  In contrast to conservative systems, in nonlinear media with gain and loss
the dynamics of localized topological structures can exhibit unique features
that can be controlled externally. We propose a robust mechanism to perform
topological transformations changing characteristics of dissipative vortices
and their complexes in a controllable way. We show that a properly chosen
control carries out the evolution of dissipative structures to regime with
spontaneous transformation of the topological excitations or drives generation
of vortices with control over the topological charge.
