  This paper presents a direct data-driven approach for computing robust
control invariant (RCI) sets and their associated state-feedback control laws
for linear time-invariant systems affected by bounded disturbances. The
proposed method utilizes a single state-input trajectory generated from the
system, to compute a polytopic RCI set with a desired complexity and an
invariance-inducing feedback controller, without the need to identify a model
of the system. The problem is formulated in terms of a set of sufficient linear
matrix inequality conditions that are then combined in a semi-definite program
to maximize the volume of the RCI set while respecting the state and input
constraints. We demonstrate through a numerical case study that the proposed
data-driven approach can generate RCI sets that are of comparable size to those
obtained by a model-based method in which exact knowledge of the system
matrices is assumed.
