Regret-optimal measurement-feedback control
- Creators
- Goel, Gautam
- Hassibi, Babak
Abstract
We consider measurement-feedback control in linear dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing an online controller which competes with the optimal dynamic sequence of control actions selected in hindsight, instead of the best controller in some specific class of controllers. This formulation of regret is attractive when the environment changes over time and no single controller achieves good performance over the entire time horizon. We show that in the measurement-feedback setting, unlike in the full-information setting, there is no single online controller which outperforms every other online controller on every disturbance, and propose a new H₂-optimal online controller as a benchmark for the online controller to compete against. We show that the corresponding regret-optimal online controller can be found via a novel reduction to the classical Nehari problem from robust control and present a tight data-dependent bound on its regret.
Additional Information
© 2021 G. Goel & B. Hassibi.Attached Files
Published - goel21a.pdf
Accepted Version - 2011.12785.pdf
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Additional details
- Eprint ID
- 109930
- Resolver ID
- CaltechAUTHORS:20210719-210216911
- Created
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2021-07-20Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field