Data-driven distributionally robust MPC for systems with uncertain dynamics

Francesco Micheli; Tyler Summers; John Lygeros

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arXiv · 2209.08869

Data-driven distributionally robust MPC for systems with uncertain dynamics

Francesco Micheli·Tyler Summers·John Lygeros

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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.

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BibTeX RIS

Francesco Micheli, Tyler Summers, John Lygeros. 2022-09-19. Data-driven distributionally robust MPC for systems with uncertain dynamics. https://arxiv.org/abs/2209.08869

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