On the Convergence of Re-Centered Chen-Fliess Series

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 letter is to present a computationally feasible method to re-center a Chen-Fliess series in order to expand its time horizon. It extends existing results in two ways. First, it takes a simpler combinatorial approach to the re-centering formula that draws directly on the analogous re-centering problem for Taylor series. Second, a convergence analysis is presented for the re-centered series. This information can be used to compute a lower bound on the radius of convergence for the output function and an estimate of the series truncation error. The method is demonstrated by simulation on a steering problem for a car-trailer system.