A Minimal Nonlinear State-Dynamics Model with Control Modulation
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2025
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| _version_ | 1866901466676985856 |
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| author | Sasaki, Kazutoshi |
| author_facet | Sasaki, Kazutoshi |
| contents | <p>We propose a minimal nonlinear dynamical framework for modeling the evolution of a generic state variable subject to internal degradation and external control. The model consists of a single state M(t) with dynamics expressed as</p> <p>\frac{dM}{dt} = -F(M) + G(M, u),</p> <p>where F(M) captures intrinsic deterioration and G(M, u) represents the modulating effect of an external input u(t). While intentionally abstract, this formulation highlights the importance of nonlinear interactions between the current state and both intrinsic and extrinsic factors. Such nonlinearities allow the model to accommodate a broad class of phenomena, including accelerating decline, threshold-like responses, and state-dependent control effectiveness. The framework is not tied to any specific system but is intended as a general conceptual structure that can be extended to multi-dimensional or application-specific settings. This brief note introduces the formulation, outlines its basic interpretive implications, and establishes a foundation for future work in which more detailed structures, functional specifications, or optimization principles may be developed.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17649098 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Minimal Nonlinear State-Dynamics Model with Control Modulation Sasaki, Kazutoshi nonlinear dynamics control theory state-dynamics optimal control minimal model <p>We propose a minimal nonlinear dynamical framework for modeling the evolution of a generic state variable subject to internal degradation and external control. The model consists of a single state M(t) with dynamics expressed as</p> <p>\frac{dM}{dt} = -F(M) + G(M, u),</p> <p>where F(M) captures intrinsic deterioration and G(M, u) represents the modulating effect of an external input u(t). While intentionally abstract, this formulation highlights the importance of nonlinear interactions between the current state and both intrinsic and extrinsic factors. Such nonlinearities allow the model to accommodate a broad class of phenomena, including accelerating decline, threshold-like responses, and state-dependent control effectiveness. The framework is not tied to any specific system but is intended as a general conceptual structure that can be extended to multi-dimensional or application-specific settings. This brief note introduces the formulation, outlines its basic interpretive implications, and establishes a foundation for future work in which more detailed structures, functional specifications, or optimization principles may be developed.</p> |
| title | A Minimal Nonlinear State-Dynamics Model with Control Modulation |
| topic | nonlinear dynamics control theory state-dynamics optimal control minimal model |
| url | https://doi.org/10.5281/zenodo.17649098 |