Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays

Figure 1

Simulation of the CS model with one leader and nine followers. (a) shows the trajectories of agents where the motion has no delay. (b)–(d) present the trajectories of agents where the movement of flocks have an effect of time delay () in time , , and , respectively. Note that the dashed line represents the trajectory of the leader, while the blue line denotes the trajectory of the follower. (a) Without time delay for . (b) With delay () for . (c) With delay () for . (d) With delay () for .

(a)

(b)

(c)

(d)