Distributional Robustness in Minimax Linear Quadratic Control with Wasserstein Distance

To address the issue of inaccurate distributions in discrete-time stochastic systems, a minimax linear quadratic control method using Wasserstein metric is proposed. Our aims to construct policy that robust against errors an empirical distribution underlying uncertainty by adopting adversary selects worst-case at each time. The opponent receives penalty proportional amount deviation from distribution. As tractable solution, closed-form expression optimal pair derived Riccati equation. We identify nontrivial stabilizability and observability conditions under which recursion converges unique positive semidefinite solution algebraic shown possess several salient features, including closed-loop stability, guaranteed-cost property, probabilistic out-of-sample performance guarantee.