Finite-time Based Synchronization Control For Complex Dynamical Networks

Nowadays,with the rapid development of computer and information science and technology,the dynamics analysis of complex networks has attracted the interest of a large number of scholars with wide applications in various fields.Synchronization,as one of the most important dynamic characteristics of complex networks,is a typical collective behavior of complex networks,which commonly exists in a variety of complex networks.Then,due to a great deal of communication interaction between network nodes,the dynamic event-triggering scheme is introduced to schedule the transmission of control signals in order to effectively save the limited network resources and decrease control costs.In addition,in engineering applications,it is often required that the system achieves transient performance over a specific time period instead of steady performance.To this end,it is of vital significance to investigate the finite-time performance(finite-time bounded synchronization and finite-time H_∞synchronization)of complex networks.Based on the above discussions,in the thesis,for the event-based discrete time-delayed complex network,we mainly investigate 1)the finite-time pinning synchronization control problem and 2)the finite-time non-fragile H_∞synchronization control problem under switched topologies.To be more specific,the main work is as follows.(1)The synchronization control issue is investigated for a kind of nonlinear discrete time-delayed complex dynamical networks.To improve energy efficiency,a dynamic event-triggering strategy is introduced to regulate the signal transmission from the controller to the actuator.Then,the event-based pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in control process.Subsequently,a new concept of finite-time boundedness in the mean square is put forward to evaluate the synchronization control performance by means of a settling-like time function.Furthermore,by using the Lyapunov stability theory and the stochastic analysis technique,a sufficient condition is provided to ensure that the synchronization error is finite-time bounded in the mean square with a prescribed error upper bound in the presence of both time delays and external noise disturbances.By solving an optimization problem with some inequality constraints,the desired controller gain matrix is parameterized to minimize the settling-like time.Finally,a numerical simulation example is carried out to illustrate the effectiveness and usefulness of the obtained theoretical results.(2)The problem of the event-triggered finite-time non-fragile H_∞synchronization control is addressed for a class of discrete time-delayed complex networks with switched topology.To decrease the unnecessary signal transmission and save control cost,the dynamic event-triggering scheme is employed in the controller-to-actuator channel where the varying triggering threshold is governed by a dynamical equation.The main purpose of this paper is to design a non-fragile synchronization controller such that the synchronization error dynamics satisfy both the finite-time boundedness and the H_∞disturbance rejection level.By constructing appropriate Lyapunov-Krasovskii functional and using the average-dwell-time technique,the desired controller gains are acquired in terms of the solution to a set of linear matrix inequalities.Finally,a numerical simulation example is provided to demonstrate the effectiveness of the proposed synchronization controller design scheme.