Investigation On Exponential Synchronization Via Various Control Techniques For Complex Networks Of Networks

In most practical systems,an individual network is only one component within a much larger complex multi-level network,and these individual networks are interde-pendent.For example,in transportation networks,there are typically highway,bus,train and airplane networks covering the same areas but behaving differently,but each of them is a network itself.In the case of complex network,the network usually can form many cluster,which can be regarded as subnetworks of the network.This comes to the networks of networks,where the subnetworks and their connections can be regarded as the nodes and interactions of the networks,respectively.In this thesis,we study the exponential synchronization of complex networks of net-works via various control techniques,including pinning adaptive control,pinning sampled-data control,pinning Feedback control.The main contribution of this thesis is as follows.(1)The pinning adaptive synchronization control problem for complex networks of networks with delayed nodes will be first addressed.Compared with[30],we take the time delay into account in the local systems for both leaders network and subnetworks,and new adaptive controllers are designed to control the fraction of nodes in each subnetwork.By employing some techniques such as Barbalat's Lemma and algebraic graph theory,we establish a unified framework to deal with the synchronization for network of networks,and the pinning control scheme is implemented to achieve the exponential synchronization of complex networks of networks under consideration.The criteria will be derived in a more rigorous way to ensure the synchronization for the network of networks.(2)The pinnning sampled-data synchronization control problem for a class of complex networks of networks with time-varying coupling delay will be first ad-dressed.By constructing novel continuous/discontinuous Lyapunov functionals and using stochastic analysis,Jensen's inequality,Barbalat's Lemma,etc.,we derive the sufficient criteria to guarantee that the complex networks of networks concerned are synchronized.In addition,the synchronization criteria are dependent on the sam-pling period,and therefore are less conservative.In both cases,the design method of the desired sampled-data synchronization controllers are provided for this frame-work.(3)A new class of complex networks of networks with Markovian jumping and time-varying coupling delay will be first addressed.Based on stability theory of dynamical systems,stochastic analysis,and matrix theory and so on,we establish a new frame to cope with the synchronization problem for the stochastic networks of networks.The mode-dependent pinning feedback controllers are expressed in.the explicit form.(4)The pinning synchronization control problem for complex networks of net-works with directed topology and time delay will be first addressed.Pinning control scheme is implemented to achieve the exponential synchronization of complex net-works of networks with directed topology and time delay.One quantitative measure is distilled from the leaders' network coupling matrix to characterize the synchro-nization of the leaders' network.The calculation of such a quantity can easily and conveniently be realized by using a normal computer.On this basis,we derive the sufficient conditions to ensure that the error between the subnetworks states and the average of leaders can converge to zero exponentially,and the feedback controllers are given specifically.