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arXiv · 2304.00381

On the Sample Complexity of the Linear Quadratic Gaussian Regulator

Abed AlRahman Al Makdah·Fabio Pasqualetti
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Abstract

In this paper we provide direct data-driven expressions for the Linear Quadratic Regulator (LQR), the Kalman filter, and the Linear Quadratic Gaussian (LQG) controller using a finite dataset of noisy input, state, and output trajectories. We show that our data-driven expressions are consistent, since they converge as the number of experimental trajectories increases, we characterize their convergence rate, and quantify their error as a function of the system and data properties. These results complement the body of literature on data-driven control and finite-sample analysis, and provide new ways to solve canonical control and estimation problems that do not assume, nor require the estimation of, a model of the system and noise and do not rely on solving implicit equations.

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BibTeXRIS

Abed AlRahman Al Makdah, Fabio Pasqualetti. 2023-04-01. On the Sample Complexity of the Linear Quadratic Gaussian Regulator. https://arxiv.org/abs/2304.00381

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