Research On Finite-time Consensus And Synchronization Of Complex Systems

With the rapid development of modern artificial intelligence technology(AI),complex systems have attracted great attention from experts and scholars due to their related research results being widely used in engineering practice and many fields of subject research.Corre-spondingly,the dynamic performance of complex systems has become a hot topic in the field of control.In the meantime,in contemporary society where complexity and timeliness are par-ticularly prominent,the project continues to put forward higher requirements for the stability and convergence rate of complex systems in various practices.Therefore,based on time op-timal control,scholars have proposed the concept of finite-time stability.Different from the traditional asymptotic stability control strategy,the finite-time control has the advantages of faster convergence speed,stronger robustness and disturbance rejection properties.Therefore,the finite-time control of complex systems has become a continuous research hotspot in the field of control at home and abroad in recent years.The relevant research undoubtedly has not only important academic value but also practical application significance.In the context of the above research,based on Graph theory,Lyapunov stability theory,linear matrix inequal-ity,impulsive control theory,event-trigger mechanism,finite-time stability theory,and other modern control theory,this dissertation studies the finite-time consensus and synchronization problems of complex network systems,and gives the corresponding sufficiency criterion.The main contributions of this dissertation are as follows:1.In the introduction,the research background and research significance of complex systems and finite-time control problems are discussed.Then,the current research status of the finite-time consensus and synchronization problem of complex systems are summarized from three different types of complex systems:complex networks,multi-agent systems and neural networks.Subsequently,the relevant preliminary,definitions,lemmas and theorems for follow-up research are given.Finally,the main research content of the subsequent chapters of this article and the arrangement of each chapter are briefly introduced.2.The finite-time synchronization problem of a class of Markov jump complex networks with non-identical nodes and impulsive effects is studied.Based on M matrix technology,Lyapunov function method,stochastic analysis technology and appropriate comparison system,sufficient conditions for Markov jump complex networks to ensure finite-time synchronization are given.Finally,a numerical example is used to verify the validity of the obtained theoretical results,that is,the controller designed in the article can synchronize the complex dynamic system with the isolated node in the finite time.3.The finite-time and fixed-time consensus of nonlinear stochastic multi-agent systems(NSMSs)with randomly occurring uncertainties(ROUs)and randomly occurring nonlinear-ities(RONs)are discussed.First,this chapter designed a non-linear control and impulsive pinning control protocol to ensure that the follower agents and the leader agents reach con-sensus within the finite time.Based on the finite-time consensus theory,stochastic analysis technology,comparison system theory and algebraic graph theory,some sufficient conditions to ensure the finite-time consensus of the systems are proposed,and the settling time relied on the initial state of the systems is estimated.Then,this chapter further designed the fixed-time controller,and based on the same analysis method,sufficient conditions are obtained to ensure that the system achieves consensus within the fixed time.It is worth noting that the estimated settling time has nothing to do with the initial state of the systems.Finally,two simulation examples are given to verify the correctness of the main results of this chapter.4.The finite-time synchronization problem of impulsive delayed neural networks with stochastic disturbances is studied.By constructing a suitable Lyapunov-Krasovskii functional,using stochastic analysis theory and linear matrix inequalities(LMIs),sufficient conditions to ensure that the networks are synchronized within the finite time are obtained.And according to the initial state,the settling time of the neural networks can be estimated.It is worth noting that,unlike many existing finite-time controllers,the control protocol designed in this chapter does not include the sign function that will cause the system to chatter.Finally,the numerical simulation is used to illustrate the validity of theoretical analysis.5.The finite-time stability and stabilization of impulsive stochastic delayed neural net-work with ROUs and RONs are studied.First,by constructing an appropriate Lyapunov-Krasovskii functional and introducing the concept of the average impulsive interval,based on LMIs,a new criterion to ensure the finite-time stability of the impulsive stochastic delayed neural network is obtained.Secondly,designed a state feedback controller to ensure that the studied object networks can be stabilized in the finite time..Finally,the numerical examples verify the validity and feasibility of the proposed results6.Based on the event-triggered impulse control method,the leader-following finite-time consensus problem of nonlinear multi-agent systems is studied.Firstly,the target controller is designed by combining discrete event-triggered impulsive control and continuous finite-time control,where the generation of the impulsive moment depends on the proposed event-triggered function.For this event trigger function,it not only determines the work time of impulsive control,but also affects the update time of the finite-time control.It is worth noting that,compared with the existing finite-time controller,the controller designed in this chap-ter does not contain any sign function,thereby overcoming the chattering phenomenon.In addition,the designed trigger function and control protocol can respectively ensure that the system eliminates Zeno behavior during the control process and achieves the ultimate leader-following finite-time consensus.Finally,simulations verify the effectiveness of the proposed control scheme.