Adaptive observer-based synchronization of two non-identical chaotic systems with unknown parameters

Abstract

In this study, adaptive observer-based synchronization of chaotic systems is considered. The master and slaves systems have different dynamics and it is assumed that the master system parameters are unknown while its states are available. First, it is assumed that the slave system parameters are known but its states are not completely available. It is shown that an observer for the slave system can be designed and applied for the purpose of synchronization. Based on a Lyapunov function, an adaptive law for master parameters estimation and a control law for the synchronization goal are extracted. Stability of the entire system including the observer dynamics has been proved. Further, it is assumed that the parameters of both master and slave systems are unknown. For this case, an adaptive nonlinear observer is designed to estimate the slave system states and two adaptive laws for estimating the unknown parameters are proposed. In addition, a proper control law to achieve the synchronization goal has been suggested, and the stability of the closed-loop system is established. Finally, the effectiveness of the proposed synchronization method is shown via simulation results.

Observer-based synchronization of uncertain chaotic systems subject to input saturation

“…Additionally, the proposed observer-based control law is compared with controller that was designed by Bagheri et al (2015). The given controller in Bagheri et al (2015) is observer based; however, the observer was designed only for the slave system and without considering the actuator saturation in synchronization problem. The simulation results are given in Figures 8 and 9.…”

“…Figure 8 indicates the synchronization errors. As shown in Figure 8(a), the observer-based controller that was designed by Bagheri et al (2015) does not show good performance in the presence of actuator saturation. However, Figure 8(b) confirms that applying the proposed saturated controller leads to robust synchronization in the presence of actuator saturation.…”

“…Time responses of the synchronization errors: (a) by controller given in Bagheri et al (2015); (b) by the proposed controller.…”

“…Observer-based synchronization for differential inclusion chaotic systems with unknown disturbances and parameters was considered in Sun and Yin (2015). Recently, Bagheri et al (2015) proposed an adaptive observer-based controller to synchronize the chaotic systems.…”

Chaos control and chaos synchronization using the state-dependent Riccati equation techniques

“…Fuzzy techniques have been utilized to solve both the chaos control problem and the chaos synchronization problem (Boulkroune et al, 2016; Wen and Jiang, 2011; Hu et al, 2011). In Pai (2012) and Bagheri et al (2015), observer-based controllers were designed to solve the synchronization problem. Finite-time controllers have been created in order to organize the finite-time stabilization and synchronization of chaotic systems (Wang et al, 2016; Xie et al, 2016;Wu et al, 2016).…”