Semilinear control systems in infinite dimensional Banach spaces are the natural framework for the description of several control problems governed by PDEs. In many models, some constraints for the state of the system may be present. In this talk, a Mayer problem associated to such systems will be discussed. In particular, a simple proof of a version of the constrained Pontryagin maximum principle, relying on infinite dimensional neighbouring feasible trajectories results, will be provided. This talk is based on a joint work with Hélène Frankowska and Elsa Maria Marchini.