Distributionally Robust Linear Quadratic Control

• Published in: arXiv.org
• Main Authors: Taşkesen, Bahar, Iancu, Dan A, Koçyiğit, Çağıl, Kuhn, Daniel
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.11.2023
• Subjects: Algorithms; Ambiguity; Cost function; Kalman filters; Linear quadratic Gaussian control; Optimal control; Robust control
• ISSN: 2331-8422

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, we consider a generalization of the discrete-time, finite-horizon LQG problem, where the noise distributions are unknown and belong to Wasserstein ambiguity sets centered at nominal (Gaussian) distributions. The objective is to minimize a worst-case cost across all distributions in the ambiguity set, including non-Gaussian distributions. Despite the added complexity, we prove that a control policy that is linear in the observations is optimal for this problem, as in the classic LQG problem. We propose a numerical solution method that efficiently characterizes this optimal control policy. Our method uses the Frank-Wolfe algorithm to identify the least-favorable distributions within the Wasserstein ambiguity sets and computes the controller's optimal policy using Kalman filter estimation under these distributions.