Targeting in the presence of noise

Targeting methods direct a trajectory from an initial state to a chosen final state in a few iterations by making a small perturbation at the first step. Existing methods have two drawbacks: they require that the map is known so that it can be back iterated from the target region and they generally fail in the presence of noise. We address the first problem by collecting the history of iterations which fall in the target region. To counteract the effects of noise, an averaged idealised trajectory is determined together with a linearisation of the map around this trajectory. A small parameter perturbation can then be made at each stage of the targeting process to keep the trajectory close to the idealised one. These methods are illustrated by an example.