Predefined-Time Robust Synchronization Control For Complex Networks

Complex networks(CNs)are networks coupled by large-scale nodes having very complex topological structures and dynamical behaviors,which have part(or all)properties of self-organization,self-similarity,attractor,small world,and scale-free.By exploring the CNs,we would like to better understand and regulate the actual complex systems in real world,such as the communication networks,social networks,neural networks in brain,public transportation networks and so on.Synchronization is a kind of important dynamic behavior of CNs.As a special case of the fixed-time synchronization,predefined-time synchronization could make the CN realize synchronization within a predefined-time,which is independent of the initial conditions,system parameters and other controller parameters.Uptill now,relatively few research attention has been put on the predefined-time synchronization of CNs.In view of the superiority of the predefined-time stability,this paper is focused on predefined-time synchronization problems for uncertain CNs by using the linear matrix inequality methods and the Lyapunov stability theories.The main contents of this thesis are as follows.Chapter 2 discusses the predefined-time synchronization control problem for CNs with parameter uncertainty.A predefined-time Lyapunov stability characterization method is firstly proposed,based on which the continuous predefined-time state feedback controller is dexterously designed.Besides,some sufficient conditions in the form of linear matrix inequalities are stablished to guarantee the addressed CNs realizing the synchronization within the predefined-time.In addition,the network parameter uncertainties,which satisfying the norm bounded constraint,are also taken into account to describe more actual networks.Finally,two numerical examples are presented to demonstrate effectiveness of the proposed control scheme.The sliding mode control has received extensive attention in recent years due to its excellent character of robustness and anti-interference.Among the existing research results of sliding mode control problems,most of the designed controller could only guarantee the system reaching the sliding mode surface within finite-time,and the sliding mode stage is still asymptotically stable.In practice,we really hope that both of the approaching phase and the sliding motion phase are predefined-time stable,thus taking full advantages of the predefined-time stability.Chapter 3 is concerned with the predefined-time synchronization problem for CNs in the presence of parameter uncertainty and external disturbance,where the nonlinear function involved is general that satisfies the sector-bounded constraint instead of the usual Lipschitz condition adopted.Firstly,an integral sliding mode surface is constructed,by using the predefined-time stability criterion and the Kronecker product,sufficient conditions in the form of linear matrix inequalities are derived to guarantee the predefined-time stability of the synchronization error system during the sliding mode phase.Then,the sliding mode control law is explicitly designed such that the error system can be driven onto the specified sliding mode surface within the predefined-time.Finally,two numerical examples are presented to illustrate feasibility of the obtained results.