Study On Finite Time Synchronization Control Of Complex Networks

Complex networks have been of interest to various scientific fields such as computer science,physics,engineering and sociology due to their wide range of applications.Complex networks can be regarded as consisting of many different nodes and connected edges,where the nodes represent complex systems with different dynamical behaviors,and the connected edges represent the dynamical behaviors between the node systems.Synchronization,as one of the most important dynamical behaviors of complex networks,is a current research topic for scholars both at home and abroad,and relevant scientific research results on synchronization of complex networks have been applied to research on secure communication,information transmission,power systems and multi-intelligent consistency.Therefore,the study of synchronous control problems of various types of complex dynamical networks not only has important application prospects in theory,but also in practice.The main content of this paper is to investigate the finite-time synchronization problems of different complex dynamic networks using adaptive control methods,Lyapunov stability theory,finite-time stability theorems and other related theories,as summarized below.A new four-dimensional chaotic system with hidden dynamics and multi-stability is investigated.Firstly,a detailed study of its dynamical behaviour is carried out using numerical analysis,and the stability of this system equilibrium point is analyzed.secondly,an adaptive control strategy is proposed to bring the new system to a synchronous state,and finally,numerical simulations are carried out to verify the effectiveness of the proposed adaptive control strategy by using Matlab.The problem of enabling general complex network models to achieve both finite-time synchronization and projective synchronization control is investigated.On the basis of achieving asymptotic projection synchronization of general complex networks,the problem of enabling them to achieve finite-time projection synchronization control is further considered.Based on the finite-time stability theorem and the theoretical derivation of the constructed Lyapunov function,a reasonable adaptive control strategy and adaptive update law are also obtained,and some sufficient conditions is proposed for the general network model to accomplish synchronization.Finally,the correctness of the proposed theoretical results is verified by numerical simulation.An effective adaptive controller is designed for the complex network with time-varying delays coupling.According to Lyapunov stability theory and parametric correlation inequalities,some sufficient conditions for the complex network to achieve finite-time projective synchronization are proposed through mathematical derivation.Finally,the classical Lorenz chaotic system is chosen as the node system of the network,and the feasibility of the derived synchronous control scheme is verified by numerical simulation.