Title: On the Global Optimality of Linear Policies for Sinkhorn Distributionally Robust Linear Quadratic Control Show Chinese title

Title: 关于线性策略在Sinkhorn分布鲁棒线性二次控制中的全局最优性

Abstract: The Linear Quadratic Gaussian (LQG) regulator is a cornerstone of optimal control theory, yet its performance can degrade significantly when the noise distributions deviate from the assumed Gaussian model. To address this limitation, this work proposes a distributionally robust generalization of the finite-horizon LQG control problem. Specifically, we assume that the noise distributions are unknown and belong to ambiguity sets defined in terms of an entropy-regularized Wasserstein distance centered at a nominal Gaussian distribution. By deriving novel bounds on this Sinkhorn discrepancy and proving structural and topological properties of the resulting ambiguity sets, we establish global optimality of linear policies. Numerical experiments showcase improved distributional robustness of our control policy. Show Chinese abstract

Abstract: 线性二次高斯（LQG）调节器是最优控制理论的基石，但当噪声分布偏离假设的高斯模型时，其性能可能会显著下降。 为解决这一限制，本研究提出了一种有限时间范围LQG控制问题的分布鲁棒推广。 具体而言，我们假设噪声分布是未知的，并属于以名义高斯分布为中心的熵正则化Wasserstein距离定义的模糊集。 通过推导这种Sinkhorn差异的新界限，并证明所得模糊集的结构和拓扑性质，我们建立了线性策略的全局最优性。 数值实验展示了我们控制策略改进的分布鲁棒性。