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arXiv · 2512.03779

Exact and Parametric Dynamical System Representation of Nonlinear Functions

Toshiyuki Ohtsuka
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Abstract

We introduce fixed-initial-state constant-input dynamical system (FISCIDS) representations for nonlinear functions. A function argument serves as a constant input to an input-affine system with a fixed initial state, and the function value is the terminal output. Every nonsingular differentially algebraic function on an open set star-shaped at the origin admits an exact quadratic FISCIDS representation. At least one analytic non-differentially-algebraic function admits such a representation. These results establish exact representation guarantees for structured finite-dimensional parametric model classes.

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Toshiyuki Ohtsuka. 2025-12-03. Exact and Parametric Dynamical System Representation of Nonlinear Functions. https://arxiv.org/abs/2512.03779

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