Controlling surface morphologies by time-delayed feedback

We propose a new method to control the roughness of a growing surface, via a time-delayed feedback scheme. The method is very general and can be applied to a wide range of non-equilibrium growth phenomena, from solid-state epitaxy to tumor growth. Possible experimental realizations are suggested. As an illustration, we consider the Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25,0.33], for a significant length of time.