  We suggest an adaptive control scheme for the control of zero-lag and cluster
synchronization in delay-coupled networks. Based on the speed-gradient method,
our scheme adapts the topology of a network such that the target state is
realized. It is robust towards different initial condition as well as changes
in the coupling parameters. The emerging topology is characterized by a
delicate interplay of excitatory and inhibitory links leading to the
stabilization of the desired cluster state. As a crucial parameter determining
this interplay we identify the delay time. Furthermore, we show how to
construct networks such that they exhibit not only a given cluster state but
also with a given oscillation frequency. We apply our method to coupled
Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in
an expansion of systems close to a Hopf bifurcation. The successful and robust
control of this generic model opens up possible applications in a wide range of
systems in physics, chemistry, technology, and life science.
