An efficient data-driven distributionally robust MPC leveraging linear programming

This paper presents a distributionally robust data-driven model predictive control (MPC) framework for discrete-time linear systems with additive disturbances, while assuming the distribution is only partially known through samples. The corresponding optimal control problem considers a distributionally robust (DR) objective over an ambiguity set of estimated disturbance expectations. A statistical learning bound is provided to validate the ambiguity set. For this control problem, polytopic hard input constraints and state chance constraints are considered. State chance constraints are formulated into linear deterministic constraints through solving a DR optimization problem with Wasserstein ambiguity set. The resulting optimal control problem can be equivalently solved by a linear program. We prove recursive feasibility and provide an average asymptotic cost bound for the corresponding MPC framework. The method is compared, demonstrated and analysed on a mass spring control example.