Research On Asymptotic Flocking In The Delayed Cucker-Smale Model

As a popular model in multi agent-system models,Cucker-Smale model has been widely studied.In practical problems,the interaction between each agent is not instantaneous,and various uncertain environmental factors often occur,resulting in delayed information transmission.Therefore,this article adds communication delays to the Cucker-Smale model.The mainly study are as follows:Chapter one introduces the research background and current domestic and international research status of the Cucker-Smale model frstly,and then describe the main work of this article and introduce some relevant basic knowledge.In chapter two,we study the asymptotic flocking behavior of a delayed Cucker Smale model with singular communication weights.We introduce some lemmas and provide relevant proofs.By constructing a new basic equation for second-order velocity-position moment,we provide a new proof idea for collision avoidance problems.The conclusion of collision avoidance between agents without adding an external force model is obtained,and a condition for the model to achieve progressive flocking behavior is obtained.In chapter three,we study the asymptotic flocking behavior of a distributed delay Cucker-Smale model with classic communication weights.By improving the proof process,we obtain exponential convergence of speed to obtain the asymptotic flocking behavior of the Cucker Smale model.At the same time,we conclude that the model achieves asymptotic flocking,and our communication function constraints are more relaxed than before.In chapter four,we summarize the work of this article and give conclusions,finally,propose prospects for future research directions.