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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220714-224600473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) | ||||||||
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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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