  We report studies of controlled interactions of localized dissipative
structures in a system described by the AC-driven damped nonlinear
Schr\"odinger equation. Extensive numerical simulations reveal a diversity of
interaction scenarios that are governed by the properties of the system driver.
In our experiments, performed with a nonlinear optical Kerr resonator, the
phase profile of the driver is used to induce interactions on demand. We
observe both merging and annihilation of localized structures, i.e.,
interactions governed by the dissipative, out-of-equilibrium nature of the
system.
