Abstract
This paper is devoted to investigating the cluster synchronization of a class of nonlinearly coupled Lur’e networks. A novel adaptive pinning control strategy is introduced, which is beneficial to achieve cluster synchronization of the Lur’e systems in the same cluster and weaken the directed connections of the Lur’e systems in different clusters. The coupled complex networks consisting of not only identical Lur’e systems but also nonidentical Lur’e systems are discussed, respectively. Based on the S-procedure and the concept of acceptable nonlinear continuous function class, sufficient conditions are obtained which prove that the complex dynamical networks can be pinned to the heterogeneous solutions for any initial values. In addition, effective and comparatively small control strengths are acquired by the designing of the adaptive updating algorithm. Finally, a numerical simulation is presented to illustrate the proposed theorems and the control schemes.
Highlights
Complex dynamical networks (CDNs), as the special examples of complex systems, could be generally regarded as composing of interacted multiple nodes or systems
Synchronization signifies the states of nodes or systems in complex networks converge to a desired trajectory
The main contribution of this article can be concluded as follows: (1) The dynamical networks composed of identical Lur’e systems and nonidentical Lur’e systems are discussed respectively, making our analysis universally valid [31]; (2) To solve the nonlinear characteristic of individual system and nonlinear coupling situation, effective methods like S-procedure and the concept of acceptable nonlinear continuous function class are introduced [30]; (3) Sufficient conditions for the cluster synchronization of the nonlinearly coupled complex networks consisting of identical and nonidentical Lur’e systems are derived in the forms of linear matrix inequality (LMI), respectively [32]; (4) Adaptive strategy is introduced in order to acquire some proper control strengths by designing the adaptive update laws, which only requires the information of the controlled nodes themselves and largely saves control costs [33]
Summary
Complex dynamical networks (CDNs), as the special examples of complex systems, could be generally regarded as composing of interacted multiple nodes or systems. Inspired by the above analysis, this work aims to study the cluster synchronization problem of coupled complex networks consisting of identical and nonidentical Lur’e systems. (2) To solve the nonlinear characteristic of individual system and nonlinear coupling situation, effective methods like S-procedure and the concept of acceptable nonlinear continuous function class are introduced [30]; (3) Sufficient conditions for the cluster synchronization of the nonlinearly coupled complex networks consisting of identical and nonidentical Lur’e systems are derived in the forms of LMI, respectively [32]; (4) Adaptive strategy is introduced in order to acquire some proper control strengths by designing the adaptive update laws, which only requires the information of the controlled nodes themselves and largely saves control costs [33].
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