Hybrid Synchronization of Uncertain Generalized Lorenz System by Adaptive Control

Abstract

This paper investigates hybrid synchronization of the uncertain generalized Lorenz system. Several useful criteria are given for synchronization of two generalized Lorenz systems, and the adaptive control law and the parameter update law are used. In comparison with those of existing synchronization methods, hybrid synchronization includes full-order synchronization, reduced-order synchronization, and modified projective synchronization. What is more, control of the stability point, complete synchronization, and antisynchronization can coexist in the same system. Numerical simulations show the effectiveness of this method in a class of chaotic systems.

Oscillation free robust adaptive synchronization of chaotic systems with parametric uncertainties

“…Literature in chaotic synchronization reports various advanced methods, which design adaptive synchronization control (ASC) approaches (Aghababa and Aghababa, 2012a; Aghababa and Aghababa, 2013; Al-Sawalha and Noorani, 2011; Cai et al, 2011; Khan et al, 2019; Vincent and Guo, 2010; Xu et al, 2008; Zhou and Xu, 2018) (among others) to control FOS and ROS of uncertain chaotic and hyperchaotic systems. Xu et al (2008) propose an ASC strategy for the FOS and ROS of unknown chaotic systems.…”

“…Ahmad et al (2016) design an ASC strategy to achieve ROS of chaotic systems with time-delay and uncertain time-varying parameters. Zhou and Xu (2018) propose an ASC technique that investigates the hybrid FOS of two identical uncertain chaotic systems. Most recently, Khan et al (2019) design an ASC scheme to study the FOS among two masters and two slave systems with different combinations of the error states.…”

“…M(i) : The reported ASC schemes in Al-Sawalha and Noorani (2011); Cai et al (2011); Khan et al (2019); Vincent and Guo (2010); Xu et al (2008); Yongguang and Zijian (2014); Zhou and Xu (2018) use feedback linearization (FL) concept to develop synchronization controllers for the FOS and ROS. The FL approaches assume that nonlinear relationships of the synchronization errors between the coupled chaotic systems are known, and the controllers cancel these nonlinear terms of the system and form a closed-loop, which exhibits linear dynamic behavior.…”

“…The presence of such disturbances causes loss of synchronization in the FL-based closed-loop chaotic systems (Khalil, 2002). The FL-based control schemes for FOS and ROS (Al-Sawalha and Noorani, 2011; Cai et al, 2011; Khan et al, 2019; Vincent and Guo, 2010; Xu et al, 2008; Yongguang and Zijian, 2014; Zhou and Xu, 2018) do not consider the effect of the USD and UTD disturbances in the overall system dynamics.…”

“…M(iii) : The rates of convergence in the ASC approaches (Ahmad et al, 2017; Al-Sawalha and Noorani, 2011; Cai et al, 2011; Khan et al, 2019; Vincent and Guo, 2010; Xu et al, 2008; Yongguang and Zijian, 2014; Zhou and Xu, 2018) are slow, which affects the performance of such ASC methods in practical applications, for example, cellular radio systems, multi-agent systems, and wireless networks, and so forth.…”