CHAOS SYNCHRONIZATION USING SUPER-TWISTING SLIDING MODE CONTROL APPLIED ON CHUA’S CIRCUIT

Chua’s circuit is the classic chaotic system and the most widely used in serval areas due to its potential for secure communication. However, developing an accurate chaos control strategy is one of the most challenging works for Chua’s circuit. This study proposes a new application of super twisting algorithm (STC) based on sliding mode control (SMC) to eliminate or synchronize the chaos behavior in the circuit. Therefore, the proposed control strategy is robust against uncertainty and effectively regulates the system with a good regulation tracking task. Using the Lyapunov stability, the property of asymptotical stability is verified. The whole of the system including the (control strategy, and Chua’s circuit) is implemented under a suitable test setup based on dSpace1104 to validate the effectiveness of our proposed control scheme. The experimental results show that the proposed control method can effectively eliminate or synchronize the chaos in the Chua's circuit

Robust adaptive synchronization of a class of uncertain chaotic systems with unknown time-delay

In this paper, a robust adaptive control strategy is proposed to synchronize a class of uncertain chaotic systems with unknown time delays. Using Lyapunov theory and Lipschitz conditions in chaotic systems, the necessary adaptation rules for estimating uncertain parameters and unknown time delays are determined. Based on the proposed adaptation rules, an adaptive controller is recommended for the robust synchronization of the aforementioned uncertain systems that prove the robust stability of the proposed control mechanism utilizing the Lyapunov theorem. Finally, to evaluate the proposed robust and adaptive control mechanism, the synchronization of two Jerk chaotic systems with finite non-linear uncertainty and external disturbances as well as unknown fixed and variable time delays are simulated. The simulation results confirm the ability of the proposed control mechanism in robust synchronization of the uncertain chaotic systems as well as to estimate uncertain and unknown parameters

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

On the impulsive synchronization control for a class of chaotic systems

The problem on chaos synchronization for a class of chaotic system is addressed. Based on impulsive control theory and by constructing a novel Lyapunov functional, new impulsive synchronization strategies are presented and possess more practical application value. Finally some typical numerical simulation examples are included to demonstrate the effectiveness of the theoretical results

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

In this paper, a novel medical image encryption method based on multi-mode synchronization of hyper-chaotic systems is presented. The synchronization of hyper-chaotic systems is of great significance in secure communication tasks such as encryption of images. Multi-mode synchronization is a novel and highly complex issue, especially if there is uncertainty and disturbance. In this work, an adaptive-robust controller is designed for multimode synchronized chaotic systems with variable and unknown parameters, despite the bounded disturbance and uncertainty with a known function in two modes. In the first case, it is a main system with some response systems, and in the second case, it is a circular synchronization. Using theorems it is proved that the two synchronization methods are equivalent. Our results show that, we are able to obtain the convergence of synchronization error and parameter estimation error to zero using Lyapunov’s method. The new laws to update time-varying parameters, estimating disturbance and uncertainty bounds are proposed such that stability of system is guaranteed. To assess the performance of the proposed synchronization method, various statistical analyzes were carried out on the encrypted medical images and standard benchmark images. The results show effective performance of the proposed synchronization technique in the medical images encryption for telemedicine application.MINECO/ FEDER under the RTI2018-098913-B100 CV20-45250 and A-TIC- 080-UGR18 project

Rikitake dynamo system, its circuit simulation and chaotic synchronization via quasi-sliding mode control

Rikitake dynamo system (1958) is a famous two-disk dynamo model that is capable of executing nonlinear chaotic oscillations similar to the chaotic oscillations as revealed by palaeomagnetic study. First, we detail the Rikitake dynamo system, its signal plots and important dynamic properties. Then a circuit design using Multisim is carried out for the Rikitake dynamo system. New synchronous quasi-sliding mode control (QSMC) for Rikitake chaotic system is studied in this paper. Furthermore, the selection on switching surface and the existence of QSMC scheme is also designed in this paper. The efficiency of the QSMC scheme is illustrated with MATLAB plots

Projective synchronization analysis for BAM neural networks with time-varying delay via novel control

In this paper, the projective synchronization of BAM neural networks with time-varying delays is studied. Firstly, a type of novel adaptive controller is introduced for the considered neural networks, which can achieve projective synchronization. Then, based on the adaptive controller, some novel and useful conditions are obtained to ensure the projective synchronization of considered neural networks. To our knowledge, different from other forms of synchronization, projective synchronization is more suitable to clearly represent the nonlinear systems’ fragile nature. Besides, we solve the projective synchronization problem between two different chaotic BAM neural networks, while most of the existing works only concerned with the projective synchronization chaotic systems with the same topologies. Compared with the controllers in previous papers, the designed controllers in this paper do not require any activation functions during the application process. Finally, an example is provided to show the effectiveness of the theoretical results

Synchronization of two fractional-order chaotic systems via nonsingular terminal Fuzzy Sliding Mode Control

La sincronización de dos sistemas caóticos complejos de orden fraccional se discute en este documento. El parámetro incertidumbre y la perturbación externa se incluyen en el modelo del sistema, y la sincronización de los sistemas considerados caóticos se implementa en base al concepto de tiempo finito. Primero, se propone una nueva superficie deslizante terminal no singular de orden fraccional que es adecuada para los sistemas de orden fraccional considerados. Se ha demostrado que una vez que las trayectorias del estado del sistema alcancen la superficie de deslizamiento propuesta, convergerán al origen dentro de un tiempo finito dado. En segundo lugar, en términos de la superficie deslizante terminal no singular establecida, que combina el control difuso y los esquemas de control de modo deslizante, se introduce una ley de control de modo deslizante difusa única novedosa y robusta que puede forzar las trayectorias del sistema de error dinámico de circuito cerrado para alcanzar el deslizamiento superficie durante un tiempo finito. Finalmente, utilizando el teorema de estabilidad fraccional de Lyapunov, se demuestra la estabilidad del método propuesto. El método propuesto se implementa para la sincronización de dos sistemas caóticos Genesio-Tesi de orden fraccional con parámetros inciertos y perturbaciones externas para verificar la efectividad del controlador de modo de deslizamiento difuso terminal no-singular de orden fraccional propuesto.The synchronization of two fractional-order complex chaotic systems is discussed in this paper. The parameter uncertainty and external disturbance are included in the system model, and the synchronization of the considered chaotic systems is implemented based on the finite-time concept. First, a novel fractional-order nonsingular terminal sliding surface which is suitable for the considered fractional-order systems is proposed. It is proven that once the state trajectories of the system reach the proposed sliding surface they will converge to the origin within a given finite time. Second, in terms of the established nonsingular terminal sliding surface, combining the fuzzy control and the sliding mode control schemes, a novel robust single fuzzy sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface over a finite time. Finally, using the fractional Lyapunov stability theorem, the stability of the proposed method is proven. The proposed method is implemented for synchronization of two fractional-order Genesio-Tesi chaotic systems with uncertain parameters and external disturbances to verify the effectiveness of the proposed fractional-order nonsingular terminal fuzzy sliding mode controller.• National Natural Science Foundation of China. Becas U1604146, U1404610, 61473115, 61203047 • Science and Technology Research Project in Henan Province. 152102210273, 162102410024 • Foundation for the University Technological Innovative Talents of Henan Province. Beca 18HASTIT019peerReviewe