Data-driven distributionally robust MPC for systems with uncertain dynamics

TL;DR

This paper introduces a data-driven distributionally robust MPC approach for unknown linear systems with uncertain dynamics, leveraging off-line data and Wasserstein ambiguity sets to ensure robust performance and safety.

Contribution

It develops a novel finite-horizon optimization framework that accounts for model and disturbance uncertainties using distributionally robust optimization with finite-sample guarantees.

Findings

Convex finite-dimensional optimization problem derived

Finite-sample guarantees established for the approach

Validated through closed-loop simulation on a numerical example

Abstract

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected data and an approximate model of the dynamics to formulate a finite-horizon optimization problem. To account for both the uncertainty related to the dynamics and the disturbance acting on the system, we resort to a distributionally robust formulation that optimizes the cost expectation while satisfying Conditional Value-at-Risk constraints with respect to the worst-case probability distributions of the uncertainties within an ambiguity set defined using the Wasserstein metric. Using results from the distributionally robust optimization literature we derive a tractable finite-dimensional convex optimization problem with finite-sample guarantees for the class of convex piecewise affine cost and constraint functions. The performance of the proposed algorithm is demonstrated in closed-loop simulation on a simple numerical example.