  We consider the problem of designing an invariant set using only a finite set
of input-state data collected from an unknown polynomial system in continuous
time. We consider noisy data, i.e., corrupted by an unknown-but-bounded
disturbance. We derive a data-dependent sum-of-squares program that enforces
invariance of a set and also optimizes the size of the invariant set while
keeping it within a set of user-defined safety constraints; the solution of
this program directly provides a polynomial invariant set and a state-feedback
controller. We numerically test the design on a system of two platooning cars.
