Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.12695 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917487709257728 |
|---|---|
| author | Okajima, Hiroshi Shirahama, Shun Hayashi, Tatsunori Matsunaga, Nobutomo |
| author_facet | Okajima, Hiroshi Shirahama, Shun Hayashi, Tatsunori Matsunaga, Nobutomo |
| contents | Model-based robust control requires not only accurate nominal models but also systematic uncertainty representations to guarantee stability and performance. However, constructing polytopic uncertainty models typically demands multiple experiments or a priori structural assumptions.This paper proposes an identification framework based on intentional periodicity induction, in which cyclic reformulation with period $N$ is applied to a linear time-invariant system to interpret noise-induced parameter fluctuations as a structured manifestation of estimation uncertainty. The $N$ parameter sets obtained from a single identification experiment -- which would coincide in the noise-free case -- are used as polytope vertices, providing systematic control over the granularity of the uncertainty description through the choice of $N$. The practical utility of the constructed polytope is demonstrated through robust $H_\infty$ state-feedback synthesis via LMI optimization at the polytope vertices; the synthesis uses only noisy identification data and is shown across Monte Carlo trials to stabilize the true plant with only marginal conservatism. Complementarily, a diagnostic assessment based on the best in-polytope point confirms that the polytope captures meaningful uncertainty information. For a third-order system under Gaussian and uniform noise, a comparison with bootstrap-inspired resampling baselines indicates that cyclic reformulation provides a competitive or favorable trade-off by utilizing the full data record; the construction is further validated on a fourth-order MIMO system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12695 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Noise to Knowledge: System Identification with Systematic Polytope Construction via Cyclic Reformulation Okajima, Hiroshi Shirahama, Shun Hayashi, Tatsunori Matsunaga, Nobutomo Systems and Control Model-based robust control requires not only accurate nominal models but also systematic uncertainty representations to guarantee stability and performance. However, constructing polytopic uncertainty models typically demands multiple experiments or a priori structural assumptions.This paper proposes an identification framework based on intentional periodicity induction, in which cyclic reformulation with period $N$ is applied to a linear time-invariant system to interpret noise-induced parameter fluctuations as a structured manifestation of estimation uncertainty. The $N$ parameter sets obtained from a single identification experiment -- which would coincide in the noise-free case -- are used as polytope vertices, providing systematic control over the granularity of the uncertainty description through the choice of $N$. The practical utility of the constructed polytope is demonstrated through robust $H_\infty$ state-feedback synthesis via LMI optimization at the polytope vertices; the synthesis uses only noisy identification data and is shown across Monte Carlo trials to stabilize the true plant with only marginal conservatism. Complementarily, a diagnostic assessment based on the best in-polytope point confirms that the polytope captures meaningful uncertainty information. For a third-order system under Gaussian and uniform noise, a comparison with bootstrap-inspired resampling baselines indicates that cyclic reformulation provides a competitive or favorable trade-off by utilizing the full data record; the construction is further validated on a fourth-order MIMO system. |
| title | From Noise to Knowledge: System Identification with Systematic Polytope Construction via Cyclic Reformulation |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2601.12695 |