Data-driven design of safe control for polynomial systems

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