TARGETING IN THE PRESENCE OF NOISE

Targeting methods direct a trajectory from an initial state to a chose n final state in a few iterations by making a small perturbation at th e first step. Existing methods have two drawbacks: they require that t he 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 firs t problem by collecting the history of iterations which fall in the ta rget region. To counteract the effects of noise, an averaged idealised trajectory is determined together with a linearisation of the map aro und this trajectory. A small parameter perturbation can then be made a t each stage of the targeting process to keep the trajectory close to the idealised one. These methods are illustrated by an example. (C) 19 98 Elsevier Science Ltd. All rights reserved.