Robust Regret Control with Uncertainty-Dependent Baseline

Fuente: arXiv
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Autores principales: Liu, Jietian, Seiler, Peter
Formato: Preprint
Publicado: 2025
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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