Learning Stabilizing Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory
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Author / Producer
Date
2021
Publication Type
Conference Paper
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yes
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Abstract
The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear controllers under quadratic costs model also known as linear quadratic regulators (LQR). We present two different semi-definite programs (SDP) which results in a controller that stabilizes all systems within an ellipsoid uncertainty set. We further show that the feasibility conditions of the proposed SDPs are \emph{equivalent}. Using the derived robust controller syntheses, we propose an efficient data dependent algorithm – \textsc{eXploration} – that with high probability quickly identifies a stabilizing controller. Our approach can be used to initialize existing algorithms that require a stabilizing controller as an input while adding constant to the regret. We further propose different heuristics which empirically reduce the number of steps taken by \textsc{eXploration} and reduce the suffered cost while searching for a stabilizing controller.
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Publication status
published
Book title
Proceedings of the 3rd Conference on Learning for Dynamics and Control
Journal / series
Volume
144
Pages / Article No.
664 - 676
Publisher
PMLR
Event
3rd Annual Learning for Dynamics & Control Conference (L4DC 2021)
Edition / version
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Software
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Date created
Subject
LQR; Stabilizing controller; Ellipsoid credibility region
Organisational unit
03908 - Krause, Andreas / Krause, Andreas
Notes
Funding
815943 - Reliable Data-Driven Decision Making in Cyber-Physical Systems (EC)
180545 - NCCR Automation (phase I) (SNF)
180545 - NCCR Automation (phase I) (SNF)