Recursively feasible Data-driven Distributionally Robust Model Predictive Control with additive disturbances

Abstract

In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly interpolated initial state constraint in combination with a simplified affine disturbance feedback policy. We consider a moment-based ambiguity set with data-driven radius for the second moment of the disturbance, where we derive a minimum number of samples in order to ensure user-given confidence bounds on the chance constraints and closed-loop performance. The paper closes with a numerical example, highlighting the performance gain and chance constraint satisfaction based on different sample sizes.

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• Stochastic MPC with Distributionally Robust Chance Constraints
• Data-driven distributionally robust MPC for constrained stochastic systems
• Recursively feasible stochastic predictive control using an interpolating initial state constraint -- extended version
• Data-driven Distributionally Robust MPC: An indirect feedback approach