Adaptive projective synchronization for a class of switched chaotic systems

Abstract

This paper addresses the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods. First, a necessary and sufficient condition is proposed to show how many state variables can realize projective synchronization under a linear feedback controller for the chaotic systems. Then, accordingly, a new algorithm is given to select all state variables that can realize projective synchronization. Furthermore, according to the results of the projective synchronization of chaotic systems, the problem of projective synchronization of the switched chaotic systems comprised by the unified chaotic systems is investigated, and an adaptive global linear feedback controller with only one input channel is designed, which can realize the projective synchronization under the arbitrary switching law. It is worth mentioning that the proposed method can also realize complete synchronization of the switched chaotic systems. Finally, the numerical simulation results verify the correctness and effectiveness of the proposed method.

Observer-based adaptive neural network control design for projective synchronization of uncertain chaotic systems

“…After that, various types of chaos synchronization have been suggested in the literature for over two decades, such as complete synchronization (Korneev et al, 2021), phase synchronization (Mao et al, 2021), lag synchronization (Mihana et al, 2020), anti-synchronization (Yu et al, 2020), impulsive synchronization (Ao et al, 2020), exponential synchronization (Xu et al, 2020), projective synchronization (Boubellouta and Boulkroune, 2019), projective-lag synchronization (Feng et al, 2021), and so on (Eroglu et al, 2017; Zouari et al, 2017). The projective synchronization technique which consists in synchronizing the dynamical states of a master-slave system with a scaling factor is one of the most popular methods for synchronization (Ren and Zhang, 2019). Up to now, for the aim of synchronizing chaotic systems, several control strategies have been aroused to design an appropriate control.…”

“…Based on the singular perturbation theory, an observer-based adaptive neural network projective chaos synchronization method is designed in this work. The considered class of chaotic systems is relatively general and includes both disturbances and uncertainties, in contrast to some existing synchronization approaches that consider the master–slave systems to be almost known (Du et al, 2009; Harb and Zohdy, 2009; Wu et al, 2017) or those in which the effects of disturbances and uncertainties are neglected (Asadollahi et al, 2020; Ren and Zhang, 2019; Wu and Ma, 2021). 2.…”

Adaptive coexistence of synchronization and anti-synchronization for a class of switched chaotic systems

“…The chaotic system and switched system have been investigated comprehensively, however, the combination of the two, which is called switched chaotic system, relatively speaking, is rarely investigated [36][37][38] . In 36 , synchronization of switched system is investigated based on Lyapunov method, and a sufficient condition is derived to ensure the synchronization between two switched systems.…”

“…In 37 , a sufficient condition for synchronization of identical master-slave switched nonlinear chaotic systems is obtained and are expressed in the form of bilinear matrix inequalities (BMIs). In 38 , the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods is addressed. The switched chaotic system is combined by the chaotic subsystems, compared with the single chaotic system, is more complex, at the same time, has higher practical value, for example, in secure communication fields.…”

Modeling, Synchronization, and FPGA Implementation of Hamiltonian Conservative Hyperchaos

“…Chaos synchronization is of vital significance to the practical application of chaos. Important works in chaos synchronization for the chaotic system and its applications in control and tracking have been done recently and in the past [35,36]. Design and implementation of the pseudo-random digital signal generator is one of the most important chaos-based application.…”