  Nonlinear control-affine systems with time-varying vector fields are
considered in the paper. We propose a unified control design scheme with
oscillating inputs for solving the trajectory tracking and stabilization
problems. This methodology is based on the approximation of a gradient like
dynamics by trajectories of the designed closed-loop system. As an intermediate
outcome, we characterize the asymptotic behavior of solutions of the considered
class of nonlinear control systems with oscillating inputs under rather general
assumptions on the generating potential function. These results are applied to
examples of nonholonomic trajectory tracking and obstacle avoidance.

Optimization and Control