Abstract
The precise anti-synchronization control of uncertain chaotic systems has always remained an interesting problem. The anti-synchronization control of multiple different orders uncertain chaotic systems increases the complexity and enhances the security of the information signal in secure communications. Hence, it confines the hacking in digital communication systems. This paper proposes a novel adaptive control technique and studies the double combination anti-synchronization of multiple different orders uncertain chaotic systems. The proposed adaptive feedback control technique consists of three fundamental nonlinear components. Each component accomplishes a different objective; (i) stability of the closed-loop, (ii) smooth and fast convergence behaviour of the anti-synchronization error, and (iii) disturbance rejection. The theoretical analysis in (i) to (iii) uses the Lyapunov stability theory. This paper also provides parameters adaptation laws that stabilize the uncertain parameters to some constants. The paper discusses the simulation results of two representative examples of four different orders uncertain chaotic systems. These examples demonstrate anti-synchronization among hyperchaotic Lü, uncertain chaotic Shimizu Morioka, uncertain second-order nonlinear duffing, and uncertain parametrically excited second-order nonlinear pendulum systems. The computer-based simulation results certify the efficiency and performance of the proposed anti-synchronization control approach and compare them with peer works.
Highlights
After the seminal work of [1], different types of synchronization have been reported in the relevant literature, including complete synchronization, generalized synchronization, phase synchronization, antiphase-synchronization (or anti-synchronization (AS)), fuzzy synchronization and lag synchronization [7,8,9,10], among others
The FL approaches assume that nonlinear relationships of the AS 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 behaviour
The proposed AS scheme can be used for encryption and decryption of an image in the secrete communication systems.The speed of the transportation of the information signal can be increased by selecting high feedback gains, but this attribute may give birth to signal saturation and the AS may lose its stability and the message signal may be interrupted during the communication process.The above issues might be tackled by the feature selection (FC) method [41,42]
Summary
Synchronization behaviour is realized when the difference of output of state variables of the coupled chaotic systems in the master-slave (drive-response) system arrangement tends to zero after a transient time, that is, lim e(t) = lim y(t) − x(t) = 0, where x(t) t→∞. The synchronization of chaotic systems has been actively investigated in various areas of applied sciences These include information process [2], reactions-diffusion systems [3], DC/AC inverter [4], neural networks [5], mechanical systems [6], secure communications [7], and power systems [8], etc. AS is a process wherein the sum of the output of state variables vanishes and advances as symmetrical oscillators in a transient time, i.e. lim e(t) = lim y(t) + x(t) = 0 A recent study of the chaos AS suggests that it could be utilized as a method to study the properties of a chaotic satellite system evolving in a circular orbit [15]
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