Threshold dynamics in time-delay systems: polynomial $β$-control in a pressing process and connections to blow-up
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911275739512832 |
|---|---|
| author | Kimura, Masato Kuma, Hirotaka Liu, Yikan Matsui, Kazunori Yamamoto, Masahiro Yang, Zhenxing |
| author_facet | Kimura, Masato Kuma, Hirotaka Liu, Yikan Matsui, Kazunori Yamamoto, Masahiro Yang, Zhenxing |
| contents | This paper addresses a press control problem in straightening machines with small time delays due to system communication. To handle this, we propose a generalized $β$-control method, which replaces conventional linear velocity control with a polynomial of degree $β\ge 1$. The resulting model is a delay differential equation (DDE), for which we derive basic properties through nondimensionalization and analysis. Numerical experiments suggest the existence of a threshold initial velocity separating overshoot and non-overshoot dynamics, which we formulate as a conjecture. Based on this, we design a control algorithm under velocity constraints and confirm its effectiveness. We also highlight a connection between threshold behavior and finite-time blow-up in DDEs. This study provides a practical control strategy and contributes new insights into threshold dynamics and blow-up phenomena in delay systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Threshold dynamics in time-delay systems: polynomial $β$-control in a pressing process and connections to blow-up Kimura, Masato Kuma, Hirotaka Liu, Yikan Matsui, Kazunori Yamamoto, Masahiro Yang, Zhenxing Optimization and Control Systems and Control Dynamical Systems 34H05, 34K35, 93C43, 34K99 This paper addresses a press control problem in straightening machines with small time delays due to system communication. To handle this, we propose a generalized $β$-control method, which replaces conventional linear velocity control with a polynomial of degree $β\ge 1$. The resulting model is a delay differential equation (DDE), for which we derive basic properties through nondimensionalization and analysis. Numerical experiments suggest the existence of a threshold initial velocity separating overshoot and non-overshoot dynamics, which we formulate as a conjecture. Based on this, we design a control algorithm under velocity constraints and confirm its effectiveness. We also highlight a connection between threshold behavior and finite-time blow-up in DDEs. This study provides a practical control strategy and contributes new insights into threshold dynamics and blow-up phenomena in delay systems. |
| title | Threshold dynamics in time-delay systems: polynomial $β$-control in a pressing process and connections to blow-up |
| topic | Optimization and Control Systems and Control Dynamical Systems 34H05, 34K35, 93C43, 34K99 |
| url | https://arxiv.org/abs/2508.07268 |