Non-identical Hyperchaotic Systems Research Articles

Robust finite-time tracking for a square fully actuated class of nonlinear systems

In this paper, the robust finite-time tracking problem is addressed for a square fully actuated class of nonlinear systems subjected to disturbances and uncertainties. Firstly, two applicable lemmas are derived and novel nonlinear sliding surfaces (manifolds) are defined by applying these lemmas. Secondly, by developing the nonsingular terminal sliding mode control, two different types of robust nonlinear control inputs are designed to meet and accomplish the aforementioned finite-time tracking objective. The global finite-time stability of the closed-loop nonlinear system is evaluated analytically and mathematically. The proposed control inputs are utilized to tackle and solve two interesting issues containing (a): the finite-time tracking problem of the unified chaotic system and (b): the finite-time synchronization of two non-identical hyperchaotic systems. Finally, based on MATLAB software, two numerical simulations are carried out to illustrate and demonstrate the effectiveness and performance of the proposed robust finite-time nonlinear control schemes.

Secure Communication Scheme Based on Synchronization of Non-Identical Hyperchaotic Systems

In this work, a secure communication scheme based on the synchronization of non-identical hyperchaotic systems is considered. Using hyperchaotic Lorenz and L u as prototype oscillators, a secure communication scheme based on synchronization of different hyperchaotic systems with unknown parameters is presented. The communication scheme consists of a transmitter, which comprises the hyperchaotic carrier and modulator, and a receiver, which comprises the hyperchaotic response and a demodulator. Appropriate controllers and parameter update laws are designed to achieve synchronization between the hyperchaotic drive and hyperchaotic response systems and achieve the estimate of unknown parameters simultaneously. The message signal is recovered by the identified parameter and the corresponding demodulation method. Numerical simulations were performed to show the validity and feasibility of the designed secure communication scheme.

Intuitionistic Fuzzy Sliding Controller for Uncertain Hyperchaotic Synchronization

In this study, the design of an intuitionistic fuzzy controller for synchronization of two non-identical hyperchaotic systems is proposed. Since hyperchaotic systems has high sensitivity to the initial condition, disturbance and parameter variability. Synchronization of hyperchaotic systems is used to test the controller performance. On the other hand, using of fuzzy logic-based controller has an increasing tendency. As known, fuzzy logic control (FLC), only membership functions are used to obtain a realistic model of the systems. But the intuitionistic fuzzy logic control (IFLC) allows us to obtain a more realistic model than FLC because it also takes into account the degree of non-membership and the degree of uncertainty beside of degree of membership to model examined system. Fuzzy logic-based controllers are hybridized with robust control methods such as sliding mode controller to improve the performance of controller. To take advantages of SMC with fuzzy logic-based IFLC, the IFSMC controller obtained by hybridizing these two methods was designed for hyperchaotic systems. To demonstrate the performance of IFSMC, the results obtained from the synchronization of hyperchaotic systems with FSMC (fuzzy sliding mode controller) and IFSMC were compared. The stability of IFSMC is proved by Lyapunov stability condition. The numerical results and analysis show the efficiency of the IFSMC with regards to synchronization control of uncertain chaotic systems having challenging external disturbances in terms of robustness, minimum tracking error.

Hybrid projective combination\u2013combination synchronization in non-identical hyperchaotic systems using adaptive control

In this paper, we investigate a hybrid projective combination–combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination–combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.

Multi-switching compound-compound anti-synchronization of non-identical hyperchaotic systems

ABSTRACT In this paper, a synchronization scheme for six non-identical hyperchaotic systems is investigated. The paper addresses a synchronization scheme of five leader (master) and one follower (slave) non-identical hyperchaotic systems. This synchronization scheme is first of its kind and different from existing schemes as instead of a scaling system a compound scaling signal is used. The presented scheme is termed as ‘multi-switching compound-compound anti-synchronization’ (MCCAS). Asymptotically stable synchronized states are established between leader and follower systems by employing nonlinear control method and Lyapunov stability criteria. Additional leader systems and hyperchaotic systems enhance the complexity of this synchronization scheme which is useful in secure communication. The information signal can be split and loaded with different signals of leader systems to increase the grade of security. To justify the theoretical results, an example is considered where Pang-Liu, Zheng, Chen, Liu and Newton-Leipnik hyperchaotic systems are considered as leader systems and Lorenz hyperchaotic system is considered as a follower system. Theoretical results are confirmed by graphical analysis.

