  Data-driven control of nonlinear systems with rigorous guarantees is a
challenging problem as it usually calls for nonconvex optimization and requires
often knowledge of the true basis functions of the system dynamics. To tackle
these drawbacks, this work is based on a data-driven polynomial representation
of general nonlinear systems exploiting Taylor polynomials. Thereby, we design
state-feedback laws that render a known equilibrium point globally
asymptotically stable while operating with respect to a desired quadratic
performance criterion. The calculation of the polynomial state feedback boils
down to a single sum-ofsquares optimization problem, and hence to
computationally tractable linear matrix inequalities. Moreover, we examine
state-input data in presence of Gaussian noise by Bayesian inference to
overcome the conservatism of deterministic noise characterizations from recent
data-driven control approaches for Gaussian noise.
