control//multi-agent control//leader-follower
Leader-follower consensus is a variant of the consensus protocol in which one agent, the leader, listens to nobody and keeps its own value, while the followers that hear it add a pull toward that value, so that the whole group converges to the leader's value instead of to the average. It is how a group of drones follows a piloted lead drone, how a convoy follows its head vehicle and how a fleet tracks a reference broadcast from a ground station.
Leader-follower consensus is a variant of the consensus protocol in which one agent, the leader, listens to nobody and keeps its own value, while the followers that hear it add a pull toward that value, so that the whole group converges to the leader's value instead of to the average. It is how a group of drones follows a piloted lead drone, how a convoy follows its head vehicle and how a fleet tracks a reference broadcast from a ground station.
The update for follower iii adds one term to ordinary consensus:
x˙i=∑j∈Niaij (xj−xi)+bi (xL−xi),\dot x_i=\sum_{j\in\mathcal N_i}a_{ij}\,(x_j-x_i)+b_i\,(x_L-x_i),x˙i=j∈Ni∑aij(xj−xi)+bi(xL−xi),
with bi>0b_i>0bi>0 if follower iii hears the leader and bi=0b_i=0bi=0 if not. If the followers' graph is connected and at least one of them hears the leader, the matrix L+BL+BL+B, with BBB the diagonal of the bib_ibi, is positive definite and every follower converges to xLx_LxL. Followers that never hear the leader directly still get there, through their neighbours.
Formation and leader-follower are consensus with offsets or with a deaf node, and a node that does not listen is a leader, even when it is an attacker.
Linear consensus cannot tell a chosen leader from a stuck sensor that keeps reporting the same value or a captured drone broadcasting a lie: all three pull the group to their value. That is why resilient consensus exists, and Byzantine fault tolerance is the general name of the threat.
The convergence speed is set by the smallest eigenvalue of L+BL+BL+B. A leader heard by many followers, or a well connected follower graph, makes it large; a leader heard by one agent at the end of a long chain makes it small.
When a leader with a good link exists, this beats symmetric consensus on simplicity and speed. The price is a single point of failure, so losing the leader needs a designed answer (promote another agent, hold position).
With offsets it moves a formation: the leader flies the route and the others hold their slots relative to it (formation control).
The word means something else in Raft, whose leader is elected to order the writes of a replicated log and averages nothing.