Learning Stabilizing Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory

• URL: http://arxiv.org/abs/2006.11022v2
• Date: Mon, 23 Nov 2020 09:40:25 GMT
• Title: Learning Stabilizing Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory
• Authors: Lenart Treven, Sebastian Curi, Mojmir Mutny, Andreas Krause
• Abstract summary: 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 propose an efficient data dependent algorithm -- textsceXploration -- that with high probability quickly identifies a stabilizing controller.
• Score: 85.29718245299341
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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