Research On The Approaches Of Finite Time Synchronization Control For Complex Networks

Currently, research on complex network has been involving lots of scientific fields, and the research of synchronization for complex networks has become the keen focus of researchers. In practical application, finite time control enjoys such advantages as strong robustness and rapidity. Therefore, research on the approaches of finite time synchronization control for complex networks is of great significance both in theoretical research and practical application.This paper develops relevant research on this aspect based on finite time stability theory and self-adaptive thought.Firstly, aiming at finite time synchronization of complex network with linear coupling, two non-smooth continuous control protocols are proposed and nonlinear part is introduced to enhance the synchronization capabilities of network. Based on the matrix theory and the finite time stability lemma of Lyapunov, finite time synchronization of complex networks is realized by selecting proper coupling strength. The validity and effectiveness of the proposed scheme are verified through synchronization simulation instances of Chen system and Lii system. Under the condition that the internal states of complex networks are unmeasurable, the finite time synchronization problem of output coupling is discussed and the sufficient conditions are obtained to ensure finite time synchronization of complex networks, and the effectiveness of the control scheme proposed is verified by the simulation of Chen system.Secondly, aiming at complex networks with unknown coupling parameters, the finit time self-adaptive synchronization problem is considered, and non-smooth control protocol and the self-adaptive law of parameters are designed, the sufficient condition is obtained of the synchronization of undirected connected networks according to stability principle so as to lower the conservative property of the value choice of coupling parameter. Finally, the feasibility of approach proposed is verified by simulation examples.Thirdly, aiming at the uncertain complex networks with nodes containing unknown nonlinear dynamic, the finite time ultimately uniformly synchronization control is discussed. By applying the approximation ability of neural network, the unknown nonlinear part is compensated. Moreover, distribution control protocol is designed applying state feedback idea. The self-adaptive law of neural network weights is developed and the sufficient conditions is obtained to realize the finite ultimately uniformly synchronization of complex networks by ultimately uniform boundedness theorem. At last, the feasibility and accuracy of the proposed scheme are verified by simulations.Finally, the research on the synchronization of complex networks is concluded and discussed, and the research direction is proposed of the further study of finite time synchronous control of complex networks.