Synchronization of chaotic oscillators by means of generalized proportional integral observers

The problem of synchronization of chaotic oscillators, using state observers, is handled through the use of a simplified perturbed linear integration model of the chaotic system output dynamics. The linear simplified model of the chaotic system does not entitle approximate linearizations, nor state coordinate transformations, but, simply, a pure linear integration model with additive unknown but bounded perturbation inputs lumping all the output dynamics nonlinearities. An extended linear state observer (here addressed as Generalized Proportional Integral (GPI) observer) is proposed for the accurate estimation of the phase variables and the perturbation input of the nonlinear output dynamics. The effectiveness of the approach is tested in the synchronization of two study cases: The GenesioTesi chaotic system and the Rossler oscillator. As an application of the estimation process, a codingdecoding process involving encrypted messages, in transmitted phase variables, is implemented using a Rossler chaotic system.