Multi-switching Synchronization of Four Non-identical Hyperchaotic Systems

The paper addresses a combination synchronization scheme achieved for different switches of three master and one slave hyperchaotic systems. An asymptotically stable synchronized state is derived for different switches of master systems and slave system by using nonlinear control method and Lyapunov stability criteria. To elaborate the presented scheme Pang–Liu hyperchaotic system, Zheng hyperchaotic system and Chen hyperchaotic system are considered as master systems and Newton–Leipnik hyperchaotic system is considered as slave system. Theoretical and graphical results converge to the same conclusion which proves the efficiency of the applied approach.

Anti-synchronization of nonlinear dynamical systems based on Gardano’s method

This letter derives new results for the design of nonlinear controller for the anti-synchronization of two non-identical 4D hyperchaotic systems. The stability results are established using two analytical approaches; Lyapunov’s second method and Gardano’s method. Since the constructing positive definite Lyapunov functions are not required for the Gardano method, the nonlinear control strategy is very effective and convenient to realize the anti-synchronization of non-identical hyperchaotic systems. Furthermore, Gardano method is used to overcome some problem in Lyapunov method which helps to achieve the convergence of error dynamics easily. This proposed method has certain significances for reducing the effort and complexity of controller implementation. Finally, numerical simulations are given to illustrate and verify the results.

Automated adaptive sliding mode control scheme for a class of real complicated systems

A class of real complicated systems, including chemical reactions, biological systems, information processing, laser systems, electrical circuits, information exchange, brain activities modelling, secure communication and other related ones can be presented through nonlinear and non-identical hyper-chaotic systems. The main goal of the present investigation is to synchronize two non-identical hyper-chaotic master/slave systems, which are given as the models of the complicated systems, based on the realization of an efficient automated adaptive sliding mode control scheme. In the research presented here, the mentioned systems need to be dealt with through the proposed control scheme, since two non-identical systems are completely synchronized. In one such case, the whole of the chosen states of the master and slave systems should be coincided after a few time steps, as long as the effect of the external disturbance, uncertainty and unknown parameters could truly be ignored. Due to the fact that the investigated hyper-chaotic systems have taken into consideration as the representation of a number of complicated processes under mentioned external disturbance, uncertainty and unknown parameters, the traditional control approaches cannot actually be realized, in satisfactory manners. With this purpose, the proposed control scheme has been designed to cope with synchronization error, in a reasonable amount of time, in order to drive applicable hyper-chaotic systems. Consequently, the performance of the proposed control scheme is considered and verified through the numerical simulations.

A new color image cryptosystem via hyperchaos synchronization

This paper proposes a novel color image cryptosystem based on synchronization of two different six-dimensional hyperchaotic systems. In the transmitter end, we apply the drive system to generate the diffusion matrices and scrambling ones, which are used to change the image pixel value and position, respectively. Thus the ciphered image is obtained. In the receiver, synchronization of two nonidentical hyperchaotic systems can be achieved by designing the appropriate controllers. The response system is employed to yield the corresponding diffusion matrices and scrambling ones using the same generation method in the encryption algorithm. Then the cipher-image can be decrypted by the decryption algorithm, which is similar to that of the encryption process but in the reversed order. The experimental results show that the presented image cryptosystem has high security and can resist noise and crop attacks.

A new impulsive synchronization of Chen hyper-chaotic system and Lü hyper-chaotic system

This work presents an impulsive synchronization scheme of the Chen hyper-chaotic system and Lü hyper-chaotic system with the assumption that all of the parameters are unknown. Sufficient conditions are derived, based on the impulsive differential stability theory, for achieving the impulsive synchronization with the desired scaling factor. By the adaptive control technique, the control laws and the corresponding parameter update laws are obtained such that the impulsive synchronization of the two non-identical hyper-chaotic systems can be realized. Simulation results also illustrate the effectiveness of the proposed control scheme.

Comment on “Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters”

Comment on “Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters”

Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters

This paper considers the anti-synchronization problem between hyperchaotic Rössler system and hyperchaotic Lorenz system. Two anti-synchronization schemes of them are proposed. Active control is applied when system parameters are known and adaptive control is employed when system parameters are unknown or uncertain. Controllers and update laws of parameters are designed based on Lyapunov stability theory. In both cases, sufficient conditions for the anti-synchronization are obtained analytically. Finally, numerical simulations are provided to show the effectiveness of the proposed schemes.