Synchronization Control For Severalkinds Of Stochastic Complex Networks

With the rapid development of network information technology represented by the Internet,human society has entered the era of complex networks.Many phenomena in the real world can be described and analyzed through complex networks.Nowadays,the research on complex networks has attracted great attention from scholars at home and abroad in the fields of computer,communication security,engineering technology and so on.In the study of complex networks and their dynamic behavior,synchronous behavior has become a key research topic in control systems.Due to the random disturbances caused by various external environments,complex networks often exhibit certain random characteristics,including random noise,random delay,Markov jumping,etc.In view of this,this thesis carries out a series of researches on the synchronization control problem of complex networks under random background.The main contents are summarized as the following aspects:The first part is dedicated to the exponential synchronization problem of Markovian jumping coupled neural networks by utilizing event-triggered pinning control.Firstly,the coupling matrix of the network and the designed pinning feedback control gain both undergo Markov switching with partial unknown transition rate.Secondly,based on a suitable Lyapunov function,stochastic analysis technique and M-matrix theory,some sufficient conditions for the network to realize exponential synchronization in mean square sense are established,and a strict proof to eliminate Zeno phenomenon is given.Finally,the correctness of the conclusion is verified by numerical simulation.The second part discusses the finite-time synchronization problem of delayed stochastic complex networks by using quantized aperiodically intermittent control.Firstly,a complex network model with random coupling time delay and stochastic disturbance is proposed.Secondly,by means of Lyapunov stability theory,Ito formula and graph theory,two types of sufficient conditions for the network to realize finite-time synchronization are derived.Finally,the theoretical results are further applied to the finite-time synchronization of stochastic coupled oscillators,and the validity and feasibility of the theoretical results are verified by a numerical example.The third part investigates the cluster synchronization problem of stochastic complex networks based on fixed-time control.By designing two different control schemes,the cluster synchronization criteria of network convergence in probability respectively are established based on the fixed-time stability theory of stochastic systems and some important inequalities.In addition,the high precision estimation of synchronization time is given,and the numerical simulation is provided to verify the effectiveness of the two control strategies.