Cluster synchronization in nonlinear complex networks under sliding mode control

Abstract

This paper investigates the cluster synchronization for network of nonlinear systems via differential mean value theorem method and sliding mode control strategy. Because of the existence of the nonlinear dynamics, the differential mean value theorem method is used to transform the nonlinear error complex network system into a linear parameter-varying system. Since the robustness to the uncertainties of the sliding mode, we can deal with the linear parametervarying system which contains the time-varying mismatched uncertainties by applying the sliding mode control strategy through the equivalent transformation. In addition, appropriate linear matrix inequality stability condition by the Lyapunov method is derived such that each subsystem in the new sliding mode is completely invariant to both matched and mismatched uncertainties. Finally, simulation example is shown to illustrate the effectiveness of the proposed method.

Bounded synchronization of complex dynamical networks with prescribed performance via event‐based transmission strategy

“…The synchronization problems of CNs with control packet loss were researched in the work of Rakkiyappan and Sakthivel 20 by designing pinning state feedback controller. In the work of Hou et al, 21 by sliding-mode control method and differential mean value theorem scheme, the cluster synchronization of complex systems is investigated. The synchronization results of CNs with impulses were considered in the work of Yang et al 22 by designing the nonchattering control.…”

Adaptive synchronisation for a class of output‐coupling complex networks with output feedback nodes

“…While some interesting conditions about the numbers of pinned nodes and the strength of couplings for the synchronisation of complex networks were gotten in [14]. Slide‐mode approach was used to address the synchronisation in [15, 16]. Ling et al and Yuan et al [17, 18] got the synchronisation result by means of the back stepping approach.…”

Finite/fixed-time synchronization for complex networks via quantized adaptive control

“…Synchronization, which means that all dynamic nodes tend common dynamic behavior, is a typical dynamic phenomenon in complex networks. In recent years, various synchronization control strategies have been provided, which mainly include impulsive control [7], adaptive control [5,12], sliding mode control [10], periodic intermittent control [18], and pinning control [20] etc.…”

“…By choosing of parameters r, θ, such that r θ ∈ (0, 1) and s and v are in different parameter ranges, which results in different settling time. When s < v, it can be seen from (10) and (28) that the settling time is dependent of the initial value. While s > v, it can be seen from (11) and (29) that the settling time is independent of the initial value, which is only dependent of the parameters of the controller.…”