Relaxation Theorems, Differential Inclusions, and Filippov′s Theorem for Relaxed Controls in Semilinear Infinite Dimensional Systems

Under suitable assumptions, trajectories of semilinear control systems in Banach spaces corresponding to relaxed controls can be uniformly approximated by trajectories corresponding to ordinary controls. Moreover, relaxed trajectories can be defined nonparametrically (that is, by relaxed differential inclusions).