  In recent years, numerous studies have focused on the mathematical modeling
of social dynamics, with self-organization, i.e., the autonomous pattern
formation, as the main driving concept. Usually, first or second order models
are employed to reproduce, at least qualitatively, certain global patterns
(such as bird flocking, milling schools of fish or queue formations in
pedestrian flows, just to mention a few). It is, however, common experience
that self-organization does not always spontaneously occur in a society. In
this review chapter we aim to describe the limitations of decentralized
controls in restoring certain desired configurations and to address the
question of whether it is possible to externally and parsimoniously influence
the dynamics to reach a given outcome. More specifically, we address the issue
of finding the sparsest control strategy for finite agent-based models in order
to lead the dynamics optimally towards a desired pattern.
