Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

The synchronization problem of chaotic systems using active modified projective nonlinear control method is rarely addressed. Thus the concentration of this study is to derive a modified projective controller to synchronize the two chaotic systems. Since, the parameter of the master and follower systems are considered known, so active methods are employed instead of adaptive methods. The validity of the proposed controller is studied by means of the Lyapunov stability theorem. Furthermore, some numerical simulations are shown to verify the validity of the theoretical discussions. The results demonstrate the effectiveness of the proposed method in both speed and accuracy points of views

Adaptive hybrid function projective synchronization of chaotic systems with fully unknown periodical time-varying parameters

In this paper, an adaptive learning control approach is presented for the hybrid functional projective synchronization (HFPS) of different chaotic systems with fully unknown periodical time-varying parameters. Differential-difference hybrid parametric learning laws and an adaptive learning control law are constructed via the Lyapunov–Krasovskii functional stability theory, which make the states of two different chaotic systems asymptotically synchronized in the sense of mean square norm. Moreover, the boundedness of the parameter estimates are also obtained. The Lorenz system and Chen system are illustrated to show the effectiveness of the hybrid functional projective synchronization scheme

A Robust Control Method for Q

A robust control approach is presented to study the problem of Q-S synchronization between Integer-order and fractional-order chaotic systems with different dimensions. Based on Laplace transformation and stability theory of linear integer-order dynamical systems, a new control law is proposed to guarantee the Q-S synchronization between n-dimensional integer-order master system and m-dimensional fractional-order slave system. This paper provides further contribution to the topic of Q-S chaos synchronization between integer-order and fractional-order systems and introduces a general control scheme that can be applied to wide classes of chaotic and hyperchaotic systems. Illustrative example and numerical simulations are used to show the effectiveness of the proposed method

An optimal control for complete synchronization of 4D Rabinovich hyperchaotic systems

This paper derives new results for the complete synchronization of 4D identical Rabinovich hyperchaotic systems by using two strategies: active and nonlinear control. Nonlinear control strategy is considered as one of the powerful tool for controlling the dynamical systems. The stabilization results of error dynamics systems are established based on Lyapunov second method. Control is designed via the relevant variables of drive and response systems. In comparison with previous strategies, the current controller (nonlinear control) focuses on convergence speed and the minimum limits of relevant variables. Better performance is to achieve full synchronization by designing the control with fewer terms. The proposed control has certain significance for reducing the time and complexity for strategy implementation