| The dynamic properties of complex networks have become one of the hot topics.Although the network topology has an important impact on the dynamic properties,it is difficult for complex networks to achieve the expected dynamic properties through their own topology.It is very meaningful to use control strategies to achieve the expected dynamic properties of complex networks.Intermittent control has more advantages than continuous control in saving energy,reducing the amount of information transmission and flexible operation,so it has attracted the attention of many scholars.However,most of the existing intermittent control is based on continuous-time state observations in the control interval.In order to improve further the control,this thesis propos a class of periodically/aperiodically intermittent discrete observation control and aperiodically intermittent discrete observation noise control,which are based on the discrete-time state observation during the control interval,and its broadens the application scope of intermittent control.In this thesis,based on Lyapunov second method,Tarjan algorithm,Kirchhoff Matrix Tree Theorem in graph theory,and stochastic analysis techniques,the dynamic properties of complex networks are studied in the following four aspects:The exponential synchronization of stochastic complex networks with and without strong connectivity is discussed,respectively.And the coupling structure of networks is time-varying.A periodically intermittent control based on discrete-time state observation,instead of continuous-time state observation during the control time,is introduced.Based on Lyapunov second method,Kirchhoff Matrix Tree Theorem in graph theory,and Tarjan algorithm,some sufficient conditions are obtained.Especially,when the proposed control degenerates to discrete-time state observable control,the theoretical results are also discussed in detail.Aperiodically intermittent discrete observation control is proposed,and the exponential stability of stochastic complex networks with Markov switching topology is studied.It is worth emphasizing that the topological structure of the stochastic control system is Markov switching and it is neither required that all switching subnetworks contain a spanning tree nor that they are strongly connected.Based on the Lyapunov second method and the Kirchhoff Matrix Tree Theorem in graph theory,the sufficient conditions for exponential stability of stochastic complex networks with Markov switching topology are established.In addition,the theoretical results are applied to the stochastic coupled oscillator system and communication network model.The almost sure exponential synchronization of complex networks is discussed by designing noise control,that is,aperiodically intermittent discrete observation noise control.It is worth noting that the state in noise work time is discretely observed rather than continuously.At the same time,based on stochastic analysis technique and Lyapunov second method,some sufficient conditions are given.Besides,the upper bounds of noise rest rate and the duration between two consecutive observations are estimated.An aperiodically intermittent discrete observation noise consensus protocol is introduced.Using the proposed noise consensus protocol,the almost sure exponential consensus of multi-agent systems is studied.By using Lyapunov second method and stochastic comparison principle,some sufficient conditions for almost sure exponential consensus of multi-agent systems are obtained.In addition,the upper bounds of the rest rate of intermittent communication noise and the duration between two consecutive observations are estimated.Furthermore,the established results are applied to the single-link robot arm systems. |
