  A theoretical framework is developed for a precise control of spatial
patterns in oscillatory media using nonlinear global feedback, where a proper
form of the feedback function corresponding to a specific pattern is predicted
through the analysis of a phase diffusion equation with global coupling. In
particular, feedback functions that generate the following spatial patterns are
analytically given: i) 2-cluster states with an arbitrary population ratio, ii)
equally populated multi-cluster states, and iii) a desynchronized state. Our
method is demonstrated numerically by using the Brusselator model in the
oscillatory regime. Experimental realization is also discussed.
