Nonlinear programming and the CBH formula in feedback stabilization of nonlinear systems with drift

This paper presents an approach for the asymptotic stabilization of strongly nonlinear systems that are affine in control and which cannot be stabilized by continuous state feedback. The approach only requires that along trajectories of the closed-loop system a chosen Lyapunov type function is decreased periodically (as opposed to monotonically) by employing controls which result from an on-line solution of a nonlinear programming satisficing problem stated in terms of expressions derived from the composition of flows via the Campbell-Baker-Hausdorff formula.