This article is from the Nonlinear Science FAQ, by James D. Meiss firstname.lastname@example.org with numerous contributions by others.
(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).