Regret of $H_\infty$ Preview Controllers
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908816643194880 |
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| author | Liu, Jietian Seiler, Peter |
| author_facet | Liu, Jietian Seiler, Peter |
| contents | This paper studies preview control in both the $H_\infty$ and regret-optimal settings. The plant is modeled as a discrete-time, linear time-invariant system subject to external disturbances. The performance baseline is the optimal non-causal controller that has full knowledge of the disturbance sequence. We first review the construction of the $H_\infty$ preview controller with $p$-steps of disturbance preview. We then show that the closed-loop $H_\infty$ performance of this preview controller converges as $p\to \infty$ to the performance of the optimal non-causal controller. Furthermore, we prove that the optimal regret of the preview controller converges to zero. These results demonstrate that increasing preview length allows controllers to asymptotically achieve non-causal performance in both the $H_\infty$ and regret frameworks. A numerical example illustrates the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01420 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regret of $H_\infty$ Preview Controllers Liu, Jietian Seiler, Peter Optimization and Control Systems and Control This paper studies preview control in both the $H_\infty$ and regret-optimal settings. The plant is modeled as a discrete-time, linear time-invariant system subject to external disturbances. The performance baseline is the optimal non-causal controller that has full knowledge of the disturbance sequence. We first review the construction of the $H_\infty$ preview controller with $p$-steps of disturbance preview. We then show that the closed-loop $H_\infty$ performance of this preview controller converges as $p\to \infty$ to the performance of the optimal non-causal controller. Furthermore, we prove that the optimal regret of the preview controller converges to zero. These results demonstrate that increasing preview length allows controllers to asymptotically achieve non-causal performance in both the $H_\infty$ and regret frameworks. A numerical example illustrates the theoretical results. |
| title | Regret of $H_\infty$ Preview Controllers |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2602.01420 |