  Eliminating disagreement in a group is usually beneficial to the social
stability. In this paper, using the well-known Hegselmann-Krause (HK) model, we
design a quite simple strategy that could resolve the opinion difference of the
system in finite time and induce the opinions synchronized to a targeted value.
To be specific, we intentionally introduce weak random noise to only one agent
to affect its opinion in the evolution and also a leader agent with fixed
opinion in a divisive group, then strictly prove that the disagreement is
finally eliminated and the opinions get synchronized to the leader's opinion in
finite time. Other than that, we calculate the finite stopping time when the
opinions synchronously reach the objective opinion value, which could provide
further guide for designing more efficient noise intervention strategy.
