Adaptive‐impulsive function projective synchronization for a class of time‐delay chaotic systems

Abstract

This article investigates the function projective synchronization (FPS) for a class of time‐delay chaotic system via nonlinear adaptive‐impulsive control. To achieve the FPS, suitable nonlinear continuous and impulsive controllers are designed based on adaptive control theory and impulsive control theory. Using the generalized Babarlat's lemma, a general condition is given to ensure the FPS. Here, the time‐delay chaotic system is assumed to satisfy the Lipschitz condition while the Lipschitz constants are estimated by augmented adaptation equations. Numerical simulation results are also presented to verify the effectiveness of the proposed synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 333–341, 2015

Generalized Projective Synchronization for Chaotic Systems via Active Control with Reduced Order

“…According to the original active control method [6], the error system (3) is rewritten as the following form (…”

“…After the first establishment of the control method to achieve generalized projective synchronization by Pecora and Carroll [4], various modified control methods have been proposed, each with its own advantages and disadvantages. These control methods include, adaptive control method [5], impulsive control method [6], and active control [7], etc.…”