Robust Regret Control with Uncertainty-Dependent Baseline
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915574158721024 |
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| author | Liu, Jietian Seiler, Peter |
| author_facet | Liu, Jietian Seiler, Peter |
| contents | This paper proposes a robust regret control framework in which the performance baseline adapts to the realization of system uncertainty. The plant is modeled as a discrete-time, uncertain linear time-invariant system with real-parametric uncertainty. The performance baseline is the optimal non-causal controller constructed with full knowledge of the disturbance and the specific realization of the uncertain plant. We show that a controller achieves robust additive regret relative to this baseline if and only if it satisfies a related, robust $H_\infty$ performance condition on a modified plant. One technical issue is that the modified plant can, in general, have a complicated nonlinear dependence on the uncertainty. We use a linear approximation step so that the robust additive regret condition can be recast as a standard $μ$-synthesis problem. A numerical example is used to demonstrate the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Regret Control with Uncertainty-Dependent Baseline Liu, Jietian Seiler, Peter Optimization and Control Systems and Control This paper proposes a robust regret control framework in which the performance baseline adapts to the realization of system uncertainty. The plant is modeled as a discrete-time, uncertain linear time-invariant system with real-parametric uncertainty. The performance baseline is the optimal non-causal controller constructed with full knowledge of the disturbance and the specific realization of the uncertain plant. We show that a controller achieves robust additive regret relative to this baseline if and only if it satisfies a related, robust $H_\infty$ performance condition on a modified plant. One technical issue is that the modified plant can, in general, have a complicated nonlinear dependence on the uncertainty. We use a linear approximation step so that the robust additive regret condition can be recast as a standard $μ$-synthesis problem. A numerical example is used to demonstrate the proposed approach. |
| title | Robust Regret Control with Uncertainty-Dependent Baseline |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2510.21415 |