ノイズを含む計測データからの直接データ駆動制御
Direct Data Driven Control Using Noisy Measurements
システム同定を行わず、ノイズを含む入出力データからLQRの最適ゲインを凸最適化で直接学習する手法を提案し、平均二乗安定性を保証する。
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著者: Ramin Esmzad, Gokul S. Sankar, Teawon Han, Hamidreza Modares
分類: eess.SY, cs.LG, cs.RO, cs.SY, math.OC
原文アブストラクト
This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned using only a single trajectory of noisy input-output data while bypassing system identification. Our approach guarantees mean-square stability (MSS) and optimal performance by leveraging convex optimization techniques that incorporate noise statistics directly into the controller synthesis. First, we establish a theoretical result showing that the MSS of an uncertain data-driven system implies the MSS of the true closed-loop system. Building on this, we develop a robust stability condition using linear matrix inequalities (LMIs) that yields a stabilizing controller gain from noisy measurements. Finally, we formulate a data-driven LQR problem as a semidefinite program (SDP) that computes an optimal gain, minimizing the steady-state covariance. Extensive simulations on benchmark systems -- including a rotary inverted pendulum and an active suspension system -- demonstrate the superior robustness and accuracy of our method compared to existing data-driven LQR approaches. The proposed framework offers a practical and theoretically grounded solution for controller design in noise-corrupted environments where system identification is infeasible.
