Distributionally Robust LQG control under Distributed Uncertainty

TL;DR

This paper introduces a distributionally robust LQG control framework that optimizes performance against worst-case noise distribution deviations constrained by relative entropy, with bounds adaptable along the entire disturbance trajectory.

Contribution

It presents a novel approach allowing distributional bounds to vary over the disturbance trajectory, enhancing robustness in LQG control under uncertainty.

Findings

Simulation results demonstrate improved robustness against distributional uncertainties.

The method effectively bounds noise distribution deviations along the entire trajectory.

Abstract

A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performances in the worst possible scenario under the constraint that the noise distributional aberrance does not exceed a certain threshold limiting the relative entropy pseudo-distance between the actual noise distribution the nominal one. The main novelty is that the bounds on the distributional aberrance can be arbitrarily distributed along the whole disturbance trajectory. We discuss why this can, in principle, be a substantial advantage and we provide simulation results that substantiate such a principle.