Research On Bipartite Consensus Problem Of Signed Networks Under Impulsive Control

Several problems that exist when using impulsive control to achieve bipartite consensus in signed networks are investigated in this thesis.Signed networks benefit from the presence of negative edge weights that enrich the dynamical behavior of the network,so it is important to ensure the effectiveness of the control.The details of the thesis are as follows.(1)The problem of leader-set selection for achieving leader-follower bipartite consensus for nonlinear signed networks under impulsive control is investigated.Based on the controllability of leader-follower,a static leader set selection scheme when the nonlinear function is bounded is presented in this thesis.Using the Lyapunov stability theory,it is then demonstrated that leader-follower control over signed networks can be achieved by impulsive control under both time-triggered and event-triggered.It is proved that boundedness is the key to the control set’s effectiveness,and the validity of the conclusion has been verified through simulation experiments.Then,the bounded constraint of the nonlinear function is liberalized to the unbounded case,and a dynamic control set selection scheme is given,which is equally theoretically justified and experimentally verified.The results show that the dynamic set actually bounds the state boundary of the system,which proves the importance of boundedness from another aspect.The combination of impulsive control and leader-follower control further reduces the cost of control,and the convergence rate can be increased by adding control nodes which makes the controllability of losses improved.The choice of leaders’ set is easier to use compared to pinning control,which makes our study more practical.(2)The problem of impulse control for stochastic delayed systems is investigated,where the impulsive signal may encounter unbounded delays.Firstly,a multi-leader model based on the mean relay is designed for the multi-leader consensus case to fill the gap of multi-leader control.Subsequently,the thesis analyzes the controller design strategy step by step from bounded delays to unbounded delays and obtains the multi-leader meansquare exponential bipartite consensus under event-triggered delayed impulsive control based on delayed probabilities.Then the control algorithm for the control process of the stochastic delayed system is obtained by using the Lyapunov function method and It(?)’s formula,etc.,to link the probability of different time delays and the system parameters.And the effectiveness of the control strategy is confirmed by simulation verification.The results show that the mean relay not only facilitates the system consensus but also smooths out the state changes brought by impulsive control.Based on this,the controller conditions for the leaderless case using mean relay are further presented,and the same simulation is performed to verify the leaderless bipartite consensus of the system.