{"ID":2850636,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.21415","arxiv_id":"2510.21415","title":"Robust Regret Control with Uncertainty-Dependent Baseline","abstract":"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.","short_abstract":"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 constru...","url_abs":"https://arxiv.org/abs/2510.21415","url_pdf":"https://arxiv.org/pdf/2510.21415v1","authors":"[\"Jietian Liu\",\"Peter Seiler\"]","published":"2025-10-24T12:55:52Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}