Research Of Synchronization Of Complex Value Networks Based On Adaptive Control

As a popularization of real-valued complex networks,complex-valued networks have received extensive attention from researchers due to their advantages of containing more information and fast calculation speed.Synchronization,as a kind of network dynamic behavior,has become an important research topic in the field of automatic control and information science.Based on the adaptive control strategy,this paper takes the complex-valued network as the research object,and studies the global finite/fixed-time synchronization problem of the discontinuous complex-valued network.The main work is as follows:Firstly,the stochastic semi-Markov process is combined with the complex-valued network system,and a complex-valued network system model with semi-Markov switching is proposed.For the discontinuous complex-valued network with semi-Markov switching,the generalized Lyapunov stability theory is applied under the designed adaptive controller,and the global fixed time synchronization condition is established in the form of linear matrix inequality.Secondly,for the fractional quaternary valued discontinuous complex valued network,under the designed fractional order adaptive controller,we apply the generalized Lyapunov functional method and matrix inequality analysis techniques to establish global Mittag-Leffler synchronization and finite time synchronization conditions in the form of linear matrix inequalities.Finally,for the nonlinear fractional-order quaternion-valued complex-valued network with hybrid coupling,by constructing the Lyapunov functional,the global finite/fixed time synchronization condition is given in the form of linear matrix inequality under the designed adaptive controller.Furthermore,an accurate estimate of the upper bound of the residence time is given.