On the Regret of $\mathcal{H}_{\infty}$ Control
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Date
2022
Publication Type
Conference Paper
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yes
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Abstract
The $\mathcal{H}_{\infty}$ synthesis approach is a cornerstone robust control design technique, but is known to be conservative in some cases. The objective of this paper is to quantify the additional cost the controller incurs planning for the worst-case scenario, by adopting an approach inspired by regret from online learning. We define the disturbance-reality gap as the difference between the predicted worst-case disturbance signal and the actual realization. The regret is shown to scale with the norm of this gap, which turns out to have a similar structure to that of the certainty equivalent controller with inaccurate predictions, obtained here in terms of the prediction error norm.
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published
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Book title
2022 IEEE 61st Conference on Decision and Control (CDC)
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Volume
Pages / Article No.
6181 - 6186
Publisher
IEEE
Event
61st IEEE Conference on Decision and Control (CDC 2022)
Edition / version
Methods
Software
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Date collected
Date created
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Organisational unit
03751 - Lygeros, John / Lygeros, John
08814 - Smith, Roy (Tit.-Prof.) (ehemalig) / Smith, Roy (Tit.-Prof.) (former)
02650 - Institut für Automatik / Automatic Control Laboratory
Notes
Conference lecture held on December 9, 2022
Funding
180545 - NCCR Automation (phase I) (SNF)
178890 - Modeling, Identification and Control of Periodic Systems in Energy Applications (SNF)
178890 - Modeling, Identification and Control of Periodic Systems in Energy Applications (SNF)
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