# 3.11] What is targeting? (nonlinear science)

## Description

This article is from the Nonlinear Science FAQ, by James D. Meiss jdm@boulder.colorado.edu with numerous contributions by
others.

# 3.11] What is targeting? (nonlinear science)

(Thanks to Serdar Iplikçi for contributing to this answer)

Targeting is the task of steering a chaotic system from any initial point to

the target, which can be either an unstable equilibrium point or an unstable

periodic orbit, in the shortest possible time, by applying relatively small

perturbations. In order to effectively control chaos, [3.8] a targeting

strategy is important. See:

Kostelich, E., C. Grebogi, E. Ott, and J. A. Yorke, "Higher

Dimensional Targeting," Phys Rev. E,. 47, , 305-310 (1993).

Barreto, E., E. Kostelich, C. Grebogi, E. Ott, and J. A. Yorke, "Efficient

Switching Between Controlled Unstable Periodic Orbits in Higher

Dimensional Chaotic Systems," Phys Rev E, 51, 4169-4172 (1995).

One application of targeting is to control a spacecraft's trajectory so that

one can find low energy orbits from one planet to another. Recently targeting

techniques have been used in the design of trajectories to asteroids and even

of a grand tour of the planets. For example,

E. Bollt and J. D. Meiss, "Targeting Chaotic Orbits to the Moon

Through Recurrence," Phys. Lett. A 204, 373-378 (1995).

http://www.cds.caltech.edu/~marsden/software/spacecraft_orbits.html

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