Data-Driven Distributionally Robust System Level Synthesis
Francesco Micheli, Anastasios Tsiamis, John Lygeros

TL;DR
This paper introduces a data-driven, distributionally robust control method for uncertain linear systems, ensuring reliable performance by accounting for model mismatch and disturbance distribution uncertainty using Wasserstein ambiguity sets.
Contribution
It develops a novel doubly robust, distributionally robust control framework leveraging System Level Synthesis and Wasserstein ambiguity sets, with theoretical guarantees and a tractable approximation.
Findings
Effective control under distributional ambiguity demonstrated in numerical example.
Bounds on sample complexity for desired confidence levels provided.
Tractable approximate formulation enables practical implementation.
Abstract
We present a novel approach for the control of uncertain, linear time-invariant systems, which are perturbed by potentially unbounded, additive disturbances. We propose a \emph{doubly robust} data-driven state-feedback controller to ensure reliable performance against both model mismatch and disturbance distribution uncertainty. Our controller, which leverages the System Level Synthesis parameterization, is designed as the solution to a distributionally robust finite-horizon optimal control problem. The goal is to minimize a cost function while satisfying constraints against the worst-case realization of the uncertainty, which is quantified using distributional ambiguity sets. The latter are defined as balls in the Wasserstein metric centered on the predictive empirical distribution computed from a set of collected trajectory data. By harnessing techniques from robust control and…
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Taxonomy
TopicsFault Detection and Control Systems · Control Systems and Identification · Advanced Control Systems Optimization
