Research On Cucker–Smale Flocking Under Random Interactions

Flocking is a form of collective behavior of a large number of interacting agents that move with a common velocity while maintaining a cohesive or geometric formation.Flocking has gained increasing interest from the various research communities in biology,robotics,control theory and sensor networks.The flocking model considered in this paper has been proposed by Cucker and Smale.In the Cucker–Smale(C–S)model,the interaction strength between pairs of agents is a smooth and decreasing function of their relative distance.This model has significant potential applications,such as unmanned aerial vehicles and formation control of multiple robots.This paper investigates some problems related to the C–S flocking under random interactions.This paper contains the study of hierarchical C–S flocking under random interactions with time-varying failure probabilities,C–S flocking subject to random failure on general digraphs,leader-follower C–S flocking with bounded missing data and random communication ranges,and C–S flocking with randomly limited communication ranges on general digraphs.The main results are listed as follows:Chapter 2 considers the hierarchical C–S flocking under random interactions with time-varying failure probabilities.Each agent,at each sampling time point,can fail to receive the information from any of its superiors in the hierarchy.Assume that the failure process is homogeneous,two-state and discrete-time Markov chain with positive transition probability matrix,and the overall leader of the flock has a free-will acceleration.In Chapter 2,we prove that the flocking would occur almost surely under some conditions on the initial state of the flock only.Chapter 3 considers the C–S flocking subject to random failure under general directed interaction topologies,which contain the hierarchical and rooted structure as special cases.At each time step,each of the agents can fail to interact with any of its neighbors.The random failures are assumed to be not independent,and the failure process considered in Chapter 2 is a special case of the one considered in Chapter 3.In this chapter,we also prove that the flocking would occur almost surely under some conditions on the initial state of the flock only.Chapter 4 considers the leader-follower C–S flocking with bounded missing data and random communication ranges.The communication topologies are determined by the relative distance and random communication ranges between agents.The goal of this chapter is to determine a lower bound on the probability that the agents asymptotically achieve a flocking behavior,and the bound depends on the initial conditions of the flock only.Chapter 5 considers the C–S flocking with randomly limited communication ranges on general digraphs.At each time step,each pair of neighboring agents can communicate with each other only when they are within some random communication range.In this chapter,we establish a lower bound on the probability that the agents converge to flocking.The bound depends on the initial conditions of the flock only.