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Regret-optimal Estimation and Control

Goel, Gautam and Hassibi, Babak (2021) Regret-optimal Estimation and Control. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210719-210206675

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Abstract

We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which compete against a clairvoyant noncausal policy, instead of the best policy selected in hindsight from some fixed parametric class. We show that the regret-optimal estimator and regret-optimal controller can be derived in state-space form using operator-theoretic techniques from robust control and present tight, data-dependent bounds on the regret incurred by our algorithms in terms of the energy of the disturbances. Our results can be viewed as extending traditional robust estimation and control, which focuses on minimizing worst-case cost, to minimizing worst-case regret. We propose regret-optimal analogs of Model-Predictive Control (MPC) and the Extended Kalman Filter (EKF) for systems with nonlinear dynamics and present numerical experiments which show that our regret-optimal algorithms can significantly outperform standard approaches to estimation and control.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2106.12097arXivDiscussion Paper
Record Number:CaltechAUTHORS:20210719-210206675
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210719-210206675
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109927
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Jul 2021 17:52
Last Modified:20 Jul 2021 17:52

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