ABSTRACT
We show that trajectories of semilinear infinite dimensional control systems where the control appears linearly can be approximated by trajectories driven by extremal controls (that is, controls taking values at extremal points of the control set). This is done under two sets of hypotheses. The results are relevant to systems driven either by ordinary or relaxed controls. There are two applications to nonlinear distributed parameter systems, one hyperbolic, the other parabolic.
