Seminar by Babak Hassibi: Distributionally Robust Control

Date & Time: October 10, 16:20-17:05
Location: Seminar Room M 3170-73 at Dept. of Automatic Control, LTH
Speaker: Babak Hassibi
Title: Distributionally Robust Control
Abstract: Traditional methods in control either assume that the disturbances are random processes with known statistics (stochastic or H_2 control) or that they are adversarial (robust or H_infinity control). Recently, there has been growing interest in a framework, called distributional robustness, that can interpolate between these two extremes. In distributionally robust control one assumes that the disturbances have a distribution that lies in a given uncertainty set and the goal is to design a controller that minimizes the worst case expected control cost over all distributions in this set. A not-very-well-known fact is that, if the uncertainty set is a Kullback-Liebler ball around a nominal Gaussian distribution, then distributionally-optimal controllers are given by central H_infinity controllers. These days Wasserstein-2 balls are mostly considered for distributional robustness because, unlike KL divergence, they do not require the support of all the distributions within the ball to be identical, and because of their connections to optimal transport theory. In this talk we consider the problem of designing distributionally robust optimal (DRO) controllers in the Wasserstien-2 metric. We characterize the optimal control policy and show that, although it lacks a finite-order state-space realization (i.e., it is non-rational), it can be characterized by a finite-dimensional parameter. Leveraging this, we develop an efficient frequency-domain algorithm to compute the optimal control policy and present a convex optimization method to construct a rational state-space controller that best approximates the optimal non-rational controller in the  H_infinity norm. This approach leads to efficiently computable control strategies and we demonstrate its advantages over conventional H_2 and H_infinity control through several examples.