Adaptive observers for robust synchronization of chaotic systems

Antonio Loria (1) , Elena Panteley (1) , Arturo Zavala (2)

1 L2S - Laboratoire des signaux et systèmes
2 IPICyT - Instituo Potosino de Investigación en Ciencia y Tecnología

We address the problem of master-slave synchronization of chaotic systems under parameter uncertainty and with partial measurements. Our approach is based on observer-design theory hence, we view the master dynamics as a system of differential equations with a state and a measurable output and we design an observer (tantamount to the slave system) which reconstructs the dynamic behavior of the master. The main technical condition that we impose is persistency of excitation (PE), a property well studied in the adaptive control literature. In the case of unknown parameters and partial measurements we show that synchronization is achievable in a practical sense, that is, with "small" error. We also illustrate our methods on particular examples of chaotic oscillators such as the Lorenz and the LÜ oscillators. Theoretical proofs are provided based on recent results on stability theory for time-varying systems.

Mots clés: Adaptive control; chaos control; chaotic systems; observers; synchronization

Domaines: Automatique; Dynamique Chaotique [nlin.CD]

Antonio Loria, Elena Panteley, Arturo Zavala. Adaptive observers for robust synchronization of chaotic systems. IEEE Transactions on Circuits and Systems Part 1 Fundamental Theory and Applications, 2009, 56 (12), pp.2703-2716. ⟨10.1109/TCSI.2009.2016636⟩. ⟨hal-00447311⟩