A novel adaptive-impulsive synchronization of fractional-order chaotic systems

Abstract

A novel adaptive-impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors' bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive-impulsive control scheme.

Cluster synchronization of community network with distributed time delays via impulsive control

“…In recent years, synchronization has gained extensive attention from various fields on account of its broad practical applications, such as regulation of power grid, parallel image processing, the operation of no-man air vehicle, the realization of chain detonation, etc. [12,13] Cluster synchronization, [14][15][16][17][18][19][20][21][22] a special synchronization of complex dynamical networks, denotes that synchronization of the nodes in the same community can be achieved, but synchronization of the nodes in different communities cannot be achieved. That is, the nodes in the same or different communities have identical or nonidentical goals.…”

Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

“…In other words, they are assumed to be bounded; meanwhile inequalities (14) and (15) are satisfied. In order to verify Assumptions 2 and 3, we give the simulation results in Figure 1, which shows the boundedness of Δ ( ) ,…”

“…Therefore, the analysis and control/synchronization of fractional-order dynamical chaotic systems are important in both theory and practice. Up till now, many control/synchronization methods, such as active control [12], active sliding mode control [13], adaptive-impulsive control [14], fuzzy adaptive control [15], and generalized projective synchronization [16] and the references therein, have been successfully applied to control/synchronize the chaos of fractional-order chaotic systems.…”

Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications

“…When the model of a system includes at least one fractional derivative or integral term, we call it a fractional-order system. As fractional-order calculus provides more accurate models of systems than integer-order calculus does, recently synchronization control schemes for fractional-order chaotic systems have been proposed, such as active control (Agrawal et al, 2012), active sliding mode control (Wang et al, 2012), adaptive–impulsive control (Andrew et al, 2015), fuzzy adaptive control (Bouzeriba et al, 2016), generalized projective synchronization (Peng and Jiang, 2008). Furthermore, a projective synchronization was discussed in Ding (2009) and Zhou et al (2015) for fractional-order chaotic systems and later, a modified projective synchronization for fractional-order hyperchaotic systems was proposed in Bai et al (2012).…”