Abstract
This article proposes a disturbance observer-based Sliding Mode Control (SMC) approach for the robust synchronization of uncertain delayed chaotic systems. This is done by, first, examining and analyzing the electronic behavior of the master and slave Sprott chaotic systems. Then, synthesizing a robust sliding mode control technique using a newly proposed sliding surface that encompasses the synchronization error between the master and slave. The external disturbances affecting the system were estimated using a disturbance observer. The proof of the semi-globally bounded synchronization between the master and slave was established using the Lyapunov stability theory. The efficiency of the proposed approach was first assessed using a simulation study, then, experimentally validated on a data security system. The obtained results confirmed the robust synchronization properties of the proposed approach in the presence of time-delays and external disturbances. The experimental validation also confirmed its ability to ensure the secure transfer of data.
Highlights
Due to their valuable characteristics, chaotic systems have long attracted the consideration of investigators worldwide [1]–[3]
DESIGN OF A DISTURBANCE OBSERVER-BASED SEMI-GLOBALLY ROBUST SYNCHRONIZER FOR THE SPROTT CHAOTIC SYSTEM In what follows, a robust sliding mode synchronizer based on the disturbance observer has been proposed for the Sprott chaotic system (1) under time-delay in states, bounded external disturbances and parametric uncertainty
The external disturbances are considered as D1 = 1.5xs sin (t), D1 = 1.5ys sin (t) andD1 = 1.5zs sin (t) − axs (t) − bzs(t − τ ), where, a = 0.01sin(a) and b = 0.01sin(b), the time delay is τ = 0.005
Summary
Due to their valuable characteristics, chaotic systems have long attracted the consideration of investigators worldwide [1]–[3]. The nonlinear, aperiodic and unstable characteristics of these systems result in their widespread applications in various fields, including secure communication [4], [5]. The butterfly effect refers to the sensitive dependence on initial conditions, in which a small variation in one state can result in more bigger variations in the later state. The chaotic behavior is undesirable because of the fact that even small disturbances may cause the states to diverge exponentially. The chaos phenomenon should be avoided or completely suppressed in practice [6]–[9]. In the past two decades, chaos synchronization has generated important interests in applied fields such
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