Chen-Fliess Series beyond their execution time

Chen-Fliess functional series provide a representation for a large class of nonlinear input-output systems. Like any infinite series, however, their applicability is limited by their radii of convergence. The goal of this research is to present a computationally feasible method to re-centering a Chen-Fliess series in order to expand its time horizon. It extends the existing results by taking a simpler combinatorial approach to obtain a close form of Chen-Fliess re-centering formula that draws directly on the analogous re-centering problem for Taylor series. This formula effectively increases the life of the representation beyond the execution time. An illustrative example is presented.