An approximate gradient-descent method for joint parameter estimation and synchronization of coupled chaotic systems

We address the problem of estimating the unknown parameters of a primary chaotic system that produces an observed time series. These observations are used to drive a secondary system in a way that ensures synchronization when the two systems have identical parameters. We propose a new method to adaptively adjust the parameters in the secondary system until synchronization is achieved. It is based on the gradient-descent optimization of a suitably defined cost function and can be systematically applied to arbitrary systems. We illustrate its application by estimating the complete parameter vector of a Lorenz system.