Pachter, L. S. and Pachter, M.
(2001)
*Optimal paths for avoiding a radiating source.*
In:
Proceedings of the 40th IEEE Conference on Decision and Control.
Vol.4.
IEEE
, Piscataway, NJ, pp. 3581-3586.
ISBN 0-78057061-9.
https://resolver.caltech.edu/CaltechAUTHORS:20170309-101645949

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## Abstract

We consider the problem of navigating between points in the plane so as to minimize the exposure to a radiating source. Specifically, given two points z_1, z_2 in the complex plane, we solve the problem of finding the path C(t) (0 ≤ t ≤ 1) such that C(0)=z_1, C(1)=z_2 and ∫^1_0 |C'(t)|/|C(t)|^k dt is minimized. The parameter k specializes to a number of interesting cases: in particular k=2 pertains to the passive sensor avoidance problem and k=4 entails the active radar avoidance problem. The avoidance paths which minimize exposure may have infinite arc-length. To overcome this problem we introduce a weighted exposure and path length optimization problem whose solution requires a variational approach. The optimal trajectory results we obtain are surprisingly intuitive in the cases of interest.

Item Type: | Book Section | |||||||||
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Additional Information: | © 2001 IEEE. | |||||||||

DOI: | 10.1109/CDC.2001.980415 | |||||||||

Record Number: | CaltechAUTHORS:20170309-101645949 | |||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170309-101645949 | |||||||||

Official Citation: | L. S. Pachter and M. Pachter, "Optimal paths for avoiding a radiating source," Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), Orlando, FL, 2001, pp. 3581-3586 vol.4. doi: 10.1109/.2001.980415 | |||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||

ID Code: | 74975 | |||||||||

Collection: | CaltechAUTHORS | |||||||||

Deposited By: | George Porter | |||||||||

Deposited On: | 10 Mar 2017 23:04 | |||||||||

Last Modified: | 15 Nov 2021 16:29 |

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