Design of Adaptive-Robust Controller for Multi-State Synchronization of Chaotic Systems with Unknown and Time-Varying Delays and Its Application in Secure Communication

Abstract

In this paper, the multi-state synchronization of chaotic systems with non-identical, unknown, and time-varying delay in the presence of external perturbations and parametric uncertainties was studied. The presence of unknown delays, unknown bounds of disturbance and uncertainty, as well as changes in system parameters complicate the determination of control function and synchronization. During a synchronization scheme using a robust-adaptive control procedure with the help of the Lyapunov stability theorem, the errors converged to zero, and the updating rules were set to estimate the system parameters and delays. To investigate the performance of the proposed design, simulations have been carried out on two Chen hyper-chaotic systems as the slave and one Chua hyper-chaotic system as the master. Our results showed that the proposed controller outperformed the state-of-the-art techniques in terms of convergence speed of synchronization, parameter estimation, and delay estimation processes. The parameters and time delays were achieved with appropriate approximation. Finally, secure communication was realized with a chaotic masking method, and our results revealed the effectiveness of the proposed method in secure telecommunications.

Medical Images Encryption Based on Adaptive-Robust Multi-Mode Synchronization of Chen Hyper-Chaotic Systems

“…In all telemedicine systems, the issue of information security is vitally significant. To this end, various approaches for the information security of these systems have been presented so far [ 12 ]. Cryptography based on chaotic theory is one of the best approaches to protect the information in secure communications.…”

“…One of the most important fields of cryptography is chaotic systems [ 9 , 10 ]. The most significant feature of chaotic systems is the high reaction to small changes in the initial conditions [ 11 , 12 ]. Much research has been conducted in this field for the last two decades since Correll et al [ 13 , 14 , 15 ] introduced the synchronization of chaotic systems.…”

Finite-Time Synchronization of Chaotic Systems using Fractional Order Nonlinear PID Adaptive Sliding Controller

“…By applying (22) in (26), the above derivative is extended as follows: Relationship (29) will be recast as follows, based on assumptions 1 and 2 stated in relations ( 14) and ( 15 The derivative of the Lyapunov function would be as follows:…”

“…Synchronization of chaotic systems has piqued the interest of scientists, with over 350,000 research papers listed in Google Scholar. Many studies have been conducted in this subject for the integer [25], fractional [26], and [(new article)] systems. Several control mechanisms have been presented thus far for this purpose.…”

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

“…Chaos plays a significant role in many fields, such as biological systems dealing with the human heart and brain [7], protected communication systems [8], smart systems [9], digital signal processing [10], data encryption [11], robotics engineering [12], adaptive control engineering [13], and nonlinear oscillator designs [14]. Recently, several fractionalorder systems are proposed to have exhibit chaotic behavior, such as a fractional-order Lotka-Volterra system, a fractional-order Chua Hartley oscillator, a fractional-order Van der Pol oscillator [15], a fractional-order Lui system [16], a fractional-order Lorenz system [17], and many other systems [18].…”