The Flocking Behavior With Random Packet Losses

Recently the research on the flocking behavior of multi-agent system has attracted the attention of many researchers.Some related results has been applied to many engineering fields such as biology,physics and control.In a system with many agents,all agents need to communicate information with their neighbors.However,these information will be lost inevitably in the process of transmission,which is called packet losses.Therefore,the investigation about packet losses between agents is an important topic in the study about flocking.It has a wide range of applications in many fields.In this dissertation,we study the flocking of a discrete Cucker-Smale model with packet losses.The key point is to use an effective method to describe the packet loss process and analyze the flocking behavior of the system.Firstly,considering the packet losses in a system described by undirected topology graph,we propose a hypothesis to describe the packet losses,which is wide enough to include four types of packet losses: random packet losses,malicious packet losses,combination of random and malicious packet losses with independent,combination of both with dependent.Further,considering the packet losses in the case when the system is described by a directed topology graph,we propose a similar hypothesis.Secondly,we study the flocking behavior of discrete Cucker-Smale model with packet losses.According to the assumption of packet losses in the case for an undirected graph,using graph theory,probability and algebraic knowledge,we can obtain a conclusions: when the decay rate is less than 1,the system achieves flocking almost surely,and when it is greater than or equal to 1,the system achieve flocking almost surely under certain initial conditions.In the end of this chapte,we use an example to verify the conclusion.Finally,we study the same problem for discrete Cucker-Smale model with a rooted leader.With a packet loss hypothesis under the directed topology,a sufficient condition for achieving flocking almost surely are obtained.Finally,the conclusions were verified by an example.