Cucker-Smale flocking over cooperation-competition networks

This paper offers a novel distributed control scheme for the Cucker-Smale model to examine the leader-follower flocking behavior on networks with both cooperative and competitive interactions among agents. The core idea of the proposed scheme is to characterize the influence of cooperation and competition between agents through positive and negative weight functions with respect to the interaction distance, respectively. Based on the tool of infinite products of super-stochastic matrices, we establish mathematical inequalities about the intensities of cooperation and competition, and further obtain the algebraic conditions that depend on factors such as the initial states of agents, topological structure and weight functions. Moreover, we also discuss the influence of these factors on the least exponential convergence rate and the final position errors among agents. The obtained theoretical results are illustrated through simulation examples.