1,171 research outputs found

    Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

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    Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods

    Synchronization of Fractional-order Chaotic Systems with Gaussian fluctuation by Sliding Mode Control

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    This paper is devoted to the problem of synchronization between fractional-order chaotic systems with Gaussian fluctuation by the method of fractional-order sliding mode control. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode control technique is carried out to realize the synchronization of the given systems. One theorem about sliding mode controller is presented to prove the proposed controller can make the system synchronize. As a case study, the presented method is applied to the fractional-order Chen-L\"u system as the drive-response dynamical system. Simulation results show a good performance of the proposed control approach in synchronizing the chaotic systems in presence of Gaussian noise

    Synchronization and antisynchronization protocol design of chaotic nonlinear gyros: an adaptive integral sliding mode approach

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    A novel control protocol design, via integral sliding mode control with parameter update laws, for synchronization and desynchronization of a chaotic nonlinear gyro with unknown parameters is the focus of this work. The error dynamics of the actual system are substructured into nominal and uncertain parts to employ adaptive integral sliding mode (AISM) control. The uncertain parameters are estimated via devised adaptive laws. Then the disagreement dynamics are guided to origin via AISM control. The stabilizing controller is also designed in terms of nominal control along with a compensating component. The control and the parameter update laws are constructed to ensure the strictly negative derivative of a Lyapunov function. Graphical results related to synchronization, desynchronization, and chaos suppression are displayed to demonstrate the potential of the proposed control

    Passivity-Sliding Mode Control of Uncertain Chaotic Systems with Stochastic Disturbances

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    This paper is concerned with the stabilization problem of uncertain chaotic systems with stochastic disturbances. A novel sliding function is designed, and then a sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time. Using a virtual state feedback control technique, sufficient condition for the mean square asymptotic stability and passivity of sliding mode dynamics is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method
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