Research On Finite-Time Synchronization Control And Its Application For Complex Networks With Time Delays

With the rapid development of complex network science,the development of complex network has reached a new height.Synchronization as a typical complex network behavior,many interesting phenomena in nature can be described by the complex network synchronization.Since finite-time stability/synchronization usually has fast convergence rate and good robustness,it has become an important research topic to analyze the synchronization capability of complex networks in finite time.Complex networks often have a large number of nodes and intricate coupling relations,so it is unrealistic to realize synchronization only by the network itself.Many effective control methods have been successfully applied in complex network synchronization.Also,due to the limitation of information transmission speed and distance,the time delay phenomenon is universal in complex networks.Therefore,this paper mainly studies the finite-time synchronization and control of complex networks with time delays.The main contents include:In the first part,the finite-time synchronization of complex networks with time delays is studied.First,an event-triggered mechanism is designed for the pinning control.Nodes are sorted at each triggered moment,and then nodes with large synchronization errors are selected for pinning.The relationship between the coupling strength and synchronization of complex networks is discussed,and a low computational complexity control gain design scheme is proposed.Then,based on the appropriate inequality technique and Lyapunov function,the finite-time synchronization criterion for the given network system model is obtained.Finally,the effectiveness and practicability of the proposed control strategy are verified by the practical example of a group of single-link robot arm systems.The second part considers the finite time synchronization problem of complex networks with hybrid-coupled time-varying delays.Based on the first part,the aperiodically intermittent control strategy is introduced into the controller design.A selection rule is designed to select the number of pinned nodes.At each triggered moment,not only the pinned nodes are re-selected,but also the number of pinning nodes is re-determined.The influence of hybrid-coupled time-varying delays on the finite-time synchronization of complex networks is considered,and the sufficient conditions for realizing the finite-time synchronization are derived.Finally,the feasibility of the theoretical results is verified by the simulation experiment.In the third part,the adaptive finite-time synchronization problem of delayed heterogeneous complex networks is studied through a preassigned-time sliding mode control approach.The state observer is designed by a combination of adaptive techniques when the boundary information of the model uncertainties and external disturbances is unknown.A novel sliding mode control law is designed to enable the state trajectories to reach the sliding surface in a preassigned convergence time.In addition,based on a partitioning strategy,the finite-time synchronization criterion of delayed heterogeneous networks in the whole finite-time interval is derived.Finally,the theoretical results are applied to the coupled pendulum system to verify its validity.