単一軌道から不安定LQRの安定化制御器を学習する手法
Learning Stabilizing Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory
未知の線形二次レギュレータに対し、楕円体不確かさ集合内の全システムを安定化するSDPベースのロバスト制御器合成と、単一軌道データから効率的に安定化制御器を同定するアルゴリズムを提案した。
著者: Lenart Treven, Sebastian Curi, Mojmir Mutny, Andreas Krause
分類: eess.SY, cs.LG, cs.RO, cs.SY
原文アブストラクト
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.
