Model Following Adaptive Control of Links for the Complex Dynamical Network via the State Observer

This paper investigates the model following adaptive control (MFAC) problem for the dynamic links of complex dynamical network, in which the dynamic links are regarded wholly as the link subsystem (LS) with the weighted values of links as its state variables. Firstly, the dynamics of LS is modeled by the Riccati matrix differential equation with the term coupled to the state of nodes. Then the asymptotic state observer of LS is constructed to overcome the limitation of it’s state unavailability. Based on this, combined with the Lyapunov stability theory, the state feedback controllers of node subsystem (NS) and LS are synthesized such that MFAC of links is ensured. Compared with the existing literature, the significant difference in this paper is that the objects of MFAC are the links instead of the nodes. Furthermore, due to the coupling effect between the nodes and the links in the complex dynamical network, the model matching conditions (MMCs) are greatly simplified, by which the NS also has the designed auxiliary tracking target when the MFAC of links is achieved. In other words, when the asymptotically MFAC for LS is realized, the NS can also asymptotically tracks the designed auxiliary tracking target. Finally, the numerical simulation is given to verify the effectiveness of the control scheme proposed in this paper.