Event-Triggered Synchronization Control And Application Of Complex Dynamical Networks

Complex system exists widely in the real world and is one of the key research topics in the 21st century.It has important practical application background and theoretical research sig-nificance.By taking complex system as a network system composed of many individuals(nodes)in the system and their relationships,complex network has become an important tool and method to describe and understand complex system.At present,the research on complex network exists in many fields,such as mathematics,physics,computer science,biology,sociology and so on.For various types of complex network systems in nature,syn-chronization is not only a common and typical aggregation behavior,but also one of the most important dynamic characteristics of complex networks.Complex dynamic networks(CDNs)as an important branch of complex networks,its synchronization problem has at-tracted widespread attention from many researchers.At the same time,in the current digital communication network,continuous transmission and reception of information is difficult to achieve in practical applications,and the traditional periodic sampling will inevitably lead to waste of energy,bandwidth and computing resources,while the event-triggered communica-tion mechanism solves such problems well.With the rapid development of the synchroniza-tion theories of complex network,power system,a huge and complex nonlinear network,has attracted many scholars’ attention.Meanwhile,new energy generation technology develops by leaps and bounds,more and more distributed energy sources are connected to the power system,while the randomness and fluctuation of distributed energy sources will make the power grid suffer more disturbances,which undoubtedly puts forward higher requirements for the stability control of the power grid.In this dissertation,we mainly study the event-triggered synchronization problems of the second order linear/nonlinear and nonlinear coupling CDNs under cooperatively directed spanning tree(CDST)topology and the distributed power control problem in power grids.The considered topology does not require the nodes in the network to be connected at any time,only the integral of the Laplace matrix corresponding to the network topology in a period of T contains a directed spanning tree.At present,most researches on the synchro-nization of CDNs under time-varying topologies consider the switching topologies,which is fixed within each switching interval.Further,by applying Lyapunov stability theory,graph theory and matrix inequality,the sufficient conditions of the synchronization of correspond-ing CDNs are given.At last,the validity of the theoretical results are verified by numerical simulations.The main contents are summarized as follows:Firstly,for general second-order linear systems in CDNs with CDST topology,an exponen-tial synchronization controller is designed based on event-triggered strategy and a sufficient condition for the network to achieve exponential synchronization is given.According to matrix inequality technology and Lyapunov stability theory,detailed theoretical analysis is provided by choosing an appropriate Lyapunov function.At the same time,the Zeno phenomenon is excluded by proving that a strictly positive lower bound exists for the event-triggered intervals.Secondly,the exponential synchronization problem of second-order nonlinear systems in CDNs with time-varying coupling matrices is studied.In order to reduce the communication frequency between nodes,an event-triggered scheme is designed.The sufficient condition for the synchronization of CDNs and the lower bound of the event-triggered intervals are proposed,which illustrates that under the given time-varying topology,not only can the exponential synchronization of CDNs be guaranteed,but also the number of the transmission of information can be reduced.The simulation results further show the correctness of the theoretical results.Thirdly,based on event-triggered strategy,we address the synchronization of nonlinear cou-pling CDNs with time-varying topology.For two different nonlinear coupling types,the corresponding controllers are designed and the sufficient conditions of exponential synchro-nization are given.The detailed theoretical proofs are provided based on Lyapunov stability theory and through clever matrix deformation.In order to exclude Zeno phenomenon,we prove that there is a minimum time interval between two adjacent communications in two cases.Finally,considering that in practical distributed power grids,the random fluctuations in pow-er of some generation nodes(wind,solar power)and load nodes may cause the frequency of entire grid to be unable to stabilize at the rated frequency.Therefore,the actual power grid is modeled as a first-order Kuramoto model(nonlinear coupling model),and a distributed controller is designed by taking the known rated frequency as the reference frequency.By controlling the power of controllable nodes such as thermal power nodes,the frequency of the whole power grids is restored to the rated frequency and the power output of each gen-eration node in the power grids is fair,so as to effectively avoid the problem of too large or too small power of generators,and achieve the rational use of power generation resources.In addition,we also consider the fair power output and frequency restoration based on the event-triggered strategy and exclude the Zeno phenomenon.The effectiveness of the de-signed controllers are also demonstrated by the simulation examples.