Competitive-Ratio and Regret-Optimal Control with General Weights

Oron Sabag, Sahin Lale, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Motivated by the online policy design approaches in learning theory, new controller design paradigms such as competitive-ratio and regret-optimal control have been recently proposed as alternatives to the classical H2 and H controllers. These metrics respectively consider the performances against a clairvoyant controller, which has access to future disturbances, in terms of ratio and difference. Even though the prior works on regret-optimal control provide its exact solution, in the competitive-ratio setting the solution is only provided for the suboptimal problem. In this work, we give the first exact solution to the optimal competitive-ratio control problem and present an explicit construction of the optimal competitive-ratio controller. A key technique that underpins our explicit solution is a reduction of the competitive-ratio control problem to the Nehari extension problem (similar to the regret-optimal control setting). The resulting optimal competitive-ratio controller is given by an explicit state space and the state-feedback law that is inherited from the H_2 controller. Inspired by this explicit solution, we generalize regret-optimal control to have weight functions on the state, input, and noise sequences and show that competitive-ratio control is an instance of this general framework. The utilization of weight functions allow penalization of particular sequences, but still enjoying the explicit and optimal solution for the regret-optimal control problem.

Original languageAmerican English
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4859-4864
Number of pages6
ISBN (Electronic)9781665467612
DOIs
StatePublished - 2022
Event61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico
Duration: 6 Dec 20229 Dec 2022

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2022-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference61st IEEE Conference on Decision and Control, CDC 2022
Country/TerritoryMexico
CityCancun
Period6/12/229/12/22

Bibliographical note

Publisher Copyright:
© 2022 IEEE.

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