Nonlinear state observers for chaotic systems and their application to communications

We present the application of a general method of state estimation to chaotic systems which does not rely on the existence of specific stability properties of the underlying system though may benefit, in terms of performance, from these properties should they exist. State estimation or reconstruction of chaotic systems from observed scalar time series has typically been concerned with the case where both the system equations and the scalar measurement functional are unknown and therefore the original state space cannot be exactly reconstructed. Here, we are specifically concerned with the related case where the state and measurement equations are known and the original state has to be reconstructed given the observable time series. We first introduce the nonlinear state observer and its application to the problem of the state estimation of chaotic systems. The problem of dealing with singularity in the observer equations is dealt with using the examples of the Lorenz and Rossler systems. Finally, we discuss the application of these systems to various communication schemes