We present the extension oil our field-induced surface hopping method for the description of the photoionization process and the simulation of time-resolved photoelectron spectra (TRPES). This is based on the combination of nonadiabatic molecular dynamics "on the fly" in the framework of TDDFT generalized for open shell systems under the influence of laser fields with the approximate quantum mechanical description of the photoionization process. Since arbitrary pulse shapes can be employed, this method can be also combined with the optimal control theory in order to steer the photoionization or to shape the outgoing electronic wavepackets. We illustrate our method for the simulation of TRPES on the prototype system of Ag(3), which involves excitation from the equilibrium triangular geometry, as well as excitation from the linear transition state, where in both cases nonadiabatic relaxation takes place in a complex manifold of electronic states. Our approach represents a generally applicable method for the prediction of time-resolved photoelectron spectra and their analysis in systems with complex electronic structure as well as many nuclear degrees freedom. This theoretical development should serve to stimulate new ultrafast experiments.