  A class of Pyragas type nonlocal feedback controllers with time-delay is
investigated for the Schl\"ogl model. The main goal is to find an optimal
kernel in the controller such that the associated solution of the controlled
equation is as close as possible to a desired spatio-temporal pattern. An
optimal kernel is the solution to a nonlinear optimal control problem with the
kernel taken as control function. The well-posedness of the optimal control
problem and necessary optimality conditions are discussed for different types
of kernels. Special emphasis is laid on time-periodic functions as desired
patterns. Here, the cross correlation between the state and the desired pattern
is invoked to set up an associated objective functional that is to be
minimized. Numerical examples are presented for the 1D Schl\"ogl model and a
class of simple step functions for the kernel.
