Distributed Error Estimation for Quasi-Synchronization of Heterogeneous Dynamical Networks

This article proposes a distributed error estimation approach to investigate the quasi-synchronization problem of heterogeneous dynamical networks with static and adaptive coupling laws under a directed communication topology. By introducing a pining control strategy, a novel class of distributed error estimation algorithms is proposed for solving the quasi-synchronization problem of heterogeneous dynamical networks with a static coupling law by exploring the local information among the neighboring nodes. By removing the assumption that the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph must be known, we also address the case of the quasi-synchronization of heterogeneous dynamical networks with nonidentical nonlinear dynamics and an adaptive coupling law. It is proved, in the sense of Lyapunov function, that the distributed error estimation for the quasi-synchronization problem of heterogeneous dynamical networks with static and adaptive coupling laws will be achieved with a bounded synchronization error level. Finally, two examples are presented to demonstrate the effectiveness of the proposed approaches.