Abstract
This paper investigates the control and synchronization of a class of 3-D uncertain fractional-order chaotic systems with external disturbances. The adding one power integrator control scheme, which is the generalization of the traditional backstepping method, is used to investigate the global stability of the control and synchronization manifold. As a result, several criteria for chaos control and synchronization are obtained. Compared with the previous results, the presented strategies can not only be applied to a class of strict-feedback systems but also be applied to more general class of fractional-order chaotic systems. In addition, the proposed controllers are robust against uncertain parameters and external disturbances. To validate the effectiveness of the proposed criteria, two illustrative examples are given.
Highlights
Chaotic systems, which are characterized by possessing at least one positive Lyapunov exponent, are a special case of nonlinear deterministic systems with unpredictable behaviors
This paper investigates the control and synchronization of a class of 3-D uncertain fractional-order chaotic systems with external disturbances
Chaos control and synchronization of fractional-order chaotic systems have attracted extensive attention of researchers and many results have been proposed by employing different control methods such as backstepping control method [2], sliding mode control method [3, 4], PID control approach [5], periodically intermittent control strategy [6], adaptive fuzzy backstepping control [7], and adaptive fuzzy prescribed performance control [8]
Summary
Chaotic systems, which are characterized by possessing at least one positive Lyapunov exponent, are a special case of nonlinear deterministic systems with unpredictable behaviors. Papers [11, 12] investigated the stabilization and synchronization of a class of fractional-order chaotic systems via backstepping approach. The stabilization problem of a class of fractional-order chaotic systems with unknown parameters by using adaptive backstepping strategy was considered in [14]. This schemes presented in papers [10,11,12,13,14] can only be used for nonlinear systems with strict-feedback structure. Motivated by the above discussions this paper considers the control and synchronization of a class of 3-D fractionalorder chaotic systems This chaotic system with uncertain parameters is assumed to be affected by external disturbances.
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