Flocking Control for Discrete-Time Cucker-Smale Model on Cooperation Networks*

This study discusses the discrete-time Cucker-Smale (C-S) model’s flocking on cooperative networks through general directed graphs. The error functions of the agent’s velocity and position are constructed to achieve the flocking behavior through the convergence analysis of the errors. The follower modifies its own velocity by a weighted value of the differential with other agents while the leader maintains a fixed constant velocity. Further, if all agents maintain the same velocity, the separation among agent will eventually cluster inside a specific upper bound. The convergence analysis of errors transformed into the products convergence of infinite sub-stochastic matrices. By means of these theory, a algebraic condition which is relyed on the initial states, the topological structure and the weight function for achieving flocking behavior is estabilished. Finally, the theoretical findings are illustrated by a number of numerical examples.