Adaptive control for synchronization of time‐delayed complex networks with multi‐weights based on semi‐linear hyperbolic PDEs

This paper studies the adaptive synchronization of complex spatio‐temporal networks modeled by semi‐linear hyperbolic partial differential equations (CSTNSLHPDEs) as well as considering time‐invariant and time‐varying delays in a one‐dimensional space. Firstly, a distributed adaptive controller is proposed, where different nodes are with different adaptive gains. Secondly, four cases, CSTNSLHPDEs with time‐invariant delays and one single weight, with time‐invariant delays and multi‐weights, with time‐varying delays and one single weight, and with time‐varying delays and multi‐weights, are successively analyzed, and synchronization conditions of these four cases are obtained by using the proposed distributed adaptive controller. In the end, examples illustrate the effectiveness of the proposed distributed adaptive controller.