Generating Series for Networks of Chen-Fliess Series

TL;DR

This paper demonstrates that interconnected nonlinear systems described by Chen-Fliess series can be explicitly represented through series computations, enabling analysis without finite-dimensional models.

Contribution

It introduces a method to compute Chen-Fliess series representations for interconnected nonlinear systems directly from their series descriptions.

Findings

Additive and multiplicative interconnections preserve Chen-Fliess series representations.

Explicit formulas for series representations are derived using formal Lie derivatives.

The approach applies to systems without finite-dimensional state space models.

Abstract

Consider a set of single-input, single-output nonlinear systems whose input-output maps are described only in terms of convergent Chen-Fliess series without any assumption that finite dimensional state space models are available. It is shown that any additive or multiplicative interconnection of such systems always has a Chen-Fliess series representation that can be computed explicitly in terms of iterated formal Lie derivatives.