Extending the Execution Time of Chen-Fliess Series

The Chen-Fliess series is a mathematical tool for representing nonlinear input-output system dynamics in control theory and its structure is rooted in the algebra of noncommutative formal power series. However, its local convergence limits its usability over extended time domains or varying operating conditions. This paper introduces a systematic re-centering methodology for extending of the Chen-Fliess series. The suggested framework guarantees accuracy and continuity in system representations across long time horizons by utilizing Chen’s identity and the algebraic features of Lie derivatives. This innovation enhances the series’ practical utility, enabling the analysis of complex nonlinear systems without the need of state space models. Finally, illustrative numerical simulations are presented to demonstrates the methodology effectiveness.