Observer‐Based Structural Balance Control via Link Subsystem Estimation in Directed Complex Dynamical Networks

This paper mainly solves the problem of structural balance control for directed complex dynamical networks. From the perspective of graph theory, a complex dynamical network is composed of nodes (node subsystem [NS]) and links between they (link subsystem [LS]), which couple with each other and dynamically change over time. Generally, the controller cannot be directly applied to the LS but rather indirectly affects the states of LS through control NS. However, a state observer for LS can be designed to solve the problem of its state being difficult to accurately measure. Thus, based on the estimation information of the observer, a structural balance controller for LS is constructed, and it is proved that the LS can asymptotically track a given structural balance matrix under the observer‐based controller, which implies that the structural balance of the directed complex dynamical network is achieved. Finally, the effectiveness of the proposed method is verified through numerical simulations.