Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller

Abstract

The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and between integer-order hyperchaotic Chen system and fractional-order hyperchaotic Rössler system is used to illustrate the effectiveness of the proposed synchronization approach. Numerical simulations coincide with the theoretical analysis.

Synchronization of Fractional-Order Chaotic Systems with Model Uncertainty and External Disturbance

“…Although scholars have made great achievements in the control of fractional-order chaotic systems, there are still many challenges and problems to be solved. For instance, there are too many combinations of controllers and control channels, and the control technology designed in [30][31][32][33][34] does not take the uncertainty of the system into account.…”

Dynamic Analysis of Complex Synchronization Schemes between Integer Order and Fractional Order Chaotic Systems with Different Dimensions

“…At present, many schemes of control have been proposed to study the problem of synchronization between integer order and fractional order chaotic systems such as anticipating synchronization [16], function projective synchronization [17], complete synchronization [18], antisynchronization [19], Q-S synchronization [20], and generalized synchronization [21]. Also, different techniques have been introduced to synchronize integer order and fractional order chaotic systems.…”

“…In [25], general control scheme has been described. A new fuzzy sliding mode method has been proposed in [26], and a sliding mode method has been designed in [27,28]. Synchronization of a class of hyperchaotic systems has been studied in [29].…”

A Robust Control Method forQ-SSynchronization between Different Dimensional Integer-Order and Fractional-Order Chaotic Systems

“…For example, general control schemes have been described in [7,8]. A sliding mode method has been designed in [9][10][11]. A synchronization method of a class of hyperchaotic systems is given in [12].…”

“…In [13], a nonlinear feedback control method has been introduced and some robust observer techniques have been used in [14,15]. Also, complete synchronization and antisynchronization have been observed, for example, in [16][17][18], and function projective synchronization has been studied in [19]. Until now, a variety of control schemes have been proposed to study the problem of chaos synchronization between different dimensional systems such as modified function projective synchronization [20], generalized matrix projective synchronization [21], generalized synchronization [22][23][24], inverse generalized synchronization [25], full state hybrid projective synchronization [26], Q-S synchronization [27], increased order synchronization [28,29], and reduced order generalized synchronization [30].…”