Wasserstein Distributionally Robust Control of Partially Observable Linear Systems: Tractable Approximation and Performance Guarantee (2203.17045v2)

Abstract: Wasserstein distributionally robust control (WDRC) is an effective method for addressing inaccurate distribution information about disturbances in stochastic systems. It provides various salient features, such as an out-of-sample performance guarantee, while most of the existing methods use full-state observations. In this paper, we develop a computationally tractable WDRC method for discrete-time partially observable linear-quadratic (LQ) control problems. The key idea is to reformulate the WDRC problem as a novel minimax control problem with an approximate Wasserstein penalty. We derive a closed-form expression of the optimal control policy of the approximate problem using a nontrivial Riccati equation. We further show the guaranteed cost property of the resulting controller and identify a provable bound for the optimality gap. Finally, we evaluate the performance of our method through numerical experiments using both Gaussian and non-Gaussian disturbances.