Reduced-order synchronization of chaotic systems: A modular adaptive design

In this paper, an adaptive algorithm is proposed for reduced-order synchronization of chaotic systems with different orders. Since the exact model of the system is not known a priory in real applications, or the parameters may change with time, adaptive control strategy is applied to make states of the slave system track those of the master, despite the uncertainties. Here, the adaptive control system is designed based on modularity approach, where the identification and control modules are designed completely independently. One of the most advantages of this algorithm, which is applied for the first time in chaos synchronization, is its flexibility in choosing a proper method for both identification and control modules. A modified recursive least square algorithm is used to identify the unknown parameters of the slave system, and the control module is designed based on active control method. As a case study, the Lorenz system and the chaotic pendulum are considered as the master and slave systems, respectively. Simulation results confirm the effectiveness of the proposed method.