State Estimation For Multi-layer Complex Dynamical Networks

As an important branch of complex network science,multi-layer complex dynamical network has been paid more and more attention in recent years.However,compared with single-layer complex dynamical network,the research on multi-layer complex dynamic network is still relatively less.There are many research fields of complex networks,including state estimation,topology identification,synchronization control,fault detection,behavior characteristic analysis and so on.Among them,state estimation is the premise of other researches.Only when the state information of network nodes is known,can topology identification and synchronization control be studied.In practice,the scale of a complex network is huge,and the topology is complex,so it is often impossible to obtain the state information of nodes in the network directly.Therefore,it is necessary to establish a state observer of the complex network to obtain the state information of nodes in time.This dissertation studies the state estimation method for three different types of multi-layer complex dynamical networks.When the nodes' state information of a multi-layer complex dynamical network is unknown,the state of nodes in the multi-layer complex dynamical network can be estimated by designing a state observer and solving the appropriate observer gain.The contributions of this dissertation are as follows:(1)The problem of state estimation for a class of multi-layer complex dynamical networks with the same number of nodes in each layer and one-to-one correspondence between nodes in each layer is studied.According to Lyapunov stability criterion,the sufficient conditions of state estimation for multi-layer complex dynamical networks with ideal state and time-varying coupling delay are given in the form of linear matrix inequality.Finally,the effectiveness of the designed state observer is verified by numerical simulation.(2)The state estimation problem of a class of multi-layer complex dynamical networks with the same number of nodes in each layer and arbitrary connection of nodes between layers is studied.The topological connection of this kind of multi-layer complex dynamical networks is more complex.Considering the ideal conditions and the cases with time-varying coupling delays in and between layers respectively,the design criteria of the controller parameters are derived based on Lyapunov stability theory.Finally,two examples of double-layer complex dynamical networks are given to verify the effectiveness of the proposed scheme.(3)For a class of multi-layer complex dynamical networks with different number and type of nodes in each layer and non one-to-one correspondence between nodes,the state observer is designed.This kind of multi-layer complex dynamical network model is more complex in topology connection and node dynamics,and the related research is the rarest.Firstly,Lyapunov stability criterion is used to prove the feasibility of the proposed state observation scheme in theory.Finally,a two-layer dynamical network model is constructed,and different node dynamics are adopted in each layer.The effectiveness of the designed observer is verified by numerical simulation.