Robust Linear Quadratic Regulator: Exact Tractable Reformulation

Wouter Jongeneel; Tyler Summers; Peyman Mohajerin Esfahani

doi:10.1109/CDC40024.2019.9028884

Robust Linear Quadratic Regulator: Exact Tractable Reformulation

Wouter Jongeneel, Tyler Summers, Peyman Mohajerin Esfahani

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

2 Citations (Scopus)

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Abstract

We consider the problem of controlling an unknown stochastic linear dynamical system subject to an infinitehorizon discounted quadratic cost. Existing approaches for handling the corresponding robust optimal control problem resort to either conservative uncertainty sets or various approximations schemes, and to our best knowledge, the current literature lacks an exact, yet tractable, solution. We propose a class of novel uncertainty sets for the system matrices of the linear system. We show that the resulting robust linear quadratic regulator problem enjoys a closed-form solution described through a generalized algebraic Riccati equation arising from dynamic game theory.

Original language	English
Title of host publication	Proceedings of the IEEE 58th Conference on Decision and Control, CDC 2019
Publisher	IEEE
Pages	6742-6747
ISBN (Electronic)	978-1-7281-1398-2
DOIs	https://doi.org/10.1109/CDC40024.2019.9028884
Publication status	Published - 2019
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: 11 Dec 2019 → 13 Dec 2019

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	11/12/19 → 13/12/19

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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title = "Robust Linear Quadratic Regulator: Exact Tractable Reformulation",

abstract = "We consider the problem of controlling an unknown stochastic linear dynamical system subject to an infinitehorizon discounted quadratic cost. Existing approaches for handling the corresponding robust optimal control problem resort to either conservative uncertainty sets or various approximations schemes, and to our best knowledge, the current literature lacks an exact, yet tractable, solution. We propose a class of novel uncertainty sets for the system matrices of the linear system. We show that the resulting robust linear quadratic regulator problem enjoys a closed-form solution described through a generalized algebraic Riccati equation arising from dynamic game theory.",

author = "Wouter Jongeneel and Tyler Summers and Esfahani, {Peyman Mohajerin}",

note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.; 58th IEEE Conference on Decision and Control, CDC 2019 ; Conference date: 11-12-2019 Through 13-12-2019",

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N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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N2 - We consider the problem of controlling an unknown stochastic linear dynamical system subject to an infinitehorizon discounted quadratic cost. Existing approaches for handling the corresponding robust optimal control problem resort to either conservative uncertainty sets or various approximations schemes, and to our best knowledge, the current literature lacks an exact, yet tractable, solution. We propose a class of novel uncertainty sets for the system matrices of the linear system. We show that the resulting robust linear quadratic regulator problem enjoys a closed-form solution described through a generalized algebraic Riccati equation arising from dynamic game theory.

AB - We consider the problem of controlling an unknown stochastic linear dynamical system subject to an infinitehorizon discounted quadratic cost. Existing approaches for handling the corresponding robust optimal control problem resort to either conservative uncertainty sets or various approximations schemes, and to our best knowledge, the current literature lacks an exact, yet tractable, solution. We propose a class of novel uncertainty sets for the system matrices of the linear system. We show that the resulting robust linear quadratic regulator problem enjoys a closed-form solution described through a generalized algebraic Riccati equation arising from dynamic game theory.

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DO - 10.1109/CDC40024.2019.9028884

M3 - Conference contribution

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BT - Proceedings of the IEEE 58th Conference on Decision and Control, CDC 2019

PB - IEEE

Y2 - 11 December 2019 through 13 December 2019

ER -

Robust Linear Quadratic Regulator: Exact Tractable Reformulation

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