. In Abramowitz, M. and Stegun, I. A., editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. U.S. Government Printing Office, Washington, DC, ninth edition.
Pachter, M. et al. (2001). Minimizing radar exposure in air vehicle path planning. In Proceedings of the 41st Israel Annual Conference on Aerospace Sciences, Tel-Aviv, Israel.
Skolnik, M. I., editor (1990). Radar Handbook. McGraw-Hill, New York, New York, second edition.
Visual Numerics, I. (1997). IMSL Math Library, volume 1. Visufal Numerics, Inc.
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© 2002 Kluwer Academic Publishers
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Pachter, M., Hebert, J. (2002). Cooperative Aircraft Control for Minimum Radar Exposure. In: Murphey, R., Pardalos, P.M. (eds) Cooperative Control and Optimization. Applied Optimization, vol 66. Springer, Boston, MA. https://doi.org/10.1007/0-306-47536-7_10
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DOI: https://doi.org/10.1007/0-306-47536-7_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4020-0549-7
Online ISBN: 978-0-306-47536-8
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