Finite Time Synchronization Of Complex Dynamical Networks Coupled By Outputs

Synchronization has been the research focus of complex dynamical networks. In this paper，finite time inner synchronization of complex dynamical networks is proposed. Compared withinfinite time inner synchronization, it is more valueable in actual engineering. The model ofcomplex dynamical networks coupled by outputs, which is used in the research, is simpler innetwork structure than the model of complex dynamical networks coupled by states. And it avoidsthe waste of resources in actual engineering as well.First, finite time inner synchronization is proposed in this paper. Based on finite time stabilitytheory, the ability of network synchronization is strengthened by the nonlinear processing ofnetwork model. The effectiveness of this method is successfully demonstrated by some illustrativeexamples. It is shown that the error between the nodes states trend towards zero in an exacted time,which means the inner synchronization has been achieved in finite time. Compared with the infinitetime inner synchronization, finite time inner synchronization can be used in actual engineeringwhile not stopping in the theoretical derivation.Second, pinning control of finite time inner synchronization is proposed in this paper. Adrivingnode is connected to at least one node in the network while all the nodes make no effect on it. Allthe nodes states are synchronizaed towards the state of driving node, which makes the result ofsynchronization can be controlled in actual engineering.Finally, finite time external synchronization of complex dynamical networks is proposed. Theeffectiveness of this method is successfully demonstrated by some illustrative examples. Based onthe finite time extern synchronization, finite time topology identification, states estimation and thefault diagnosis can be researched in the future.