Research On Impulsive Synchronization And Control Of Stochastic Complex Networks

Complex networks have attracted a great deal of attention of scholars from different fields,since complex networks have the interdisciplinary characteristics of communication,computation science and control science,etc.Synchronization of complex network has become a research hot topic.In this dissertation,we mainly investigate the problem of synchronization control of complex networks and consensus of multi-agent systems.The study subjects are stochastic complex networks and stochastic multi-agent systems.Considering a variety of different constraints,we investigate about the problem of mean square consensus of leader-following multi-agent systems with measurement noises and time delays,exponential consensus of nonlinear stochastic multi-agent systems with random occurring uncertainty and random occurring nonlinearity via impulsive pinning control,impulsive pinning control algorithm of stochastic multi-agent systems with unbounded distributed delays,finite time synchronization of Markovian jumping stochastic complex dynamical systems with mix delays via hybrid control strategy,respectively.Some basic analysis tools of dynamic system theory such as Lyapunov stability theory,impulsive Halanay inequality,linear matrix inequality,Gronwall-Bellman-Halanay type inequality,impulsive control theory,finite time stability theory and modern control theory are applied.Sufficient conditions for the complex network system to achieve synchronization are established by using the state feedback control protocol,impulsive control protocol,impulsive pinning control protocol,hybrid control protocol and other control scheme.The main contents and innovative points are presented as follows:1.The research background and significance of stochastic synchronization of complex networks and stochastic multi-agent consensus are introduced.The dynamic characteristics of complex network,complex network topology,constraints of complex network,synchronization control strategy of complex networks are summarized,respectively.Some preliminaries and related theorems,lemmas and definitions are given.Finally the main research contents and chapters arrangement are introduced.2.The mean square consensus problem of dynamical networks of leader-following multi-agent systems with measurement noises and time-varying delays are investigated.We consider that the fixed undirected communication topologies are connected.A neighbor-based tracking algorithm together with distributed estimators are presented.Using tools of algebraic graph theory and the Gronwall-Bellman-Halanay type inequality,we establish sufficient conditions to reach consensus in mean square sense via the proposed consensus protocols.3.Exponential consensus of nonlinear stochastic multi-agent systems is investigated.we consider a class of nonlinear stochastic multi-agent systems that are subject to timevarying delays,randomly occurring uncertainties and randomly occurring nonlinearities.Impulsive pinning control algorithms are proposed to ensure that follower agents track the leader under a fixed topology.On the basis of the Lyapunov function and the Halanay differential inequality of impulsive dynamical systems,we derive sufficient conditions for the globally exponential consensus of the multi-agent systems.4.The exponential consensus problem is investigated for a class of stochastic multiagent systems with discrete time-varying delays and unbounded distributed delays.Two kinds of delayed impulsive pinning control protocol are presented,which are different from the existing results of free-delayed impulsive pinning controllers.By employing the method of Lyapunov function theory and the Halanay inequality of impulsive type,sufficient conditions are derived to guarantee that the stochastic multi-agent systems are exponentially consensus in mean square under the presented impulsive pinning control protocol.It is shown that the global exponential consensus of stochastic multi-agent systems can be effectively realized by controlling a small fraction of agents in multi-agent systems via delayed impulses.5.Finite-time synchronization problem for a class of Markovian jumping stochastic complex dynamical systems with mixed time delays is investigated.Hybrid controllers including nonlinear controller and impulsive controller are designed for the model to be finite-time stabilization.Based on stochastic analysis technique,Lyapunov function method and the technique of inequalities,some sufficient criterion for the stochastic complex dynamical networks are presented which guarantee the finite-time synchronization for the model considered.Finally,the conclusions and some topics for future work are given.