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Optimal Competitive-Ratio Control

Sabag, Oron and Lale, Sahin and Hassibi, Babak (2022) Optimal Competitive-Ratio Control. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220714-224600473

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Abstract

Inspired by competitive policy designs approaches in online learning, new control paradigms such as competitive-ratio and regret-optimal control have been recently proposed as alternatives to the classical H₂ and H_∞ approaches. These competitive metrics compare the control cost of the designed controller against the cost of a clairvoyant controller, which has access to past, present, and future disturbances in terms of ratio and difference, respectively. While prior work provided the optimal solution for the regret-optimal control problem, in competitive-ratio control, the solution is only provided for the sub-optimal problem. In this work, we derive the optimal solution to the competitive-ratio control problem. We show that the optimal competitive ratio formula can be computed as the maximal eigenvalue of a simple matrix, and provide a state-space controller that achieves the optimal competitive ratio. We conduct an extensive numerical study to verify this analytical solution, and demonstrate that the optimal competitive-ratio controller outperforms other controllers on several large scale practical systems. The key techniques that underpin our explicit solution is a reduction of the control problem to a Nehari problem, along with a novel factorization of the clairvoyant controller's cost. We reveal an interesting relation between the explicit solutions that now exist for both competitive control paradigms by formulating a regret-optimal control framework with weight functions that can also be utilized for practical purposes.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://doi.org/10.48550/arXiv.2206.01782arXivDiscussion Paper
ORCID:
AuthorORCID
Sabag, Oron0000-0002-7907-1463
Lale, Sahin0000-0002-7191-346X
Hassibi, Babak0000-0002-1375-5838
Additional Information:Attribution 4.0 International (CC BY 4.0)
Record Number:CaltechAUTHORS:20220714-224600473
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220714-224600473
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115592
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:15 Jul 2022 23:29
Last Modified:23 Dec 2022 00:53

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