Exact and Parametric Dynamical System Representation of Nonlinear Functions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917122045640704 |
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| author | Ohtsuka, Toshiyuki |
| author_facet | Ohtsuka, Toshiyuki |
| contents | Parametric representations of various functions are fundamental tools in science and engineering. This paper introduces a fixed-initial-state constant-input dynamical system (FISCIDS) representation, which provides an exact and parametric model for a broad class of nonlinear functions. A FISCIDS representation of a given nonlinear function consists of an input-affine dynamical system with a fixed initial state and constant input. The argument of the function is applied as the constant input to the input-affine system, and the value of the function is the output of the input-affine system at a fixed terminal time. We show that any differentially algebraic function has a quadratic FISCIDS representation. We also show that there exists an analytic function that is not differentially algebraic but has a quadratic FISCIDS representation. Therefore, most functions in practical problems in science and engineering can be represented by a quadratic FISCIDS representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact and Parametric Dynamical System Representation of Nonlinear Functions Ohtsuka, Toshiyuki Systems and Control Dynamical Systems Parametric representations of various functions are fundamental tools in science and engineering. This paper introduces a fixed-initial-state constant-input dynamical system (FISCIDS) representation, which provides an exact and parametric model for a broad class of nonlinear functions. A FISCIDS representation of a given nonlinear function consists of an input-affine dynamical system with a fixed initial state and constant input. The argument of the function is applied as the constant input to the input-affine system, and the value of the function is the output of the input-affine system at a fixed terminal time. We show that any differentially algebraic function has a quadratic FISCIDS representation. We also show that there exists an analytic function that is not differentially algebraic but has a quadratic FISCIDS representation. Therefore, most functions in practical problems in science and engineering can be represented by a quadratic FISCIDS representation. |
| title | Exact and Parametric Dynamical System Representation of Nonlinear Functions |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2512.03779 |