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research article

Regret optimal control for uncertain stochastic systems

Martin, Andrea  
•
Furieri, Luca  
•
Dorfler, Florian
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November 1, 2024
European Journal Of Control

We consider control of uncertain linear time-varying stochastic systems from the perspective of regret minimization. Specifically, we focus on the problem of designing a feedback controller that minimizes the loss relative to a clairvoyant optimal policy that has foreknowledge of both the system dynamics and the exogenous disturbances. In this competitive framework, establishing robustness guarantees proves challenging as, differently from the case where the model is known, the clairvoyant optimal policy is not only inapplicable, but also impossible to compute without knowledge of the system parameters. To address this challenge, we embrace a scenario optimization approach, and we propose minimizing regret robustly over a finite set of randomly sampled system parameters. We prove that this policy optimization problem can be solved through semidefinite programming, and that the corresponding solution retains strong probabilistic out-of-sample regret guarantees in face of the uncertain dynamics. Our method naturally extends to include satisfaction of safety constraints with high probability. We validate our theoretical results and showcase the potential of our approach by means of numerical simulations.

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Type
research article
DOI
10.1016/j.ejcon.2024.101051
Web of Science ID

WOS:001359142700001

Author(s)
Martin, Andrea  

École Polytechnique Fédérale de Lausanne

Furieri, Luca  

École Polytechnique Fédérale de Lausanne

Dorfler, Florian

Swiss Federal Institutes of Technology Domain

Lygeros, John

Swiss Federal Institutes of Technology Domain

Ferrari-Trecate, Giancarlo  

École Polytechnique Fédérale de Lausanne

Date Issued

2024-11-01

Publisher

ELSEVIER

Published in
European Journal Of Control
Article Number

101051

Subjects

Predictive control

•

Stochastic systems

•

Regret minimization

•

Scenario optimization

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
SCI-STI-GFT  
FunderFunding(s)Grant NumberGrant URL

Swiss National Science Foundation (SNSF)

51NF40_180545

Swiss National Science Foundation (SNSF)

PZ00P2_208951

Available on Infoscience
January 28, 2025
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/245840
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