This technical communique presents a method which aims at improving input design searching in some dynamical systems. The original idea of the proposed method is the combination of a dynamic programming method working on square wave inputs followed by a Quasi-Newton algorithm working on infinite differential switching mode inputs. These infinite differential functions approximate square wave inputs in order to enlarge the set of admissible inputs while ensuring a reasonable computation requirement which is not the case of classical methods based on dynamic programming only. Moreover, they correspond to practical inputs. The precise description of the approach is followed by an application in aerospace sciences.