Shadowing and prediction of dynamical systems

In this paper, we illustrate how the notion of shadowing can be applied to the prediction problem for dynamical systems. We start with the assumption that we observer a sequence of states from a dynamical system and that we have identified a reasonably accurate model of the system. Our objective is to use this model in a type of observer design where the error between predicted and real values is fed into the observer in order to correct the prediction and increase the shadowing length.