An adaptive observer design for auto-synchronization of Lorenz system

Synchronization of chaotic systems with unknown parameters, or namely auto-synchronization, has aroused a lot of interest in the past few years. In this paper, we are interested in solving one of the critical cases in Lorenz system. Based on the past researches, it was concluded that the auto-synchronization of Lorenz system was inachievable if the unknown parameters resided in all of its three dynamical equations while only the first state was measurable. However, as demonstrated in this paper, this problem can be resolved by an adaptive observer following simple design rules. The design is justified with the conditional Lyapunov exponents, and its effectiveness is clearly illustrated in simulations. © 2008 World Scientific Publishing Company.