Adaptive output regulation and circuit realization for a class of attenuated coupled networks

In this paper, an adaptive regulation method for couplings and its physical implementation are presented to deal with the problem of output synchronization of networks. The networks are supposed to suffer from a fault described by network attenuation. For the sake of eliminating the adverse impact of network attenuation, a self-regulating network is introduced by adjusting coupling strength based on adaptive technique. By using the Lyapunov stability theory for a synchronization error system, asymptotic output synchronization of the overall networks can be established for the attenuated couplings even without any control input. Moreover, based on the adaptive regulation strategy, an approach for application of knowledge of electricity is proposed to physically realize the self-regulating networks. Finally, numerical simulations on a Rössler oscillator network are given to illustrate the effectiveness of the derived results.