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In this paper, we propose a novel approach for computing robust backwardreachable sets from noisy data for unknown constrained linear systems subjectto bounded disturbances. In particular, we develop an algorithm for obtainingzonotopic inner approximations that can be used for control purposes. It isshown that such sets, if built on an extended space including states andinputs, can be used to embed the system's one-step evolution in the computedextended regions. Such a result is then exploited to build a set-theoreticmodel predictive controller that, offline, builds a recursive family of robustdata-driven reachable sets, and online, computes recursively admissible controlactions without explicitly resorting to either a model of the system or theavailable data.The validity of the proposed data-driven solution is verified bymeans of a numerical simulation and its performance is contrasted with themodel-based counterpart.

Data-Driven Robust Backward Reachable Sets for Set-Theoretic Model Predictive Control