Exact and Parametric Dynamical System Representation of Nonlinear Functions
arXiv:2512.03779
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.
8 pages, 2 figures; Revised manuscript with expanded motivation, constructive results, and proofs