This paper presents an approach to the construction of stabilizing feedback for strongly non-linear systems. The class of systems of interest includes systems with drift which are a. ne in the controls and which cannot be stabilized by continuous state feedback. The approach is independent of the selection of a Lyapunov function, but requires the on-line solution of a non-linear programming satisficing problem stated in terms of expressions resulting from the composition of flows via the Campbell - Baker - Hausdorff formula.