Adaptive Tracking Control of Chaotic Systems With Applications to Synchronization

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We address the problem of controlled synchronization of a class of uncertain chaotic systems. Our approach follows techniques of adaptive tracking control and identification of dynamic systems from recent developments of control theory. In particular, we use new notions of the so-called property of persistency of excitation—known to be sufficient and necessary for parameter estimation—to construct adaptive algorithms that ensure perfect tracking/synchronization and parameter estimation of chaotic systems with parameter uncertainty. Our theoretical findings are supported by particular examples and simulation studies on systems such as the Lorenz and RÖssler oscillators and the Duffing equation. </para>