Re-centered Chen-Fliess Series: Convergence and Error Analysis
Boudaghi, Farnaz
Boudaghi, Farnaz
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Abstract
Chen-Fliess series provide a coordinate-free representation for a broad class of nonlinear input-output systems, but their practical use is limited by finite radii of convergence, which restrict both the admissible time interval and input magnitude. This talk presents a re-centering framework for extending the effective time horizon of Chen-Fliess series without recomputing coefficients from an underlying state-space model. The derivation follows a simple combinatorial viewpoint inspired by Taylor-series re-centering, where Chen�s identity replaces the binomial theorem in the noncommutative setting. In addition to deriving the re-centering formula, the talk investigates the convergence of the re-centered series. Explicit growth parameters are obtained for both globally and locally convergent cases. Each re-centering step introduces approximation error arising from both finite truncation and deviations in the re-centered coefficients. Understanding how these errors propagate over repeated re-centering steps is essential for practical implementation. To this end, the talk develops a methodology for quantifying the error induced by truncation and re-centering of a Chen-Fliess series. Explicit upper bounds are derived for truncation error, re-centering error, and their combined effect in terms of the convergence properties of the associated Chen-Fliess series. Analytical examples and simulation studies demonstrate that re-centering can significantly extend the useful time horizon of truncated Chen-Fliess representations while maintaining computable accuracy guarantees.
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Date
1/1/2026
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Graduate Student
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Oral Presentation
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Electrical engineering
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College of Engineering and Mathematical Sciences
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Engineering