In the present work we investigate the behavior of a group of agents guided by an

exogenous broadcast control, a velocity signal. The agents are modelled by single

integrators and are assumed oblivious to their own position. The broadcast control is

detected and employed by an arbitrary subgroup of agents, referred to as leaders. The

velocity signal and the set of leaders are assumed to be time-invariant or piecewise

time invariant. A system without leaders is referred to as autonomous system. The

leaders add the detected broadcast velocity to their autonomous velocity. This

paradigm has been applied to several models of dynamics, linear and non-linear:

• Linear Dynamics with fixed topology, Uniform and Scaled Influence

• Linear and Deviated Linear cyclic pursuit, cyclic unidirectional fixed

topology

• Bearing-only Cyclic Pursuit, direct and deviated

• Systems with finite visibility

o Piecewise linear with Uniform influence

o Distributed potential based dynamics

For each of the above models we investigate the effect of the broadcast velocity and

of the set of leaders on the emergent behavior of the system. We show that in all

linear cases, except for the deviated cyclic pursuit, the agents align asymptotically in

the direction of the broadcast velocity and move with a speed proportional to the ratio

of the number of leaders to the total number of agents. In the linear deviated cyclic

pursuit, the emergent behavior depends also on the deviation angle. We show that

there is a critical deviation angle where circular movement patterns are obtained.

In the Bearing-only cyclic pursuit model, we show that there exists a bound on the

magnitude of the external velocity that ensures that in finite time, some agent captures

all others and moves with velocity corresponding to the broadcast control. In the

Deviated Bearing-only cyclic pursuit model, the existence of a bound on the

magnitude of the broadcast velocity, ensuring convergence to a moving point, is

limited to the value of the deviation angle.

In a piecewise linear system, even without exogenous control, the graph may

disconnect. Agents' positions converge exponentially to one or more line(s) parallel

to the direction of the broadcast velocity, corresponding to the sub-graphs that have

resulted from the topological changes.

The potential based model has the property that without exogenous control, it

disables links disconnections, thus never losing neighbors.

In order to preserve the “never lose neighbors” property in the presence of

broadcast guidance, we introduce adaptive gains on the control applied by leaders that

vanish when a neighbor approaches the visibility range. With this gain and navigation-like potential, it is shown that the agents asymptotically converge to a stable state, moving in the direction of the broadcast velocity.