Distributed tracking control of structural balance for complex dynamical networks based on the coupling targets of nodes and links

Abstract

Abstract In this paper, the complex dynamical networks (CDNs) with dynamic connections are regarded as an interconnected systems composed of intercoupling links’ subsystem (LS) and nodes’ subsystem (NS). Different from the previous researches on structural balance control of CDNs, the directed CDNs’ structural balance problem is solved. Considering the state of links cannot be measured accurately in practice, we can control the nodes’ state and enforce the weights of links to satisfy the conditions of structural balance via effective coupling. To achieve this aim, a coupling strategy between a predetermined matrix of the structural balance and a reference tracking target of NS is established by the correlative control method. Here, the controller in NS is used to track the reference tracking target, and indirectly let LS track the predetermined matrix and reach a structural balance by the effective coupling for directed and undirected networks. Finally, numerical simulations are presented to verify the theoretical results.

Keywords

• Complex dynamical networks
• Structural balance
• Links
• Effective coupling
• Correlative control